Daily Papers

Ordinal regression refers to classifying object instances into ordinal categories. It has been widely studied in many scenarios, such as medical disease grading, movie rating, etc. Known methods focused only on learning inter-class ordinal relationships, but still incur limitations in distinguishing adjacent categories thus far. In this paper, we propose a simple sequence prediction framework for ordinal regression called Ord2Seq, which, for the first time, transforms each ordinal category label into a special label sequence and thus regards an ordinal regression task as a sequence prediction process. In this way, we decompose an ordinal regression task into a series of recursive binary classification steps, so as to subtly distinguish adjacent categories. Comprehensive experiments show the effectiveness of distinguishing adjacent categories for performance improvement and our new approach exceeds state-of-the-art performances in four different scenarios. Codes are available at https://github.com/wjh892521292/Ord2Seq.

Watch time prediction (WTP) has emerged as a pivotal task in short video recommendation systems, designed to quantify user engagement through continuous interaction modeling. Predicting users' watch times on videos often encounters fundamental challenges, including wide value ranges and imbalanced data distributions, which can lead to significant estimation bias when directly applying regression techniques. Recent studies have attempted to address these issues by converting the continuous watch time estimation into an ordinal regression task. While these methods demonstrate partial effectiveness, they exhibit notable limitations: (1) the discretization process frequently relies on bucket partitioning, inherently reducing prediction flexibility and accuracy and (2) the interdependencies among different partition intervals remain underutilized, missing opportunities for effective error correction. Inspired by language modeling paradigms, we propose a novel Generative Regression (GR) framework that reformulates WTP as a sequence generation task. Our approach employs structural discretization to enable nearly lossless value reconstruction while maintaining prediction fidelity. Through carefully designed vocabulary construction and label encoding schemes, each watch time is bijectively mapped to a token sequence. To mitigate the training-inference discrepancy caused by teacher-forcing, we introduce a curriculum learning with embedding mixup strategy that gradually transitions from guided to free-generation modes. We evaluate our method against state-of-the-art approaches on two public datasets and one industrial dataset. We also perform online A/B testing on the Kuaishou App to confirm the real-world effectiveness. The results conclusively show that GR outperforms existing techniques significantly.

Survival prediction is a complicated ordinal regression task that aims to predict the ranking risk of death, which generally benefits from the integration of histology and genomic data. Despite the progress in joint learning from pathology and genomics, existing methods still suffer from challenging issues: 1) Due to the large size of pathological images, it is difficult to effectively represent the gigapixel whole slide images (WSIs). 2) Interactions within tumor microenvironment (TME) in histology are essential for survival analysis. Although current approaches attempt to model these interactions via co-attention between histology and genomic data, they focus on only dense local similarity across modalities, which fails to capture global consistency between potential structures, i.e. TME-related interactions of histology and co-expression of genomic data. To address these challenges, we propose a Multimodal Optimal Transport-based Co-Attention Transformer framework with global structure consistency, in which optimal transport (OT) is applied to match patches of a WSI and genes embeddings for selecting informative patches to represent the gigapixel WSI. More importantly, OT-based co-attention provides a global awareness to effectively capture structural interactions within TME for survival prediction. To overcome high computational complexity of OT, we propose a robust and efficient implementation over micro-batch of WSI patches by approximating the original OT with unbalanced mini-batch OT. Extensive experiments show the superiority of our method on five benchmark datasets compared to the state-of-the-art methods. The code is released.

Remote sensing has emerged as a critical tool for large-scale Earth monitoring and land management. In this paper, we introduce AgriPotential, a novel benchmark dataset composed of Sentinel-2 satellite imagery spanning multiple months. The dataset provides pixel-level annotations of agricultural potentials for three major crop types - viticulture, market gardening, and field crops - across five ordinal classes. AgriPotential supports a broad range of machine learning tasks, including ordinal regression, multi-label classification, and spatio-temporal modeling. The data covers diverse areas in Southern France, offering rich spectral information. AgriPotential is the first public dataset designed specifically for agricultural potential prediction, aiming to improve data-driven approaches to sustainable land use planning. The dataset and the code are freely accessible at: https://zenodo.org/records/15556484

This paper shows that the autoregressive model is an effective and scalable monocular depth estimator. Our idea is simple: We tackle the monocular depth estimation (MDE) task with an autoregressive prediction paradigm, based on two core designs. First, our depth autoregressive model (DAR) treats the depth map of different resolutions as a set of tokens, and conducts the low-to-high resolution autoregressive objective with a patch-wise casual mask. Second, our DAR recursively discretizes the entire depth range into more compact intervals, and attains the coarse-to-fine granularity autoregressive objective in an ordinal-regression manner. By coupling these two autoregressive objectives, our DAR establishes new state-of-the-art (SOTA) on KITTI and NYU Depth v2 by clear margins. Further, our scalable approach allows us to scale the model up to 2.0B and achieve the best RMSE of 1.799 on the KITTI dataset (5% improvement) compared to 1.896 by the current SOTA (Depth Anything). DAR further showcases zero-shot generalization ability on unseen datasets. These results suggest that DAR yields superior performance with an autoregressive prediction paradigm, providing a promising approach to equip modern autoregressive large models (e.g., GPT-4o) with depth estimation capabilities.

Training classifiers is difficult with severe class imbalance, but many rare events are the culmination of a sequence with much more common intermediate outcomes. For example, in online marketing a user first sees an ad, then may click on it, and finally may make a purchase; estimating the probability of purchases is difficult because of their rarity. We show both theoretically and through data experiments that the more abundant data in earlier steps may be leveraged to improve estimation of probabilities of rare events. We present PRESTO, a relaxation of the proportional odds model for ordinal regression. Instead of estimating weights for one separating hyperplane that is shifted by separate intercepts for each of the estimated Bayes decision boundaries between adjacent pairs of categorical responses, we estimate separate weights for each of these transitions. We impose an L1 penalty on the differences between weights for the same feature in adjacent weight vectors in order to shrink towards the proportional odds model. We prove that PRESTO consistently estimates the decision boundary weights under a sparsity assumption. Synthetic and real data experiments show that our method can estimate rare probabilities in this setting better than both logistic regression on the rare category, which fails to borrow strength from more abundant categories, and the proportional odds model, which is too inflexible.

Language models contain ranking-based knowledge and are powerful solvers of in-context ranking tasks. For instance, they may have parametric knowledge about the ordering of countries by size or may be able to rank reviews by sentiment. Recent work focuses on pairwise, pointwise, and listwise prompting techniques to elicit a language model's ranking knowledge. However, we find that even with careful calibration and constrained decoding, prompting-based techniques may not always be self-consistent in the rankings they produce. This motivates us to explore an alternative approach that is inspired by an unsupervised probing method called Contrast-Consistent Search (CCS). The idea is to train a probing model guided by a logical constraint: a model's representation of a statement and its negation must be mapped to contrastive true-false poles consistently across multiple statements. We hypothesize that similar constraints apply to ranking tasks where all items are related via consistent pairwise or listwise comparisons. To this end, we extend the binary CCS method to Contrast-Consistent Ranking (CCR) by adapting existing ranking methods such as the Max-Margin Loss, Triplet Loss, and Ordinal Regression objective. Our results confirm that, for the same language model, CCR probing outperforms prompting and even performs on a par with prompting much larger language models.

We introduce MedMNIST v2, a large-scale MNIST-like dataset collection of standardized biomedical images, including 12 datasets for 2D and 6 datasets for 3D. All images are pre-processed into a small size of 28x28 (2D) or 28x28x28 (3D) with the corresponding classification labels so that no background knowledge is required for users. Covering primary data modalities in biomedical images, MedMNIST v2 is designed to perform classification on lightweight 2D and 3D images with various dataset scales (from 100 to 100,000) and diverse tasks (binary/multi-class, ordinal regression, and multi-label). The resulting dataset, consisting of 708,069 2D images and 10,214 3D images in total, could support numerous research / educational purposes in biomedical image analysis, computer vision, and machine learning. We benchmark several baseline methods on MedMNIST v2, including 2D / 3D neural networks and open-source / commercial AutoML tools. The data and code are publicly available at https://medmnist.com/.

We propose XL-DURel, a finetuned, multilingual Sentence Transformer model optimized for ordinal Word-in-Context classification. We test several loss functions for regression and ranking tasks managing to outperform previous models on ordinal and binary data with a ranking objective based on angular distance in complex space. We further show that binary WiC can be treated as a special case of ordinal WiC and that optimizing models for the general ordinal task improves performance on the more specific binary task. This paves the way for a unified treatment of WiC modeling across different task formulations.

We propose a general method for measuring complex variables on a continuous, interval spectrum by combining supervised deep learning with the Constructing Measures approach to faceted Rasch item response theory (IRT). We decompose the target construct, hate speech in our case, into multiple constituent components that are labeled as ordinal survey items. Those survey responses are transformed via IRT into a debiased, continuous outcome measure. Our method estimates the survey interpretation bias of the human labelers and eliminates that influence on the generated continuous measure. We further estimate the response quality of each labeler using faceted IRT, allowing responses from low-quality labelers to be removed. Our faceted Rasch scaling procedure integrates naturally with a multitask deep learning architecture for automated prediction on new data. The ratings on the theorized components of the target outcome are used as supervised, ordinal variables for the neural networks' internal concept learning. We test the use of an activation function (ordinal softmax) and loss function (ordinal cross-entropy) designed to exploit the structure of ordinal outcome variables. Our multitask architecture leads to a new form of model interpretation because each continuous prediction can be directly explained by the constituent components in the penultimate layer. We demonstrate this new method on a dataset of 50,000 social media comments sourced from YouTube, Twitter, and Reddit and labeled by 11,000 U.S.-based Amazon Mechanical Turk workers to measure a continuous spectrum from hate speech to counterspeech. We evaluate Universal Sentence Encoders, BERT, and RoBERTa as language representation models for the comment text, and compare our predictive accuracy to Google Jigsaw's Perspective API models, showing significant improvement over this standard benchmark.

Image ranking is to rank images based on some known ranked images. In this paper, we propose an improved linear ordinal distance metric learning approach based on the linear distance metric learning model. By decomposing the distance metric A as L^TL, the problem can be cast as looking for a linear map between two sets of points in different spaces, meanwhile maintaining some data structures. The ordinal relation of the labels can be maintained via classical multidimensional scaling, a popular tool for dimension reduction in statistics. A least squares fitting term is then introduced to the cost function, which can also maintain the local data structure. The resulting model is an unconstrained problem, and can better fit the data structure. Extensive numerical results demonstrate the improvement of the new approach over the linear distance metric learning model both in speed and ranking performance.

Alignment techniques for LLMs rely on optimizing preference-based objectives -- where these preferences are typically elicited as ordinal, binary choices between responses. Recent work has focused on improving label quality or mitigating particular biases, but we identify a more fundamental limitation: these methods collect the wrong kind of data. We prove an impossibility result: no algorithm relying solely on ordinal comparisons can systematically recover the most preferred model. Intuitively, ordinal data lacks the information needed to resolve tradeoffs -- e.g., fixing a factual error on one prompt versus improving style on another. We show that selecting the optimal model requires recovering preferences over models (rather than just responses), which can only be identified given cardinal feedback about response quality. To address this, we collect and publicly release a dataset of 25,000 cardinal judgments using willingness-to-pay elicitations, a well-established tool from experimental economics. Empirically, we find that incorporating cardinal feedback into preference fine-tuning allows models to prioritize high-impact improvements and outperform ordinal-only methods on downstream benchmarks, such as Arena-Hard.

We present a method to integrate Large Language Models (LLMs) and traditional tabular data classification techniques, addressing LLMs challenges like data serialization sensitivity and biases. We introduce two strategies utilizing LLMs for ranking categorical variables and generating priors on correlations between continuous variables and targets, enhancing performance in few-shot scenarios. We focus on Logistic Regression, introducing MonotonicLR that employs a non-linear monotonic function for mapping ordinals to cardinals while preserving LLM-determined orders. Validation against baseline models reveals the superior performance of our approach, especially in low-data scenarios, while remaining interpretable.

Over the broad landscape of experimental design, regression has been a powerful tool to accurately predict the outcome metrics of a system or model given a set of parameters, but has been traditionally restricted to methods which are only applicable to a specific task. In this paper, we propose OmniPred, a framework for training language models as universal end-to-end regressors over (x,y) evaluation data from diverse real world experiments. Using data sourced from Google Vizier, one of the largest blackbox optimization databases in the world, our extensive experiments demonstrate that through only textual representations of mathematical parameters and values, language models are capable of very precise numerical regression, and if given the opportunity to train over multiple tasks, can significantly outperform traditional regression models.

Quantile regression is a fundamental problem in statistical learning motivated by a need to quantify uncertainty in predictions, or to model a diverse population without being overly reductive. For instance, epidemiological forecasts, cost estimates, and revenue predictions all benefit from being able to quantify the range of possible values accurately. As such, many models have been developed for this problem over many years of research in statistics, machine learning, and related fields. Rather than proposing yet another (new) algorithm for quantile regression we adopt a meta viewpoint: we investigate methods for aggregating any number of conditional quantile models, in order to improve accuracy and robustness. We consider weighted ensembles where weights may vary over not only individual models, but also over quantile levels, and feature values. All of the models we consider in this paper can be fit using modern deep learning toolkits, and hence are widely accessible (from an implementation point of view) and scalable. To improve the accuracy of the predicted quantiles (or equivalently, prediction intervals), we develop tools for ensuring that quantiles remain monotonically ordered, and apply conformal calibration methods. These can be used without any modification of the original library of base models. We also review some basic theory surrounding quantile aggregation and related scoring rules, and contribute a few new results to this literature (for example, the fact that post sorting or post isotonic regression can only improve the weighted interval score). Finally, we provide an extensive suite of empirical comparisons across 34 data sets from two different benchmark repositories.

Although the existing causal inference literature focuses on the forward-looking perspective by estimating effects of causes, the backward-looking perspective can provide insights into causes of effects. In backward-looking causal inference, the probability of necessity measures the probability that a certain event is caused by the treatment given the observed treatment and outcome. Most existing results focus on binary outcomes. Motivated by applications with ordinal outcomes, we propose a general definition of the probability of necessity. However, identifying the probability of necessity is challenging because it involves the joint distribution of the potential outcomes. We propose a novel assumption of monotonic incremental treatment effect to identify the probability of necessity with ordinal outcomes. We also discuss the testable implications of this key identification assumption. When it fails, we derive explicit formulas of the sharp large-sample bounds on the probability of necessity.

As Learning-to-Rank (LTR) approaches primarily seek to improve ranking quality, their output scores are not scale-calibrated by design. This fundamentally limits LTR usage in score-sensitive applications. Though a simple multi-objective approach that combines a regression and a ranking objective can effectively learn scale-calibrated scores, we argue that the two objectives are not necessarily compatible, which makes the trade-off less ideal for either of them. In this paper, we propose a practical regression compatible ranking (RCR) approach that achieves a better trade-off, where the two ranking and regression components are proved to be mutually aligned. Although the same idea applies to ranking with both binary and graded relevance, we mainly focus on binary labels in this paper. We evaluate the proposed approach on several public LTR benchmarks and show that it consistently achieves either best or competitive result in terms of both regression and ranking metrics, and significantly improves the Pareto frontiers in the context of multi-objective optimization. Furthermore, we evaluated the proposed approach on YouTube Search and found that it not only improved the ranking quality of the production pCTR model, but also brought gains to the click prediction accuracy. The proposed approach has been successfully deployed in the YouTube production system.

Pretrained time series models have enabled inference-only forecasting systems that produce accurate predictions without task-specific training. However, existing approaches largely focus on univariate forecasting, limiting their applicability in real-world scenarios where multivariate data and covariates play a crucial role. We present Chronos-2, a pretrained model capable of handling univariate, multivariate, and covariate-informed forecasting tasks in a zero-shot manner. Chronos-2 employs a group attention mechanism that facilitates in-context learning (ICL) through efficient information sharing across multiple time series within a group, which may represent sets of related series, variates of a multivariate series, or targets and covariates in a forecasting task. These general capabilities are achieved through training on synthetic datasets that impose diverse multivariate structures on univariate series. Chronos-2 delivers state-of-the-art performance across three comprehensive benchmarks: fev-bench, GIFT-Eval, and Chronos Benchmark II. On fev-bench, which emphasizes multivariate and covariate-informed forecasting, Chronos-2's universal ICL capabilities lead to substantial improvements over existing models. On tasks involving covariates, it consistently outperforms baselines by a wide margin. Case studies in the energy and retail domains further highlight its practical advantages. The in-context learning capabilities of Chronos-2 establish it as a general-purpose forecasting model that can be used "as is" in real-world forecasting pipelines.

Should prediction models always deliver a prediction? In the pursuit of maximum predictive performance, critical considerations of reliability and fairness are often overshadowed, particularly when it comes to the role of uncertainty. Selective regression, also known as the "reject option," allows models to abstain from predictions in cases of considerable uncertainty. Initially proposed seven decades ago, approaches to selective regression have mostly focused on distribution-based proxies for measuring uncertainty, particularly conditional variance. However, this focus neglects the significant influence of model-specific biases on a model's performance. In this paper, we propose a novel approach to selective regression by leveraging conformal prediction, which provides grounded confidence measures for individual predictions based on model-specific biases. In addition, we propose a standardized evaluation framework to allow proper comparison of selective regression approaches. Via an extensive experimental approach, we demonstrate how our proposed approach, conformalized selective regression, demonstrates an advantage over multiple state-of-the-art baselines.

Conformal prediction (CP) for regression can be challenging, especially when the output distribution is heteroscedastic, multimodal, or skewed. Some of the issues can be addressed by estimating a distribution over the output, but in reality, such approaches can be sensitive to estimation error and yield unstable intervals.~Here, we circumvent the challenges by converting regression to a classification problem and then use CP for classification to obtain CP sets for regression.~To preserve the ordering of the continuous-output space, we design a new loss function and make necessary modifications to the CP classification techniques.~Empirical results on many benchmarks shows that this simple approach gives surprisingly good results on many practical problems.

Our motivation is to shed light the performance of the widely popular "R-Learner." Like many other methods for estimating conditional average treatment effects (CATEs), R-Learning can be expressed as a weighted pseudo-outcome regression (POR). Previous comparisons of POR techniques have paid careful attention to the choice of pseudo-outcome transformation. However, we argue that the dominant driver of performance is actually the choice of weights. Specifically, we argue that R-Learning implicitly performs an inverse-variance weighted form of POR. These weights stabilize the regression and allow for convenient simplifications of bias terms.

While recent preference alignment algorithms for language models have demonstrated promising results, supervised fine-tuning (SFT) remains imperative for achieving successful convergence. In this paper, we study the crucial role of SFT within the context of preference alignment, emphasizing that a minor penalty for the disfavored generation style is sufficient for preference-aligned SFT. Building on this foundation, we introduce a straightforward and innovative reference model-free monolithic odds ratio preference optimization algorithm, ORPO, eliminating the necessity for an additional preference alignment phase. We demonstrate, both empirically and theoretically, that the odds ratio is a sensible choice for contrasting favored and disfavored styles during SFT across the diverse sizes from 125M to 7B. Specifically, fine-tuning Phi-2 (2.7B), Llama-2 (7B), and Mistral (7B) with ORPO on the UltraFeedback alone surpasses the performance of state-of-the-art language models with more than 7B and 13B parameters: achieving up to 12.20% on AlpacaEval_{2.0} (Figure 1), 66.19% on IFEval (instruction-level loose, Table 6), and 7.32 in MT-Bench (Figure 12). We release code and model checkpoints for Mistral-ORPO-alpha (7B) and Mistral-ORPO-beta (7B).

Conformal prediction is a theoretically grounded framework for constructing predictive intervals. We study conformal prediction with missing values in the covariates -- a setting that brings new challenges to uncertainty quantification. We first show that the marginal coverage guarantee of conformal prediction holds on imputed data for any missingness distribution and almost all imputation functions. However, we emphasize that the average coverage varies depending on the pattern of missing values: conformal methods tend to construct prediction intervals that under-cover the response conditionally to some missing patterns. This motivates our novel generalized conformalized quantile regression framework, missing data augmentation, which yields prediction intervals that are valid conditionally to the patterns of missing values, despite their exponential number. We then show that a universally consistent quantile regression algorithm trained on the imputed data is Bayes optimal for the pinball risk, thus achieving valid coverage conditionally to any given data point. Moreover, we examine the case of a linear model, which demonstrates the importance of our proposal in overcoming the heteroskedasticity induced by missing values. Using synthetic and data from critical care, we corroborate our theory and report improved performance of our methods.

This paper proposes a method for the automatic creation of variables (in the case of regression) that complement the information contained in the initial input vector. The method works as a pre-processing step in which the continuous values of the variable to be regressed are discretized into a set of intervals which are then used to define value thresholds. Then classifiers are trained to predict whether the value to be regressed is less than or equal to each of these thresholds. The different outputs of the classifiers are then concatenated in the form of an additional vector of variables that enriches the initial vector of the regression problem. The implemented system can thus be considered as a generic pre-processing tool. We tested the proposed enrichment method with 5 types of regressors and evaluated it in 33 regression datasets. Our experimental results confirm the interest of the approach.

Decoding-based regression, which reformulates regression as a sequence generation task, has emerged as a promising paradigm of applying large language models for numerical prediction. However, its progress is hindered by the misalignment between discrete token-level objectives (e.g., cross-entropy) and continuous numerical values. Existing approaches relying on token-level constraints often fail to capture the global magnitude of the target value, limiting their precision and generalization. In this paper, we propose to unlock the potential of decoding-based regression via Reinforcement Learning (RL). We formulate the generation process as a Markov Decision Process, utilizing sequence-level rewards to enforce global numerical coherence. Extensive experiments on tabular regression and code metric regression demonstrate that our method (specifically with ReMax and GRPO) consistently outperforms both state-of-the-art token-level baselines and traditional regression heads, showing the superiority of introducing sequence-level signals. Our analysis further reveals that RL significantly enhances sampling efficiency and predictive precision, establishing decoding-based regression as a robust and accurate paradigm for general-purpose numerical prediction.

We begin the study of list-decodable linear regression using batches. In this setting only an alpha in (0,1] fraction of the batches are genuine. Each genuine batch contains ge n i.i.d. samples from a common unknown distribution and the remaining batches may contain arbitrary or even adversarial samples. We derive a polynomial time algorithm that for any nge tilde Omega(1/alpha) returns a list of size mathcal O(1/alpha^2) such that one of the items in the list is close to the true regression parameter. The algorithm requires only mathcal{O}(d/alpha^2) genuine batches and works under fairly general assumptions on the distribution. The results demonstrate the utility of batch structure, which allows for the first polynomial time algorithm for list-decodable regression, which may be impossible for the non-batch setting, as suggested by a recent SQ lower bound diakonikolas2021statistical for the non-batch setting.

Constructing prediction sets with coverage guarantees for unobserved outcomes is a core problem in modern statistics. Methods for predictive inference have been developed for a wide range of settings, but usually only consider test data points one at a time. Here we study the problem of distribution-free predictive inference for a batch of multiple test points, aiming to construct prediction sets for functions -- such as the mean or median -- of any number of unobserved test datapoints. This setting includes constructing simultaneous prediction sets with a high probability of coverage, and selecting datapoints satisfying a specified condition while controlling the number of false claims. For the general task of predictive inference on a function of a batch of test points, we introduce a methodology called batch predictive inference (batch PI), and provide a distribution-free coverage guarantee under exchangeability of the calibration and test data. Batch PI requires the quantiles of a rank ordering function defined on certain subsets of ranks. While computing these quantiles is NP-hard in general, we show that it can be done efficiently in many cases of interest, most notably for batch score functions with a compositional structure -- which includes examples of interest such as the mean -- via a dynamic programming algorithm that we develop. Batch PI has advantages over naive approaches (such as partitioning the calibration data or directly extending conformal prediction) in many settings, as it can deliver informative prediction sets even using small calibration sample sizes. We illustrate that our procedures provide informative inference across the use cases mentioned above, through experiments on both simulated data and a drug-target interaction dataset.

We introduce a general, flexible, parametric survival modelling framework which encompasses key shapes of hazard function (constant, increasing, decreasing, up-then-down, down-then-up), various common survival distributions (log-logistic, Burr type XII, Weibull, Gompertz), and includes defective distributions (i.e., cure models). This generality is achieved using four basic distributional parameters: two scale-type parameters and two shape parameters. Generalising to covariate dependence, the scale-type regression components correspond to accelerated failure time (AFT) and proportional hazards (PH) models. Therefore, this general formulation unifies the most popular survival models which allows us to consider the practical value of possible modelling choices for survival data. Furthermore, in line with our proposed flexible baseline distribution, we advocate the use of multi-parameter regression in which more than one distributional parameter depends on covariates - rather than the usual convention of having a single covariate-dependent (scale) parameter. While many choices are available, we suggest introducing covariates through just one or other of the two scale parameters, which covers AFT and PH models, in combination with a `power' shape parameter, which allows for more complex non-AFT/non-PH effects, while the other shape parameter remains covariate-independent, and handles automatic selection of the baseline distribution. We explore inferential issues in simulations, both with and without a covariate, with particular focus on evidence concerning the need, or otherwise, to include both AFT and PH parameters. We illustrate the efficacy of our modelling framework by investigating differences between treatment groups using data from a lung cancer study and a melanoma study. Censoring is accommodated throughout.

In representation learning, regression has traditionally received less attention than classification. Directly applying representation learning techniques designed for classification to regression often results in fragmented representations in the latent space, yielding sub-optimal performance. In this paper, we argue that the potential of contrastive learning for regression has been overshadowed due to the neglect of two crucial aspects: ordinality-awareness and hardness. To address these challenges, we advocate "mixup your own contrastive pairs for supervised contrastive regression", instead of relying solely on real/augmented samples. Specifically, we propose Supervised Contrastive Learning for Regression with Mixup (SupReMix). It takes anchor-inclusive mixtures (mixup of the anchor and a distinct negative sample) as hard negative pairs and anchor-exclusive mixtures (mixup of two distinct negative samples) as hard positive pairs at the embedding level. This strategy formulates harder contrastive pairs by integrating richer ordinal information. Through extensive experiments on six regression datasets including 2D images, volumetric images, text, tabular data, and time-series signals, coupled with theoretical analysis, we demonstrate that SupReMix pre-training fosters continuous ordered representations of regression data, resulting in significant improvement in regression performance. Furthermore, SupReMix is superior to other approaches in a range of regression challenges including transfer learning, imbalanced training data, and scenarios with fewer training samples.

Preference learning has gained significant attention in tasks involving subjective human judgments, such as speech emotion recognition (SER) and image aesthetic assessment. While pairwise frameworks such as RankNet offer robust modeling of relative preferences, they are inherently limited to local comparisons and struggle to capture global ranking consistency. To address these limitations, we propose RankList, a novel listwise preference learning framework that generalizes RankNet to structured list-level supervision. Our formulation explicitly models local and non-local ranking constraints within a probabilistic framework. The paper introduces a log-sum-exp approximation to improve training efficiency. We further extend RankList with skip-wise comparisons, enabling progressive exposure to complex list structures and enhancing global ranking fidelity. Extensive experiments demonstrate the superiority of our method across diverse modalities. On benchmark SER datasets (MSP-Podcast, IEMOCAP, BIIC Podcast), RankList achieves consistent improvements in Kendall's Tau and ranking accuracy compared to standard listwise baselines. We also validate our approach on aesthetic image ranking using the Artistic Image Aesthetics dataset, highlighting its broad applicability. Through ablation and cross-domain studies, we show that RankList not only improves in-domain ranking but also generalizes better across datasets. Our framework offers a unified, extensible approach for modeling ordered preferences in subjective learning scenarios.

This paper presents OLinear, a linear-based multivariate time series forecasting model that operates in an orthogonally transformed domain. Recent forecasting models typically adopt the temporal forecast (TF) paradigm, which directly encode and decode time series in the time domain. However, the entangled step-wise dependencies in series data can hinder the performance of TF. To address this, some forecasters conduct encoding and decoding in the transformed domain using fixed, dataset-independent bases (e.g., sine and cosine signals in the Fourier transform). In contrast, we utilize OrthoTrans, a data-adaptive transformation based on an orthogonal matrix that diagonalizes the series' temporal Pearson correlation matrix. This approach enables more effective encoding and decoding in the decorrelated feature domain and can serve as a plug-in module to enhance existing forecasters. To enhance the representation learning for multivariate time series, we introduce a customized linear layer, NormLin, which employs a normalized weight matrix to capture multivariate dependencies. Empirically, the NormLin module shows a surprising performance advantage over multi-head self-attention, while requiring nearly half the FLOPs. Extensive experiments on 24 benchmarks and 140 forecasting tasks demonstrate that OLinear consistently achieves state-of-the-art performance with high efficiency. Notably, as a plug-in replacement for self-attention, the NormLin module consistently enhances Transformer-based forecasters. The code and datasets are available at https://anonymous.4open.science/r/OLinear

We present a new distribution-free conformal prediction algorithm for sequential data (e.g., time series), called the sequential predictive conformal inference (SPCI). We specifically account for the nature that time series data are non-exchangeable, and thus many existing conformal prediction algorithms are not applicable. The main idea is to adaptively re-estimate the conditional quantile of non-conformity scores (e.g., prediction residuals), upon exploiting the temporal dependence among them. More precisely, we cast the problem of conformal prediction interval as predicting the quantile of a future residual, given a user-specified point prediction algorithm. Theoretically, we establish asymptotic valid conditional coverage upon extending consistency analyses in quantile regression. Using simulation and real-data experiments, we demonstrate a significant reduction in interval width of SPCI compared to other existing methods under the desired empirical coverage.

We propose a penalized nonparametric approach to estimating the quantile regression process (QRP) in a nonseparable model using rectifier quadratic unit (ReQU) activated deep neural networks and introduce a novel penalty function to enforce non-crossing of quantile regression curves. We establish the non-asymptotic excess risk bounds for the estimated QRP and derive the mean integrated squared error for the estimated QRP under mild smoothness and regularity conditions. To establish these non-asymptotic risk and estimation error bounds, we also develop a new error bound for approximating C^s smooth functions with s >0 and their derivatives using ReQU activated neural networks. This is a new approximation result for ReQU networks and is of independent interest and may be useful in other problems. Our numerical experiments demonstrate that the proposed method is competitive with or outperforms two existing methods, including methods using reproducing kernels and random forests, for nonparametric quantile regression.

Uniform random exploration in decision-making systems supports off-policy learning via supervision but incurs high regret, making it impractical for many applications. Conversely, non-uniform exploration offers better immediate performance but lacks support for off-policy learning. Recent research suggests that regression oracles can bridge this gap by combining non-uniform exploration with supervised learning. In this paper, we analyze these approaches within a real-world industrial context at Adyen, a large global payments processor characterized by batch logged delayed feedback, short-term memory, and dynamic action spaces under the Empirical Risk Minimization (ERM) framework. Our analysis reveals that while regression oracles significantly improve performance, they introduce challenges due to rigid algorithmic assumptions. Specifically, we observe that as a policy improves, subsequent generations may perform worse due to shifts in the reward distribution and increased class imbalance in the training data. This degradation occurs de spite improvements in other aspects of the training data, leading to decreased performance in successive policy iterations. We further explore the long-term impact of regression oracles, identifying a potential "oscillation effect." This effect arises when regression oracles influence probability estimates and the realizability of subsequent policy models, leading to fluctuations in performance across iterations. Our findings highlight the need for more adaptable algorithms that can leverage the benefits of regression oracles without introducing instability in policy performance over time.

Standard methods for detecting discontinuities in conditional means are not applicable to outcomes that are complex, non-Euclidean objects like distributions, networks, or covariance matrices. This article develops a nonparametric test for jumps in conditional means when outcomes lie in a non-Euclidean metric space. Using local Fr\'echet regressionx2014which generalizes standard regression to metric-space valued datax2014the method estimates a mean path on either side of a candidate cutoff, extending existing k-sample tests to a flexible regression setting. Key theoretical contributions include a central limit theorem for the local estimator of the conditional Fr\'echet variance and the asymptotic validity and consistency of the proposed test. Simulations confirm nominal size control and robust power in finite samples. Two applications demonstrate the method's value by revealing effects invisible to scalar-based tests. First, I detect a sharp change in work-from-home compositions at Washington State's income threshold for non-compete enforceability during COVID-19, highlighting remote work's role as a bargaining margin. Second, I find that countries restructure their input-output networks after losing preferential US trade access. These findings underscore that analyzing regression functions within their native metric spaces can reveal structural discontinuities that scalar summaries would miss.

The paper studies the linear model for Bitcoin price which includes regression features based on Bitcoin currency statistics, mining processes, Google search trends, Wikipedia pages visits. The pattern of deviation of regression model prediction from real prices is simpler comparing to price time series. It is assumed that this pattern can be predicted by an experienced expert. In such a way, using the combination of the regression model and expert correction, one can receive better results than with either regression model or expert opinion only. It is shown that Bayesian approach makes it possible to utilize the probabilistic approach using distributions with fat tails and take into account the outliers in Bitcoin price time series.

This article introduces Regression Discontinuity Design (RDD) with Distribution-Valued Outcomes (R3D), extending the standard RDD framework to settings where the outcome is a distribution rather than a scalar. Such settings arise when treatment is assigned at a higher level of aggregation than the outcome-for example, when a subsidy is allocated based on a firm-level revenue cutoff while the outcome of interest is the distribution of employee wages within the firm. Since standard RDD methods cannot accommodate such two-level randomness, I propose a novel approach based on random distributions. The target estimand is a "local average quantile treatment effect", which averages across random quantiles. To estimate this target, I introduce two related approaches: one that extends local polynomial regression to random quantiles and another based on local Fr\'echet regression, a form of functional regression. For both estimators, I establish asymptotic normality and develop uniform, debiased confidence bands together with a data-driven bandwidth selection procedure. Simulations validate these theoretical properties and show existing methods to be biased and inconsistent in this setting. I then apply the proposed methods to study the effects of gubernatorial party control on within-state income distributions in the US, using a close-election design. The results suggest a classic equality-efficiency tradeoff under Democratic governorship, driven by reductions in income at the top of the distribution.

The technique of data augmentation (DA) is often used in machine learning for regularization purposes to better generalize under i.i.d. settings. In this work, we present a unifying framework with topics in causal inference to make a case for the use of DA beyond just the i.i.d. setting, but for generalization across interventions as well. Specifically, we argue that when the outcome generating mechanism is invariant to our choice of DA, then such augmentations can effectively be thought of as interventions on the treatment generating mechanism itself. This can potentially help to reduce bias in causal effect estimation arising from hidden confounders. In the presence of such unobserved confounding we typically make use of instrumental variables (IVs) -- sources of treatment randomization that are conditionally independent of the outcome. However, IVs may not be as readily available as DA for many applications, which is the main motivation behind this work. By appropriately regularizing IV based estimators, we introduce the concept of IV-like (IVL) regression for mitigating confounding bias and improving predictive performance across interventions even when certain IV properties are relaxed. Finally, we cast parameterized DA as an IVL regression problem and show that when used in composition can simulate a worst-case application of such DA, further improving performance on causal estimation and generalization tasks beyond what simple DA may offer. This is shown both theoretically for the population case and via simulation experiments for the finite sample case using a simple linear example. We also present real data experiments to support our case.

Covariates provide valuable information on external factors that influence time series and are critical in many real-world time series forecasting tasks. For example, in retail, covariates may indicate promotions or peak dates such as holiday seasons that heavily influence demand forecasts. Recent advances in pretraining large language model architectures for time series forecasting have led to highly accurate forecasters. However, the majority of these models do not readily use covariates as they are often specific to a certain task or domain. This paper introduces a new method to incorporate covariates into pretrained time series forecasting models. Our proposed approach incorporates covariate information into pretrained forecasting models through modular blocks that inject past and future covariate information, without necessarily modifying the pretrained model in consideration. In order to evaluate our approach, we introduce a benchmark composed of 32 different synthetic datasets with varying dynamics to evaluate the effectivity of forecasting models with covariates. Extensive evaluations on both synthetic and real datasets show that our approach effectively incorporates covariate information into pretrained models, outperforming existing baselines.

In many industries, predicting metric outcomes of large systems is a fundamental problem, driven largely by traditional tabular regression. However, such methods struggle on complex systems data in the wild such as configuration files or system logs, where feature engineering is often infeasible. We propose text-to-text regression as a general, scalable alternative. For predicting resource efficiency on Borg, Google's massive compute cluster scheduling system, a 60M parameter encoder-decoder, trained from random initialization, achieves up to a near perfect 0.99 (0.9 average) rank correlation across the entire fleet, and 100x lower MSE than tabular approaches. The model also easily adapts to new tasks in only 500 few-shot examples and captures the densities of complex outcome distributions. Ablation studies highlight the importance of using encoders, increasing sequence length, and the model's inherent uncertainty quantification. These findings pave the way for universal simulators of real-world outcomes.

In mental health counseling, a variety of earlier studies have focused on dialogue modeling. However, most of these studies give limited to no emphasis on the quality of interaction between a patient and a therapist. The therapeutic bond between a patient and a therapist directly correlates with effective mental health counseling. It involves developing the patient's trust on the therapist over the course of counseling. To assess the therapeutic bond in counseling, we introduce trust as a therapist-assistive metric. Our definition of trust involves patients' willingness and openness to express themselves and, consequently, receive better care. We conceptualize it as a dynamic trajectory observable through textual interactions during the counseling. To facilitate trust modeling, we present MENTAL-TRUST, a novel counseling dataset comprising manual annotation of 212 counseling sessions with first-of-its-kind seven expert-verified ordinal trust levels. We project our problem statement as an ordinal classification task for trust quantification and propose a new benchmark, TrustBench, comprising a suite of classical and state-of-the-art language models on MENTAL-TRUST. We evaluate the performance across a suite of metrics and lay out an exhaustive set of findings. Our study aims to unfold how trust evolves in therapeutic interactions.

We present Natural Gradient Boosting (NGBoost), an algorithm for generic probabilistic prediction via gradient boosting. Typical regression models return a point estimate, conditional on covariates, but probabilistic regression models output a full probability distribution over the outcome space, conditional on the covariates. This allows for predictive uncertainty estimation -- crucial in applications like healthcare and weather forecasting. NGBoost generalizes gradient boosting to probabilistic regression by treating the parameters of the conditional distribution as targets for a multiparameter boosting algorithm. Furthermore, we show how the Natural Gradient is required to correct the training dynamics of our multiparameter boosting approach. NGBoost can be used with any base learner, any family of distributions with continuous parameters, and any scoring rule. NGBoost matches or exceeds the performance of existing methods for probabilistic prediction while offering additional benefits in flexibility, scalability, and usability. An open-source implementation is available at github.com/stanfordmlgroup/ngboost.

Understanding causality should be a core requirement of any attempt to build real impact through AI. Due to the inherent unobservability of counterfactuals, large randomised trials (RCTs) are the standard for causal inference. But large experiments are generically expensive, and randomisation carries its own costs, e.g. when suboptimal decisions are trialed. Recent work has proposed more sample-efficient alternatives to RCTs, but these are not adaptable to the downstream application for which the causal effect is sought. In this work, we develop a task-specific approach to experimental design and derive sampling strategies customised to particular downstream applications. Across a range of important tasks, real-world datasets, and sample sizes, our method outperforms other benchmarks, e.g. requiring an order-of-magnitude less data to match RCT performance on targeted marketing tasks.

We develop a method to generate predictive regions that cover a multivariate response variable with a user-specified probability. Our work is composed of two components. First, we use a deep generative model to learn a representation of the response that has a unimodal distribution. Existing multiple-output quantile regression approaches are effective in such cases, so we apply them on the learned representation, and then transform the solution to the original space of the response. This process results in a flexible and informative region that can have an arbitrary shape, a property that existing methods lack. Second, we propose an extension of conformal prediction to the multivariate response setting that modifies any method to return sets with a pre-specified coverage level. The desired coverage is theoretically guaranteed in the finite-sample case for any distribution. Experiments conducted on both real and synthetic data show that our method constructs regions that are significantly smaller compared to existing techniques.

Weighting methods in causal inference have been widely used to achieve a desirable level of covariate balancing. However, the existing weighting methods have desirable theoretical properties only when a certain model, either the propensity score or outcome regression model, is correctly specified. In addition, the corresponding estimators do not behave well for finite samples due to large variance even when the model is correctly specified. In this paper, we consider to use the integral probability metric (IPM), which is a metric between two probability measures, for covariate balancing. Optimal weights are determined so that weighted empirical distributions for the treated and control groups have the smallest IPM value for a given set of discriminators. We prove that the corresponding estimator can be consistent without correctly specifying any model (neither the propensity score nor the outcome regression model). In addition, we empirically show that our proposed method outperforms existing weighting methods with large margins for finite samples.

We study the problem of online prediction, in which at each time step t, an individual x_t arrives, whose label we must predict. Each individual is associated with various groups, defined based on their features such as age, sex, race etc., which may intersect. Our goal is to make predictions that have regret guarantees not just overall but also simultaneously on each sub-sequence comprised of the members of any single group. Previous work such as [Blum & Lykouris] and [Lee et al] provide attractive regret guarantees for these problems; however, these are computationally intractable on large model classes. We show that a simple modification of the sleeping experts technique of [Blum & Lykouris] yields an efficient reduction to the well-understood problem of obtaining diminishing external regret absent group considerations. Our approach gives similar regret guarantees compared to [Blum & Lykouris]; however, we run in time linear in the number of groups, and are oracle-efficient in the hypothesis class. This in particular implies that our algorithm is efficient whenever the number of groups is polynomially bounded and the external-regret problem can be solved efficiently, an improvement on [Blum & Lykouris]'s stronger condition that the model class must be small. Our approach can handle online linear regression and online combinatorial optimization problems like online shortest paths. Beyond providing theoretical regret bounds, we evaluate this algorithm with an extensive set of experiments on synthetic data and on two real data sets -- Medical costs and the Adult income dataset, both instantiated with intersecting groups defined in terms of race, sex, and other demographic characteristics. We find that uniformly across groups, our algorithm gives substantial error improvements compared to running a standard online linear regression algorithm with no groupwise regret guarantees.

Given a matrix Ain R^{ntimes d} and a vector bin R^n, we consider the regression problem with ell_infty guarantees: finding a vector x'in R^d such that |x'-x^*|_infty leq epsilon{d}cdot |Ax^*-b|_2cdot |A^dagger| where x^*=argmin_{xin R^d}|Ax-b|_2. One popular approach for solving such ell_2 regression problem is via sketching: picking a structured random matrix Sin R^{mtimes n} with mll n and SA can be quickly computed, solve the ``sketched'' regression problem argmin_{xin R^d} |SAx-Sb|_2. In this paper, we show that in order to obtain such ell_infty guarantee for ell_2 regression, one has to use sketching matrices that are dense. To the best of our knowledge, this is the first user case in which dense sketching matrices are necessary. On the algorithmic side, we prove that there exists a distribution of dense sketching matrices with m=epsilon^{-2}dlog^3(n/delta) such that solving the sketched regression problem gives the ell_infty guarantee, with probability at least 1-delta. Moreover, the matrix SA can be computed in time O(ndlog n). Our row count is nearly-optimal up to logarithmic factors, and significantly improves the result in [Price, Song and Woodruff, ICALP'17], in which a super-linear in d rows, m=Omega(epsilon^{-2}d^{1+gamma}) for gamma=Theta(frac{loglog n{log d}}) is required. We also develop a novel analytical framework for ell_infty guarantee regression that utilizes the Oblivious Coordinate-wise Embedding (OCE) property introduced in [Song and Yu, ICML'21]. Our analysis is arguably much simpler and more general than [Price, Song and Woodruff, ICALP'17], and it extends to dense sketches for tensor product of vectors.

We present an online post-hoc calibration method, called Online Platt Scaling (OPS), which combines the Platt scaling technique with online logistic regression. We demonstrate that OPS smoothly adapts between i.i.d. and non-i.i.d. settings with distribution drift. Further, in scenarios where the best Platt scaling model is itself miscalibrated, we enhance OPS by incorporating a recently developed technique called calibeating to make it more robust. Theoretically, our resulting OPS+calibeating method is guaranteed to be calibrated for adversarial outcome sequences. Empirically, it is effective on a range of synthetic and real-world datasets, with and without distribution drifts, achieving superior performance without hyperparameter tuning. Finally, we extend all OPS ideas to the beta scaling method.

Noise plagues many numerical datasets, where the recorded values in the data may fail to match the true underlying values due to reasons including: erroneous sensors, data entry/processing mistakes, or imperfect human estimates. We consider general regression settings with covariates and a potentially corrupted response whose observed values may contain errors. By accounting for various uncertainties, we introduced veracity scores that distinguish between genuine errors and natural data fluctuations, conditioned on the available covariate information in the dataset. We propose a simple yet efficient filtering procedure for eliminating potential errors, and establish theoretical guarantees for our method. We also contribute a new error detection benchmark involving 5 regression datasets with real-world numerical errors (for which the true values are also known). In this benchmark and additional simulation studies, our method identifies incorrect values with better precision/recall than other approaches.

We seek to identify the most relevant benefits offered by Medicare Advantage Health Plans that drive membership and market share. As an example, we explore plans operating in a single county in New Jersey between 2018 and 2023. A dataset of benefits from publicly available data sources was created and the variance inflation factor was applied to identify the correlation between the extracted features, to avoid multicollinearity and overparameterization problems. We categorized the variable Market Share and used it as a multinomial response variable with three categories: less than 0.3\%, 0.3\% to 1.5\%, and over 1.5\%. Categories were chosen to achieve approximately uniform distribution of plans (47, 60, and 65 respectively). We built a multinomial Lasso model using 5-fold cross-validation to tune the penalty parameter. Lasso forced some features to be dropped from the model, which reduces the risk of overfitting and increases the interpretability of the results. For each category, important variables are different. Certain brands drive market share, as do PPO plans and prescription drug coverage. Benefits, particularly ancillary benefits that are not part of CMS's required benefits, appear to have little influence, while financial terms such as deductibles, copays, and out-of-pocket limits are associated with higher market share. Finally, we evaluated the predictive accuracy of the Lasso model with the test set. The accuracy is 0.76.

We study the connection between multicalibration and boosting for squared error regression. First we prove a useful characterization of multicalibration in terms of a ``swap regret'' like condition on squared error. Using this characterization, we give an exceedingly simple algorithm that can be analyzed both as a boosting algorithm for regression and as a multicalibration algorithm for a class H that makes use only of a standard squared error regression oracle for H. We give a weak learning assumption on H that ensures convergence to Bayes optimality without the need to make any realizability assumptions -- giving us an agnostic boosting algorithm for regression. We then show that our weak learning assumption on H is both necessary and sufficient for multicalibration with respect to H to imply Bayes optimality. We also show that if H satisfies our weak learning condition relative to another class C then multicalibration with respect to H implies multicalibration with respect to C. Finally we investigate the empirical performance of our algorithm experimentally using an open source implementation that we make available. Our code repository can be found at https://github.com/Declancharrison/Level-Set-Boosting.

Action recognition models have achieved promising results in understanding instructional videos. However, they often rely on dominant, dataset-specific action sequences rather than true video comprehension, a problem that we define as ordinal bias. To address this issue, we propose two effective video manipulation methods: Action Masking, which masks frames of frequently co-occurring actions, and Sequence Shuffling, which randomizes the order of action segments. Through comprehensive experiments, we demonstrate that current models exhibit significant performance drops when confronted with nonstandard action sequences, underscoring their vulnerability to ordinal bias. Our findings emphasize the importance of rethinking evaluation strategies and developing models capable of generalizing beyond fixed action patterns in diverse instructional videos.

Time series research has gathered lots of interests in the last decade, especially for Time Series Classification (TSC) and Time Series Forecasting (TSF). Research in TSC has greatly benefited from the University of California Riverside and University of East Anglia (UCR/UEA) Time Series Archives. On the other hand, the advancement in Time Series Forecasting relies on time series forecasting competitions such as the Makridakis competitions, NN3 and NN5 Neural Network competitions, and a few Kaggle competitions. Each year, thousands of papers proposing new algorithms for TSC and TSF have utilized these benchmarking archives. These algorithms are designed for these specific problems, but may not be useful for tasks such as predicting the heart rate of a person using photoplethysmogram (PPG) and accelerometer data. We refer to this problem as Time Series Extrinsic Regression (TSER), where we are interested in a more general methodology of predicting a single continuous value, from univariate or multivariate time series. This prediction can be from the same time series or not directly related to the predictor time series and does not necessarily need to be a future value or depend heavily on recent values. To the best of our knowledge, research into TSER has received much less attention in the time series research community and there are no models developed for general time series extrinsic regression problems. Most models are developed for a specific problem. Therefore, we aim to motivate and support the research into TSER by introducing the first TSER benchmarking archive. This archive contains 19 datasets from different domains, with varying number of dimensions, unequal length dimensions, and missing values. In this paper, we introduce the datasets in this archive and did an initial benchmark on existing models.

We consider the problem of subset selection where one is given multiple rankings of items and the goal is to select the highest ``quality'' subset. Score functions from the multiwinner voting literature have been used to aggregate rankings into quality scores for subsets. We study this setting of subset selection problems when, in addition, rankings may contain systemic or unconscious biases toward a group of items. For a general model of input rankings and biases, we show that requiring the selected subset to satisfy group fairness constraints can improve the quality of the selection with respect to unbiased rankings. Importantly, we show that for fairness constraints to be effective, different multiwinner score functions may require a drastically different number of rankings: While for some functions, fairness constraints need an exponential number of rankings to recover a close-to-optimal solution, for others, this dependency is only polynomial. This result relies on a novel notion of ``smoothness'' of submodular functions in this setting that quantifies how well a function can ``correctly'' assess the quality of items in the presence of bias. The results in this paper can be used to guide the choice of multiwinner score functions for the subset selection setting considered here; we additionally provide a tool to empirically enable this.

Negative binomial regression is essential for analyzing over-dispersed count data in in comparative studies, but parameter estimation becomes computationally challenging in large screens requiring millions of comparisons. We investigate using a pre-trained transformer to produce estimates of negative binomial regression parameters from observed count data, trained through synthetic data generation to learn to invert the process of generating counts from parameters. The transformer method achieved better parameter accuracy than maximum likelihood optimization while being 20 times faster. However, comparisons unexpectedly revealed that method of moment estimates performed as well as maximum likelihood optimization in accuracy, while being 1,000 times faster and producing better-calibrated and more powerful tests, making it the most efficient solution for this application.

Ranking and scoring are ubiquitous. We consider the setting in which an institution, called a ranker, evaluates a set of individuals based on demographic, behavioral or other characteristics. The final output is a ranking that represents the relative quality of the individuals. While automatic and therefore seemingly objective, rankers can, and often do, discriminate against individuals and systematically disadvantage members of protected groups. This warrants a careful study of the fairness of a ranking scheme. In this paper we propose fairness measures for ranked outputs. We develop a data generation procedure that allows us to systematically control the degree of unfairness in the output, and study the behavior of our measures on these datasets. We then apply our proposed measures to several real datasets, and demonstrate cases of unfairness. Finally, we show preliminary results of incorporating our ranked fairness measures into an optimization framework, and show potential for improving fairness of ranked outputs while maintaining accuracy.

The assumption that response and predictor belong to the same statistical unit may be violated in practice. Unbiased estimation and recovery of true label ordering based on unlabeled data are challenging tasks and have attracted increasing attentions in the recent literature. In this paper, we present a relatively complete analysis of label permutation problem for the generalized linear model with multivariate responses. The theory is established under different scenarios, with knowledge of true parameters, with partial knowledge of underlying label permutation matrix and without any knowledge. Our results remove the stringent conditions required by the current literature and are further extended to the missing observation setting which has never been considered in the field of label permutation problem. On computational side, we propose two methods, "maximum likelihood estimation" algorithm and "two-step estimation" algorithm, to accommodate for different settings. When the proportion of permuted labels is moderate, both methods work effectively. Multiple numerical experiments are provided and corroborate our theoretical findings.

Reward models are critical for aligning models to follow instructions, and are typically trained following one of two popular paradigms: Bradley-Terry style or Regression style. However, there is a lack of evidence that either approach is better than the other, when adequately matched for data. This is primarily because these approaches require data collected in different (but incompatible) formats, meaning that adequately matched data is not available in existing public datasets. To tackle this problem, we release preference annotations (designed for Bradley-Terry training) to complement existing ratings (designed for Regression style training) in the HelpSteer2 dataset. To improve data interpretability, preference annotations are accompanied with human-written justifications. Using this data, we conduct the first head-to-head comparison of Bradley-Terry and Regression models when adequately matched for data. Based on insights derived from such a comparison, we propose a novel approach to combine Bradley-Terry and Regression reward modeling. A Llama-3.1-70B-Instruct model tuned with this approach scores 94.1 on RewardBench, emerging top of more than 140 reward models as of 1 Oct 2024. We also demonstrate the effectiveness of this reward model at aligning models to follow instructions in RLHF. We open-source this dataset (CC-BY-4.0 license) at https://huggingface.co/datasets/nvidia/HelpSteer2 and openly release the trained Reward Model at https://huggingface.co/nvidia/Llama-3.1-Nemotron-70B-Reward

Estimating the impact of continuous treatment variables (e.g., dosage amount) on binary outcomes presents significant challenges in modeling and estimation because many existing approaches make strong assumptions that do not hold for certain continuous treatment variables. For instance, traditional logistic regression makes strong linearity assumptions that do not hold for continuous treatment variables like time of initiation. In this work, we propose a semiparametric regression framework that decomposes effects into two interpretable components: a prognostic score that captures baseline outcome risk based on a combination of clinical, genetic, and sociodemographic features, and a treatment-interaction score that flexibly models the optimal treatment level via a nonparametric link function. By connecting these two parametric scores with Nadaraya-Watson regression, our approach is both interpretable and flexible. The potential of our approach is demonstrated through numerical simulations that show empirical estimation convergence. We conclude by applying our approach to a real-world case study using the International Warfarin Pharmacogenomics Consortium (IWPC) dataset to show our approach's clinical utility by deriving personalized warfarin dosing recommendations that integrate both genetic and clinical data, providing insights towards enhancing patient safety and therapeutic efficacy in anticoagulation therapy.

Mathematical word problem-solving has long been recognized as a complex task for small language models (SLMs). A recent study hypothesized that the smallest model size, needed to achieve over 80% accuracy on the GSM8K benchmark, is 34 billion parameters. To reach this level of performance with smaller models, researcher often train SLMs to generate Python code or use tools to help avoid calculation errors. Additionally, they employ ensembling, where outputs of up to 100 model runs are combined to arrive at a more accurate result. Result selection is done using consensus, majority vote or a separate a verifier model used in conjunction with the SLM. Ensembling provides a substantial boost in accuracy but at a significant cost increase with multiple calls to the model (e.g., Phi-GSM uses top-48 to boost the performance from 68.2 to 81.5). In this work, we present Orca-Math, a 7-billion-parameter SLM based on the Mistral-7B, which achieves 86.81% on GSM8k without the need for multiple model calls or the use of verifiers, code execution or any other external tools. Our approach has the following key elements: (1) A high quality synthetic dataset of 200K math problems created using a multi-agent setup where agents collaborate to create the data, (2) An iterative learning techniques that enables the SLM to practice solving problems, receive feedback on its solutions and learn from preference pairs incorporating the SLM solutions and the feedback. When trained with Supervised Fine-Tuning alone, Orca-Math achieves 81.50% on GSM8k pass@1 metric. With iterative preference learning, Orca-Math achieves 86.81% pass@1. Orca-Math surpasses the performance of significantly larger models such as LLAMA-2-70B, WizardMath-70B, Gemini-Pro, ChatGPT-3.5. It also significantly outperforms other smaller models while using much smaller data (hundreds of thousands vs. millions of problems).

This study investigates the use of Large Language Models (LLMs) for predicting human-perceived misery scores from natural language descriptions of real-world scenarios. The task is framed as a regression problem, where the model assigns a scalar value from 0 to 100 to each input statement. We evaluate multiple prompting strategies, including zero-shot, fixed-context few-shot, and retrieval-based prompting using BERT sentence embeddings. Few-shot approaches consistently outperform zero-shot baselines, underscoring the value of contextual examples in affective prediction. To move beyond static evaluation, we introduce the "Misery Game Show", a novel gamified framework inspired by a television format. It tests LLMs through structured rounds involving ordinal comparison, binary classification, scalar estimation, and feedback-driven reasoning. This setup enables us to assess not only predictive accuracy but also the model's ability to adapt based on corrective feedback. The gamified evaluation highlights the broader potential of LLMs in dynamic emotional reasoning tasks beyond standard regression. Code and data link: https://github.com/abhi1nandy2/Misery_Data_Exps_GitHub

LLM-as-a-judge has become a promising paradigm for using large language models (LLMs) to evaluate natural language generation (NLG), but the uncertainty of its evaluation remains underexplored. This lack of reliability may limit its deployment in many applications. This work presents the first framework to analyze the uncertainty by offering a prediction interval of LLM-based scoring via conformal prediction. Conformal prediction constructs continuous prediction intervals from a single evaluation run, and we design an ordinal boundary adjustment for discrete rating tasks. We also suggest a midpoint-based score within the interval as a low-bias alternative to raw model score and weighted average. We perform extensive experiments and analysis, which show that conformal prediction can provide valid prediction interval with coverage guarantees. We also explore the usefulness of interval midpoint and judge reprompting for better judgment.

Symbolic regression (SR) is an area of interpretable machine learning that aims to identify mathematical expressions, often composed of simple functions, that best fit in a given set of covariates X and response y. In recent years, deep symbolic regression (DSR) has emerged as a popular method in the field by leveraging deep reinforcement learning to solve the complicated combinatorial search problem. In this work, we propose an alternative framework (GFN-SR) to approach SR with deep learning. We model the construction of an expression tree as traversing through a directed acyclic graph (DAG) so that GFlowNet can learn a stochastic policy to generate such trees sequentially. Enhanced with an adaptive reward baseline, our method is capable of generating a diverse set of best-fitting expressions. Notably, we observe that GFN-SR outperforms other SR algorithms in noisy data regimes, owing to its ability to learn a distribution of rewards over a space of candidate solutions.

Reinforcement learning from human feedback (RLHF) has become a key method for aligning large language models (LLMs) with human preferences through the use of reward models. However, traditional reward models typically generate point estimates, which oversimplify the diversity and complexity of human values and preferences. In this paper, we introduce Quantile Reward Models (QRMs), a novel approach to reward modeling that learns a distribution over rewards instead of a single scalar value. Our method uses quantile regression to estimate a full, potentially multimodal distribution over preferences, providing a more powerful and nuanced representation of preferences. This distributional approach can better capture the diversity of human values, addresses label noise, and accommodates conflicting preferences by modeling them as distinct modes in the distribution. Our experimental results show that QRM outperforms comparable traditional point-estimate models on RewardBench. Furthermore, we demonstrate that the additional information provided by the distributional estimates can be utilized in downstream applications, such as risk-aware reinforcement learning, resulting in LLM policies that generate fewer extremely negative responses. Our code and model are released at https://github.com/Nicolinho/QRM.

Randomized controlled trials (RCTs) are considered the gold standard for estimating the average treatment effect (ATE) of interventions. One use of RCTs is to study the causes of global poverty -- a subject explicitly cited in the 2019 Nobel Memorial Prize awarded to Duflo, Banerjee, and Kremer "for their experimental approach to alleviating global poverty." Because the ATE is a population summary, anti-poverty experiments often seek to unpack the effect variation around the ATE by conditioning (CATE) on tabular variables such as age and ethnicity that were measured during the RCT data collection. Although such variables are key to unpacking CATE, using only such variables may fail to capture historical, geographical, or neighborhood-specific contributors to effect variation, as tabular RCT data are often only observed near the time of the experiment. In global poverty research, when the location of the experiment units is approximately known, satellite imagery can provide a window into such factors important for understanding heterogeneity. However, there is no method that specifically enables applied researchers to analyze CATE from images. In this paper, using a deep probabilistic modeling framework, we develop such a method that estimates latent clusters of images by identifying images with similar treatment effects distributions. Our interpretable image CATE model also includes a sensitivity factor that quantifies the importance of image segments contributing to the effect cluster prediction. We compare the proposed methods against alternatives in simulation; also, we show how the model works in an actual RCT, estimating the effects of an anti-poverty intervention in northern Uganda and obtaining a posterior predictive distribution over effects for the rest of the country where no experimental data was collected. We make all models available in open-source software.

State of the art Symbolic Regression (SR) methods currently build specialized models, while the application of Large Language Models (LLMs) remains largely unexplored. In this work, we introduce the first comprehensive framework that utilizes LLMs for the task of SR. We propose In-Context Symbolic Regression (ICSR), an SR method which iteratively refines a functional form with an LLM and determines its coefficients with an external optimizer. ICSR leverages LLMs' strong mathematical prior both to propose an initial set of possible functions given the observations and to refine them based on their errors. Our findings reveal that LLMs are able to successfully find symbolic equations that fit the given data, matching or outperforming the overall performance of the best SR baselines on four popular benchmarks, while yielding simpler equations with better out of distribution generalization.

We study code-to-metric regression: predicting numeric outcomes of code executions, a challenging task due to the open-ended nature of programming languages. While prior methods have resorted to heavy and domain-specific feature engineering, we show that a single unified Regression Language Model (RLM) can simultaneously predict directly from text, (i) the memory footprint of code across multiple high-level languages such as Python and C++, (ii) the latency of Triton GPU kernels, and (iii) the accuracy and speed of trained neural networks represented in ONNX. In particular, a relatively small 300M parameter RLM initialized from T5Gemma, obtains > 0.9 Spearman-rank on competitive programming submissions from APPS, and a single unified model achieves > 0.5 average Spearman-rank across 17 separate languages from CodeNet. Furthermore, the RLM can obtain the highest average Kendall-Tau of 0.46 on five classic NAS design spaces previously dominated by graph neural networks, and simultaneously predict architecture latencies on numerous hardware platforms.

Relations such as "is influenced by", "is known for" or "is a competitor of" are inherently graded: we can rank entity pairs based on how well they satisfy these relations, but it is hard to draw a line between those pairs that satisfy them and those that do not. Such graded relations play a central role in many applications, yet they are typically not covered by existing Knowledge Graphs. In this paper, we consider the possibility of using Large Language Models (LLMs) to fill this gap. To this end, we introduce a new benchmark, in which entity pairs have to be ranked according to how much they satisfy a given graded relation. The task is formulated as a few-shot ranking problem, where models only have access to a description of the relation and five prototypical instances. We use the proposed benchmark to evaluate state-of-the-art relation embedding strategies as well as several recent LLMs, covering both publicly available LLMs and closed models such as GPT-4. Overall, we find a strong correlation between model size and performance, with smaller Language Models struggling to outperform a naive baseline. The results of the largest Flan-T5 and OPT models are remarkably strong, although a clear gap with human performance remains.

Calibrated uncertainty estimates in machine learning are crucial to many fields such as autonomous vehicles, medicine, and weather and climate forecasting. While there is extensive literature on uncertainty calibration for classification, the classification findings do not always translate to regression. As a result, modern models for predicting uncertainty in regression settings typically produce uncalibrated and overconfident estimates. To address these gaps, we present a calibration method for regression settings that does not assume a particular uncertainty distribution over the error: Calibrating Regression Uncertainty Distributions Empirically (CRUDE). CRUDE makes the weaker assumption that error distributions have a constant arbitrary shape across the output space, shifted by predicted mean and scaled by predicted standard deviation. We detail a theoretical connection between CRUDE and conformal inference. Across an extensive set of regression tasks, CRUDE demonstrates consistently sharper, better calibrated, and more accurate uncertainty estimates than state-of-the-art techniques.

Recent advances in GUI agents have achieved remarkable grounding and action-prediction performance, yet existing models struggle with unreliable reward signals and limited online trajectory generation. In this paper, we introduce Orcust, a framework that integrates Principle-Constrained Reward Modeling (PCRM) and Online VM-Grounded Trajectory Construction (OVTC) to enhance reasoning reliability and data efficiency in interactive GUI tasks. We leverages environment-verifiable and LLM-derived principle to enforce interpretable reward signals that constrain long chain-of-thought reasoning and rule-based feedback. OVTC spins up instrumented virtual machines to autonomously collect structured GUI interaction trajectories with explicit procedural and structural objectives, enabling the training of a stepwise reward model that robustly captures human preferences and adheres to task-specific constraints. Extensive experiments on standard GUI benchmarks covering perceptual grounding, foundational operations, and end-to-end task execution reveal that Orcust achieves state-of-the-art performance, improving by 22.2\% on ScreenSpot and 23.9\% on ScreenSpot-Pro over the base model (i.e. Qwen2.5-VL-7B). The results demonstrate Orcust's effectiveness in enhancing the reasoning, adaptability and scalability of GUI agents across various environments and task complexities.

Multivariate probabilistic time series forecasts are commonly evaluated via proper scoring rules, i.e., functions that are minimal in expectation for the ground-truth distribution. However, this property is not sufficient to guarantee good discrimination in the non-asymptotic regime. In this paper, we provide the first systematic finite-sample study of proper scoring rules for time-series forecasting evaluation. Through a power analysis, we identify the "region of reliability" of a scoring rule, i.e., the set of practical conditions where it can be relied on to identify forecasting errors. We carry out our analysis on a comprehensive synthetic benchmark, specifically designed to test several key discrepancies between ground-truth and forecast distributions, and we gauge the generalizability of our findings to real-world tasks with an application to an electricity production problem. Our results reveal critical shortcomings in the evaluation of multivariate probabilistic forecasts as commonly performed in the literature.

This paper studies the challenging problem of estimating causal effects from observational data, in the presence of unobserved confounders. The two-stage least square (TSLS) method and its variants with a standard instrumental variable (IV) are commonly used to eliminate confounding bias, including the bias caused by unobserved confounders, but they rely on the linearity assumption. Besides, the strict condition of unconfounded instruments posed on a standard IV is too strong to be practical. To address these challenging and practical problems of the standard IV method (linearity assumption and the strict condition), in this paper, we use a conditional IV (CIV) to relax the unconfounded instrument condition of standard IV and propose a non-linear CIV regression with Confounding Balancing Representation Learning, CBRL.CIV, for jointly eliminating the confounding bias from unobserved confounders and balancing the observed confounders, without the linearity assumption. We theoretically demonstrate the soundness of CBRL.CIV. Extensive experiments on synthetic and two real-world datasets show the competitive performance of CBRL.CIV against state-of-the-art IV-based estimators and superiority in dealing with the non-linear situation.

Due to their crucial role in all NLP, several benchmarks have been proposed to evaluate pretrained language models. In spite of these efforts, no public benchmark of diverse nature currently exists for evaluation of Arabic. This makes it challenging to measure progress for both Arabic and multilingual language models. This challenge is compounded by the fact that any benchmark targeting Arabic needs to take into account the fact that Arabic is not a single language but rather a collection of languages and varieties. In this work, we introduce ORCA, a publicly available benchmark for Arabic language understanding evaluation. ORCA is carefully constructed to cover diverse Arabic varieties and a wide range of challenging Arabic understanding tasks exploiting 60 different datasets across seven NLU task clusters. To measure current progress in Arabic NLU, we use ORCA to offer a comprehensive comparison between 18 multilingual and Arabic language models. We also provide a public leaderboard with a unified single-number evaluation metric (ORCA score) to facilitate future research.

We consider a class of assortment optimization problems in an offline data-driven setting. A firm does not know the underlying customer choice model but has access to an offline dataset consisting of the historically offered assortment set, customer choice, and revenue. The objective is to use the offline dataset to find an optimal assortment. Due to the combinatorial nature of assortment optimization, the problem of insufficient data coverage is likely to occur in the offline dataset. Therefore, designing a provably efficient offline learning algorithm becomes a significant challenge. To this end, we propose an algorithm referred to as Pessimistic ASsortment opTimizAtion (PASTA for short) designed based on the principle of pessimism, that can correctly identify the optimal assortment by only requiring the offline data to cover the optimal assortment under general settings. In particular, we establish a regret bound for the offline assortment optimization problem under the celebrated multinomial logit model. We also propose an efficient computational procedure to solve our pessimistic assortment optimization problem. Numerical studies demonstrate the superiority of the proposed method over the existing baseline method.

The rise of large language models (LLMs) has brought a critical need for high-quality human-labeled data, particularly for processes like human feedback and evaluation. A common practice is to label data via consensus annotation over crowdworker judgments. However, annotators' judgments for subjective tasks can differ in many ways: they may have different qualitative judgments about an example, and they may map those to a labeling scheme in different ways. We show that these nuances can be captured by natural language explanations, and propose a method to rescale ordinal annotations and explanations using LLMs. Specifically, we feed annotators' Likert ratings and corresponding explanations into an LLM and prompt it to produce a numeric score anchored in a scoring rubric. These scores should reflect the annotators' underlying assessments of the example. The rubric can be designed or modified after annotation, and include distinctions that may not have been known when the original error taxonomy was devised. We explore our technique in the context of rating system outputs for a document-grounded question answering task, where LLMs achieve near-human performance. Our method rescales the raw judgments without impacting agreement and brings the scores closer to human judgments grounded in the same scoring rubric.

Symbolic regression (SR) is the problem of learning a symbolic expression from numerical data. Recently, deep neural models trained on procedurally-generated synthetic datasets showed competitive performance compared to more classical Genetic Programming (GP) algorithms. Unlike their GP counterparts, these neural approaches are trained to generate expressions from datasets given as context. This allows them to produce accurate expressions in a single forward pass at test time. However, they usually do not benefit from search abilities, which result in low performance compared to GP on out-of-distribution datasets. In this paper, we propose a novel method which provides the best of both worlds, based on a Monte-Carlo Tree Search procedure using a context-aware neural mutation model, which is initially pre-trained to learn promising mutations, and further refined from successful experiences in an online fashion. The approach demonstrates state-of-the-art performance on the well-known SRBench benchmark.

We propose causal isotonic calibration, a novel nonparametric method for calibrating predictors of heterogeneous treatment effects. Furthermore, we introduce cross-calibration, a data-efficient variant of calibration that eliminates the need for hold-out calibration sets. Cross-calibration leverages cross-fitted predictors and generates a single calibrated predictor using all available data. Under weak conditions that do not assume monotonicity, we establish that both causal isotonic calibration and cross-calibration achieve fast doubly-robust calibration rates, as long as either the propensity score or outcome regression is estimated accurately in a suitable sense. The proposed causal isotonic calibrator can be wrapped around any black-box learning algorithm, providing robust and distribution-free calibration guarantees while preserving predictive performance.

Sorting is a fundamental operation of all computer systems, having been a long-standing significant research topic. Beyond the problem formulation of traditional sorting algorithms, we consider sorting problems for more abstract yet expressive inputs, e.g., multi-digit images and image fragments, through a neural sorting network. To learn a mapping from a high-dimensional input to an ordinal variable, the differentiability of sorting networks needs to be guaranteed. In this paper we define a softening error by a differentiable swap function, and develop an error-free swap function that holds a non-decreasing condition and differentiability. Furthermore, a permutation-equivariant Transformer network with multi-head attention is adopted to capture dependency between given inputs and also leverage its model capacity with self-attention. Experiments on diverse sorting benchmarks show that our methods perform better than or comparable to baseline methods.

Scaling pre-training compute has proven effective for achieving mulitlinguality, but does the same hold for test-time scaling? In this work, we introduce MCLM, a multilingual math benchmark featuring competition-level problems in 55 languages. We test three test-time scaling methods-Outcome Reward Modeling (ORM), Process Reward Modeling (ORM), and Budget Forcing (BF)-on both Qwen2.5-1.5B Math and MR1-1.5B, a multilingual LLM we trained for extended reasoning. Our experiments show that using Qwen2.5-1.5B Math with ORM achieves a score of 35.8 on MCLM, while BF on MR1-1.5B attains 35.2. Although "thinking LLMs" have recently garnered significant attention, we find that their performance is comparable to traditional scaling methods like best-of-N once constrained to similar levels of inference FLOPs. Moreover, while BF yields a 20-point improvement on English AIME, it provides only a 1.94-point average gain across other languages-a pattern consistent across the other test-time scaling methods we studied-higlighting that test-time scaling may not generalize as effectively to multilingual tasks. To foster further research, we release MCLM, MR1-1.5B, and evaluation results.

The quality of many modern machine learning models improves as model complexity increases, an effect that has been quantified, for predictive performance, with the non-monotonic double descent learning curve. Here, we address the overarching question: is there an analogous theory of double descent for models which estimate uncertainty? We provide a partially affirmative and partially negative answer in the setting of Gaussian processes (GP). Under standard assumptions, we prove that higher model quality for optimally-tuned GPs (including uncertainty prediction) under marginal likelihood is realized for larger input dimensions, and therefore exhibits a monotone error curve. After showing that marginal likelihood does not naturally exhibit double descent in the input dimension, we highlight related forms of posterior predictive loss that do exhibit non-monotonicity. Finally, we verify empirically that our results hold for real data, beyond our considered assumptions, and we explore consequences involving synthetic covariates.

High-quality preference data is essential for aligning foundation models with human values through preference learning. However, manual annotation of such data is often time-consuming and costly. Recent methods often adopt a self-rewarding approach, where the target model generates and annotates its own preference data, but this can lead to inaccuracies since the reward model shares weights with the target model, thereby amplifying inherent biases. To address these issues, we propose Anyprefer, a framework designed to synthesize high-quality preference data for aligning the target model. Anyprefer frames the data synthesis process as a cooperative two-player Markov Game, where the target model and the judge model collaborate together. Here, a series of external tools are introduced to assist the judge model in accurately rewarding the target model's responses, mitigating biases in the rewarding process. In addition, a feedback mechanism is introduced to optimize prompts for both models, enhancing collaboration and improving data quality. The synthesized data is compiled into a new preference dataset, Anyprefer-V1, consisting of 58K high-quality preference pairs. Extensive experiments show that Anyprefer significantly improves model alignment performance across four main applications, covering 21 datasets, achieving average improvements of 18.55% in five natural language generation datasets, 3.66% in nine vision-language understanding datasets, 30.05% in three medical image analysis datasets, and 16.00% in four visuo-motor control tasks.

Cross-validation is the de facto standard for predictive model evaluation and selection. In proper use, it provides an unbiased estimate of a model's predictive performance. However, data sets often undergo various forms of data-dependent preprocessing, such as mean-centering, rescaling, dimensionality reduction, and outlier removal. It is often believed that such preprocessing stages, if done in an unsupervised manner (that does not incorporate the class labels or response values) are generally safe to do prior to cross-validation. In this paper, we study three commonly-practiced preprocessing procedures prior to a regression analysis: (i) variance-based feature selection; (ii) grouping of rare categorical features; and (iii) feature rescaling. We demonstrate that unsupervised preprocessing can, in fact, introduce a substantial bias into cross-validation estimates and potentially hurt model selection. This bias may be either positive or negative and its exact magnitude depends on all the parameters of the problem in an intricate manner. Further research is needed to understand the real-world impact of this bias across different application domains, particularly when dealing with small sample sizes and high-dimensional data.

Symbolic regression (SR) is a challenging task in machine learning that involves finding a mathematical expression for a function based on its values. Recent advancements in SR have demonstrated the effectiveness of pretrained transformer-based models in generating equations as sequences, leveraging large-scale pretraining on synthetic datasets and offering notable advantages in terms of inference time over GP-based methods. However, these models primarily rely on supervised pretraining goals borrowed from text generation and overlook equation-specific objectives like accuracy and complexity. To address this, we propose TPSR, a Transformer-based Planning strategy for Symbolic Regression that incorporates Monte Carlo Tree Search into the transformer decoding process. Unlike conventional decoding strategies, TPSR enables the integration of non-differentiable feedback, such as fitting accuracy and complexity, as external sources of knowledge into the transformer-based equation generation process. Extensive experiments on various datasets show that our approach outperforms state-of-the-art methods, enhancing the model's fitting-complexity trade-off, extrapolation abilities, and robustness to noise

Personalized treatment effect estimates are often of interest in high-stakes applications -- thus, before deploying a model estimating such effects in practice, one needs to be sure that the best candidate from the ever-growing machine learning toolbox for this task was chosen. Unfortunately, due to the absence of counterfactual information in practice, it is usually not possible to rely on standard validation metrics for doing so, leading to a well-known model selection dilemma in the treatment effect estimation literature. While some solutions have recently been investigated, systematic understanding of the strengths and weaknesses of different model selection criteria is still lacking. In this paper, instead of attempting to declare a global `winner', we therefore empirically investigate success- and failure modes of different selection criteria. We highlight that there is a complex interplay between selection strategies, candidate estimators and the data used for comparing them, and provide interesting insights into the relative (dis)advantages of different criteria alongside desiderata for the design of further illuminating empirical studies in this context.

Language models have recently been shown capable of performing regression tasks wherein numeric predictions are represented as decoded strings. In this work, we provide theoretical grounds for this capability and furthermore investigate the utility of causal auto-regressive sequence models when they are applied to any feature representation. We find that, despite being trained in the usual way - for next-token prediction via cross-entropy loss - decoding-based regression is as performant as traditional approaches for tabular regression tasks, while being flexible enough to capture arbitrary distributions, such as in the task of density estimation.

Ensuring equitable treatment (fairness) across protected attributes (such as gender or ethnicity) is a critical issue in machine learning. Most existing literature focuses on binary classification, but achieving fairness in regression tasks-such as insurance pricing or hiring score assessments-is equally important. Moreover, anti-discrimination laws also apply to continuous attributes, such as age, for which many existing methods are not applicable. In practice, multiple protected attributes can exist simultaneously; however, methods targeting fairness across several attributes often overlook so-called "fairness gerrymandering", thereby ignoring disparities among intersectional subgroups (e.g., African-American women or Hispanic men). In this paper, we propose a distance covariance regularisation framework that mitigates the association between model predictions and protected attributes, in line with the fairness definition of demographic parity, and that captures both linear and nonlinear dependencies. To enhance applicability in the presence of multiple protected attributes, we extend our framework by incorporating two multivariate dependence measures based on distance covariance: the previously proposed joint distance covariance (JdCov) and our novel concatenated distance covariance (CCdCov), which effectively address fairness gerrymandering in both regression and classification tasks involving protected attributes of various types. We discuss and illustrate how to calibrate regularisation strength, including a method based on Jensen-Shannon divergence, which quantifies dissimilarities in prediction distributions across groups. We apply our framework to the COMPAS recidivism dataset and a large motor insurance claims dataset.

In nature, the behaviors of many complex systems can be described by parsimonious math equations. Automatically distilling these equations from limited data is cast as a symbolic regression process which hitherto remains a grand challenge. Keen efforts in recent years have been placed on tackling this issue and demonstrated success in symbolic regression. However, there still exist bottlenecks that current methods struggle to break when the discrete search space tends toward infinity and especially when the underlying math formula is intricate. To this end, we propose a novel Reinforcement Symbolic Regression Machine (RSRM) that masters the capability of uncovering complex math equations from only scarce data. The RSRM model is composed of three key modules: (1) a Monte Carlo tree search (MCTS) agent that explores optimal math expression trees consisting of pre-defined math operators and variables, (2) a Double Q-learning block that helps reduce the feasible search space of MCTS via properly understanding the distribution of reward, and (3) a modulated sub-tree discovery block that heuristically learns and defines new math operators to improve representation ability of math expression trees. Biding of these modules yields the state-of-the-art performance of RSRM in symbolic regression as demonstrated by multiple sets of benchmark examples. The RSRM model shows clear superiority over several representative baseline models.

Many social and environmental phenomena are associated with macroscopic changes in the built environment, captured by satellite imagery on a global scale and with daily temporal resolution. While widely used for prediction, these images and especially image sequences remain underutilized for causal inference, especially in the context of randomized controlled trials (RCTs), where causal identification is established by design. In this paper, we develop and compare a set of general tools for analyzing Conditional Average Treatment Effects (CATEs) from temporal satellite data that can be applied to any RCT where geographical identifiers are available. Through a simulation study, we analyze different modeling strategies for estimating CATE in sequences of satellite images. We find that image sequence representation models with more parameters generally yield a greater ability to detect heterogeneity. To explore the role of model and data choice in practice, we apply the approaches to two influential RCTs -- Banerjee et al. (2015), a poverty study in Cusco, Peru, and Bolsen et al. (2014), a water conservation experiment in Georgia, USA. We benchmark our image sequence models against image-only, tabular-only, and combined image-tabular data sources, summarizing practical implications for investigators in a multivariate analysis. Land cover classifications over satellite images facilitate interpretation of what image features drive heterogeneity. We also show robustness to data and model choice of satellite-based generalization of the RCT results to larger geographical areas outside the original. Overall, this paper shows how satellite sequence data can be incorporated into the analysis of RCTs, and provides evidence about the implications of data, model, and evaluation metric choice for causal analysis.

Scaling visual generation models is essential for real-world content creation, yet requires substantial training and computational expenses. Alternatively, test-time scaling has garnered growing attention due to resource efficiency and promising performance. In this work, we present TTS-VAR, the first general test-time scaling framework for visual auto-regressive (VAR) models, modeling the generation process as a path searching problem. To dynamically balance computational efficiency with exploration capacity, we first introduce an adaptive descending batch size schedule throughout the causal generation process. Besides, inspired by VAR's hierarchical coarse-to-fine multi-scale generation, our framework integrates two key components: (i) At coarse scales, we observe that generated tokens are hard for evaluation, possibly leading to erroneous acceptance of inferior samples or rejection of superior samples. Noticing that the coarse scales contain sufficient structural information, we propose clustering-based diversity search. It preserves structural variety through semantic feature clustering, enabling later selection on samples with higher potential. (ii) In fine scales, resampling-based potential selection prioritizes promising candidates using potential scores, which are defined as reward functions incorporating multi-scale generation history. Experiments on the powerful VAR model Infinity show a notable 8.7% GenEval score improvement (from 0.69 to 0.75). Key insights reveal that early-stage structural features effectively influence final quality, and resampling efficacy varies across generation scales. Code is available at https://github.com/ali-vilab/TTS-VAR.

Image-level regression is an important task in Earth observation, where visual domain and label shifts are a core challenge hampering generalization. However, cross-domain regression within remote sensing data remains understudied due to the absence of suited datasets. We introduce a new dataset with aerial and satellite imagery in five countries with three forest-related regression tasks. To match real-world applicative interests, we compare methods through a restrictive setup where no prior on the target domain is available during training, and models are adapted with limited information during testing. Building on the assumption that ordered relationships generalize better, we propose manifold diffusion for regression as a strong baseline for transduction in low-data regimes. Our comparison highlights the comparative advantages of inductive and transductive methods in cross-domain regression.

Offline reinforcement learning (RL), where the agent aims to learn the optimal policy based on the data collected by a behavior policy, has attracted increasing attention in recent years. While offline RL with linear function approximation has been extensively studied with optimal results achieved under certain assumptions, many works shift their interest to offline RL with non-linear function approximation. However, limited works on offline RL with non-linear function approximation have instance-dependent regret guarantees. In this paper, we propose an oracle-efficient algorithm, dubbed Pessimistic Nonlinear Least-Square Value Iteration (PNLSVI), for offline RL with non-linear function approximation. Our algorithmic design comprises three innovative components: (1) a variance-based weighted regression scheme that can be applied to a wide range of function classes, (2) a subroutine for variance estimation, and (3) a planning phase that utilizes a pessimistic value iteration approach. Our algorithm enjoys a regret bound that has a tight dependency on the function class complexity and achieves minimax optimal instance-dependent regret when specialized to linear function approximation. Our work extends the previous instance-dependent results within simpler function classes, such as linear and differentiable function to a more general framework.

Recent works have shown a reduction from contextual bandits to online regression under a realizability assumption [Foster and Rakhlin, 2020, Foster and Krishnamurthy, 2021]. In this work, we investigate the use of neural networks for such online regression and associated Neural Contextual Bandits (NeuCBs). Using existing results for wide networks, one can readily show a {O}(T) regret for online regression with square loss, which via the reduction implies a {O}(K T^{3/4}) regret for NeuCBs. Departing from this standard approach, we first show a O(log T) regret for online regression with almost convex losses that satisfy QG (Quadratic Growth) condition, a generalization of the PL (Polyak-\L ojasiewicz) condition, and that have a unique minima. Although not directly applicable to wide networks since they do not have unique minima, we show that adding a suitable small random perturbation to the network predictions surprisingly makes the loss satisfy QG with unique minima. Based on such a perturbed prediction, we show a {O}(log T) regret for online regression with both squared loss and KL loss, and subsequently convert these respectively to mathcal{O}(KT) and mathcal{O}(KL^* + K) regret for NeuCB, where L^* is the loss of the best policy. Separately, we also show that existing regret bounds for NeuCBs are Omega(T) or assume i.i.d. contexts, unlike this work. Finally, our experimental results on various datasets demonstrate that our algorithms, especially the one based on KL loss, persistently outperform existing algorithms.

Reinforcement Learning with Verifiable Rewards (RLVR) for large language models (LLMs) has achieved remarkable progress in enhancing LLMs' reasoning capabilities on tasks with clear correctness criteria, such as mathematical reasoning tasks. Several training metrics, such as entropy or response length, have been observed to correlate with different reasoning behaviors in reinforcement learning. Prior approaches incorporate such priors through reward or advantage shaping, which often relies on hand-crafted penalties and preferences (e.g., higher-is-better or lower-is-better). However, without careful hyperparameter tuning, these directional priors can be overly biased and may lead to failure. To this end, we introduce Conditional advANtage estimatiON (CANON), amplifying the impact of the target metric without presuming its direction. Specifically, CANON regroups the sampled responses into two groups based on the higher or lower value of a target metric, measures which metric trend contributes to better performance through inter-group comparison, and identifies the better response within the same group. In summary, CANON based on entropy consistently outperforms prior methods across three LLMs on both math reasoning and high-complexity logic tasks. When applied to response length, CANON further improves token efficiency, yielding a more favorable Pareto frontier in the performance-cost trade-off.

Machine learning models trained on Earth observation data, such as satellite imagery, have demonstrated significant promise in predicting household-level wealth indices, enabling the creation of high-resolution wealth maps that can be leveraged across multiple causal trials. However, because standard training objectives prioritize overall predictive accuracy, these predictions inherently suffer from shrinkage toward the mean, leading to attenuated estimates of causal treatment effects and limiting their utility in policy. Existing debiasing methods, such as Prediction-Powered Inference, can handle this attenuation bias but require additional fresh ground-truth data at the downstream stage of causal inference, which restricts their applicability in data-scarce environments. Here, we introduce and evaluate two correction methods -- linear calibration correction and Tweedie's correction -- that substantially reduce prediction bias without relying on newly collected labeled data. Linear calibration corrects bias through a straightforward linear transformation derived from held-out calibration data, whereas Tweedie's correction leverages empirical Bayes principles to directly address shrinkage-induced biases by exploiting score functions derived from the model's learning patterns. Through analytical exercises and experiments using Demographic and Health Survey data, we demonstrate that the proposed methods meet or outperform existing approaches that either require (a) adjustments to training pipelines or (b) additional labeled data. These approaches may represent a promising avenue for improving the reliability of causal inference when direct outcome measures are limited or unavailable, enabling a "one map, many trials" paradigm where a single upstream data creation team produces predictions usable by many downstream teams across diverse ML pipelines.

Existing research on instruction following largely focuses on tasks with simple instructions and short responses. In this work, we explore multi-constraint instruction following for generating long-form text. We create Suri, a dataset with 20K human-written long-form texts paired with LLM-generated backtranslated instructions that contain multiple complex constraints. Because of prohibitive challenges associated with collecting human preference judgments on long-form texts, preference-tuning algorithms such as DPO are infeasible in our setting; thus, we propose Instructional ORPO (I-ORPO), an alignment method based on the ORPO algorithm. Instead of receiving negative feedback from dispreferred responses, I-ORPO obtains negative feedback from synthetically corrupted instructions generated by an LLM. Using Suri, we perform supervised and I-ORPO fine-tuning on Mistral-7b-Instruct-v0.2. The resulting models, Suri-SFT and Suri-I-ORPO, generate significantly longer texts (~5K tokens) than base models without significant quality deterioration. Our human evaluation shows that while both SFT and I-ORPO models satisfy most constraints, Suri-I-ORPO generations are generally preferred for their coherent and informative incorporation of the constraints. We release our code at https://github.com/chtmp223/suri.

Automated model selection is often proposed to users to choose which machine learning model (or method) to apply to a given regression task. In this paper, we show that combining different regression models can yield better results than selecting a single ('best') regression model, and outline an efficient method that obtains optimally weighted convex linear combination from a heterogeneous set of regression models. More specifically, in this paper, a heuristic weight optimization, used in a preceding conference paper, is replaced by an exact optimization algorithm using convex quadratic programming. We prove convexity of the quadratic programming formulation for the straightforward formulation and for a formulation with weighted data points. The novel weight optimization is not only (more) exact but also more efficient. The methods we develop in this paper are implemented and made available via github-open source. They can be executed on commonly available hardware and offer a transparent and easy to interpret interface. The results indicate that the approach outperforms model selection methods on a range of data sets, including data sets with mixed variable type from drug discovery applications.

In this paper, we introduce a novel theoretical framework for multi-task regression, applying random matrix theory to provide precise performance estimations, under high-dimensional, non-Gaussian data distributions. We formulate a multi-task optimization problem as a regularization technique to enable single-task models to leverage multi-task learning information. We derive a closed-form solution for multi-task optimization in the context of linear models. Our analysis provides valuable insights by linking the multi-task learning performance to various model statistics such as raw data covariances, signal-generating hyperplanes, noise levels, as well as the size and number of datasets. We finally propose a consistent estimation of training and testing errors, thereby offering a robust foundation for hyperparameter optimization in multi-task regression scenarios. Experimental validations on both synthetic and real-world datasets in regression and multivariate time series forecasting demonstrate improvements on univariate models, incorporating our method into the training loss and thus leveraging multivariate information.

We study regressions with multiple treatments and a set of controls that is flexible enough to purge omitted variable bias. We show that these regressions generally fail to estimate convex averages of heterogeneous treatment effects -- instead, estimates of each treatment's effect are contaminated by non-convex averages of the effects of other treatments. We discuss three estimation approaches that avoid such contamination bias, including the targeting of easiest-to-estimate weighted average effects. A re-analysis of nine empirical applications finds economically and statistically meaningful contamination bias in observational studies; contamination bias in experimental studies is more limited due to smaller variability in propensity scores.

Suppose Alice trains an open-weight language model and Bob uses a blackbox derivative of Alice's model to produce text. Can Alice prove that Bob is using her model, either by querying Bob's derivative model (query setting) or from the text alone (observational setting)? We formulate this question as an independence testing problem--in which the null hypothesis is that Bob's model or text is independent of Alice's randomized training run--and investigate it through the lens of palimpsestic memorization in language models: models are more likely to memorize data seen later in training, so we can test whether Bob is using Alice's model using test statistics that capture correlation between Bob's model or text and the ordering of training examples in Alice's training run. If Alice has randomly shuffled her training data, then any significant correlation amounts to exactly quantifiable statistical evidence against the null hypothesis, regardless of the composition of Alice's training data. In the query setting, we directly estimate (via prompting) the likelihood Bob's model gives to Alice's training examples and order; we correlate the likelihoods of over 40 fine-tunes of various Pythia and OLMo base models ranging from 1B to 12B parameters with the base model's training data order, achieving a p-value on the order of at most 1e-8 in all but six cases. In the observational setting, we try two approaches based on estimating 1) the likelihood of Bob's text overlapping with spans of Alice's training examples and 2) the likelihood of Bob's text with respect to different versions of Alice's model we obtain by repeating the last phase (e.g., 1%) of her training run on reshuffled data. The second approach can reliably distinguish Bob's text from as little as a few hundred tokens; the first does not involve any retraining but requires many more tokens (several hundred thousand) to achieve high power.

We study the problem of model selection in causal inference, specifically for the case of conditional average treatment effect (CATE) estimation under binary treatments. Unlike model selection in machine learning, there is no perfect analogue of cross-validation as we do not observe the counterfactual potential outcome for any data point. Towards this, there have been a variety of proxy metrics proposed in the literature, that depend on auxiliary nuisance models estimated from the observed data (propensity score model, outcome regression model). However, the effectiveness of these metrics has only been studied on synthetic datasets as we can access the counterfactual data for them. We conduct an extensive empirical analysis to judge the performance of these metrics introduced in the literature, and novel ones introduced in this work, where we utilize the latest advances in generative modeling to incorporate multiple realistic datasets. Our analysis suggests novel model selection strategies based on careful hyperparameter tuning of CATE estimators and causal ensembling.

Efficiently and flexibly estimating treatment effect heterogeneity is an important task in a wide variety of settings ranging from medicine to marketing, and there are a considerable number of promising conditional average treatment effect estimators currently available. These, however, typically rely on the assumption that the measured covariates are enough to justify conditional exchangeability. We propose the P-learner, motivated by the R- and DR-learner, a tailored two-stage loss function for learning heterogeneous treatment effects in settings where exchangeability given observed covariates is an implausible assumption, and we wish to rely on proxy variables for causal inference. Our proposed estimator can be implemented by off-the-shelf loss-minimizing machine learning methods, which in the case of kernel regression satisfies an oracle bound on the estimated error as long as the nuisance components are estimated reasonably well.

Multilevel data are prevalent in many real-world applications. However, it remains an open research problem to identify and justify a class of models that flexibly capture a wide range of multilevel data. Motivated by the versatility of the mixture of experts (MoE) models in fitting regression data, in this article we extend upon the MoE and study a class of mixed MoE (MMoE) models for multilevel data. Under some regularity conditions, we prove that the MMoE is dense in the space of any continuous mixed effects models in the sense of weak convergence. As a result, the MMoE has a potential to accurately resemble almost all characteristics inherited in multilevel data, including the marginal distributions, dependence structures, regression links, random intercepts and random slopes. In a particular case where the multilevel data is hierarchical, we further show that a nested version of the MMoE universally approximates a broad range of dependence structures of the random effects among different factor levels.

We present a constraint-based algorithm for learning causal structures from observational time-series data, in the presence of latent confounders. We assume a discrete-time, stationary structural vector autoregressive process, with both temporal and contemporaneous causal relations. One may ask if temporal and contemporaneous relations should be treated differently. The presented algorithm gradually refines a causal graph by learning long-term temporal relations before short-term ones, where contemporaneous relations are learned last. This ordering of causal relations to be learnt leads to a reduction in the required number of statistical tests. We validate this reduction empirically and demonstrate that it leads to higher accuracy for synthetic data and more plausible causal graphs for real-world data compared to state-of-the-art algorithms.

In symbolic regression, the goal is to find an analytical expression that accurately fits experimental data with the minimal use of mathematical symbols such as operators, variables, and constants. However, the combinatorial space of possible expressions can make it challenging for traditional evolutionary algorithms to find the correct expression in a reasonable amount of time. To address this issue, Neural Symbolic Regression (NSR) algorithms have been developed that can quickly identify patterns in the data and generate analytical expressions. However, these methods, in their current form, lack the capability to incorporate user-defined prior knowledge, which is often required in natural sciences and engineering fields. To overcome this limitation, we propose a novel neural symbolic regression method, named Neural Symbolic Regression with Hypothesis (NSRwH) that enables the explicit incorporation of assumptions about the expected structure of the ground-truth expression into the prediction process. Our experiments demonstrate that the proposed conditioned deep learning model outperforms its unconditioned counterparts in terms of accuracy while also providing control over the predicted expression structure.

Sparse linear regression is one of the most basic questions in machine learning and statistics. Here, we are given as input a design matrix X in R^{N times d} and measurements or labels {y} in R^N where {y} = {X} {w}^* + {xi}, and {xi} is the noise in the measurements. Importantly, we have the additional constraint that the unknown signal vector {w}^* is sparse: it has k non-zero entries where k is much smaller than the ambient dimension. Our goal is to output a prediction vector {w} that has small prediction error: 1{N}cdot |{X} {w}^* - {X} {w}|^2_2. Information-theoretically, we know what is best possible in terms of measurements: under most natural noise distributions, we can get prediction error at most epsilon with roughly N = O(k log d/epsilon) samples. Computationally, this currently needs d^{Omega(k)} run-time. Alternately, with N = O(d), we can get polynomial-time. Thus, there is an exponential gap (in the dependence on d) between the two and we do not know if it is possible to get d^{o(k)} run-time and o(d) samples. We give the first generic positive result for worst-case design matrices {X}: For any {X}, we show that if the support of {w}^* is chosen at random, we can get prediction error epsilon with N = poly(k, log d, 1/epsilon) samples and run-time poly(d,N). This run-time holds for any design matrix {X} with condition number up to 2^{poly(d)}. Previously, such results were known for worst-case {w}^*, but only for random design matrices from well-behaved families, matrices that have a very low condition number (poly(log d); e.g., as studied in compressed sensing), or those with special structural properties.

Learning to rank is a key component of many e-commerce search engines. In learning to rank, one is interested in optimising the global ordering of a list of items according to their utility for users.Popular approaches learn a scoring function that scores items individually (i.e. without the context of other items in the list) by optimising a pointwise, pairwise or listwise loss. The list is then sorted in the descending order of the scores. Possible interactions between items present in the same list are taken into account in the training phase at the loss level. However, during inference, items are scored individually, and possible interactions between them are not considered. In this paper, we propose a context-aware neural network model that learns item scores by applying a self-attention mechanism. The relevance of a given item is thus determined in the context of all other items present in the list, both in training and in inference. We empirically demonstrate significant performance gains of self-attention based neural architecture over Multi-LayerPerceptron baselines, in particular on a dataset coming from search logs of a large scale e-commerce marketplace, Allegro.pl. This effect is consistent across popular pointwise, pairwise and listwise losses.Finally, we report new state-of-the-art results on MSLR-WEB30K, the learning to rank benchmark.

Offline Reinforcement Learning (ORL) is a promising approach to reduce the high sample complexity of traditional Reinforcement Learning (RL) by eliminating the need for continuous environmental interactions. ORL exploits a dataset of pre-collected transitions and thus expands the range of application of RL to tasks in which the excessive environment queries increase training time and decrease efficiency, such as in modern AAA games. This paper introduces OfflineMania a novel environment for ORL research. It is inspired by the iconic TrackMania series and developed using the Unity 3D game engine. The environment simulates a single-agent racing game in which the objective is to complete the track through optimal navigation. We provide a variety of datasets to assess ORL performance. These datasets, created from policies of varying ability and in different sizes, aim to offer a challenging testbed for algorithm development and evaluation. We further establish a set of baselines for a range of Online RL, ORL, and hybrid Offline to Online RL approaches using our environment.

Cricket, "a Gentleman's Game", is a prominent sport rising worldwide. Due to the rising competitiveness of the sport, players and team management have become more professional with their approach. Prior studies predicted individual performance or chose the best team but did not highlight the batter's potential. On the other hand, our research aims to evaluate a player's impact while considering his control in various circumstances. This paper seeks to understand the conundrum behind this impactful performance by determining how much control a player has over the circumstances and generating the "Effective Runs",a new measure we propose. We first gathered the fundamental cricket data from open-source datasets; however, variables like pitch, weather, and control were not readily available for all matches. As a result, we compiled our corpus data by analyzing the commentary of the match summaries. This gave us an insight into the particular game's weather and pitch conditions. Furthermore, ball-by-ball inspection from the commentary led us to determine the control of the shots played by the batter. We collected data for the entire One Day International career, up to February 2022, of 3 prominent cricket players: Rohit G Sharma, David A Warner, and Kane S Williamson. Lastly, to prepare the dataset, we encoded, scaled, and split the dataset to train and test Machine Learning Algorithms. We used Multiple Linear Regression (MLR), Polynomial Regression, Support Vector Regression (SVR), Decision Tree Regression, and Random Forest Regression on each player's data individually to train them and predict the Impact the player will have on the game. Multiple Linear Regression and Random Forest give the best predictions accuracy of 90.16 percent and 87.12 percent, respectively.

Depression has proven to be a significant public health issue, profoundly affecting the psychological well-being of individuals. If it remains undiagnosed, depression can lead to severe health issues, which can manifest physically and even lead to suicide. Generally, Diagnosing depression or any other mental disorder involves conducting semi-structured interviews alongside supplementary questionnaires, including variants of the Patient Health Questionnaire (PHQ) by Clinicians and mental health professionals. This approach places significant reliance on the experience and judgment of trained physicians, making the diagnosis susceptible to personal biases. Given that the underlying mechanisms causing depression are still being actively researched, physicians often face challenges in diagnosing and treating the condition, particularly in its early stages of clinical presentation. Recently, significant strides have been made in Artificial neural computing to solve problems involving text, image, and speech in various domains. Our analysis has aimed to leverage these state-of-the-art (SOTA) models in our experiments to achieve optimal outcomes leveraging multiple modalities. The experiments were performed on the Extended Distress Analysis Interview Corpus Wizard of Oz dataset (E-DAIC) corpus presented in the Audio/Visual Emotion Challenge (AVEC) 2019 Challenge. The proposed solutions demonstrate better results achieved by Proprietary and Open-source Large Language Models (LLMs), which achieved a Root Mean Square Error (RMSE) score of 3.98 on Textual Modality, beating the AVEC 2019 challenge baseline results and current SOTA regression analysis architectures. Additionally, the proposed solution achieved an accuracy of 71.43% in the classification task. The paper also includes a novel audio-visual multi-modal network that predicts PHQ-8 scores with an RMSE of 6.51.

Symbolic regression plays a crucial role in modern scientific research thanks to its capability of discovering concise and interpretable mathematical expressions from data. A grand challenge lies in the arduous search for parsimonious and generalizable mathematical formulas, in an infinite search space, while intending to fit the training data. Existing algorithms have faced a critical bottleneck of accuracy and efficiency over a decade when handling problems of complexity, which essentially hinders the pace of applying symbolic regression for scientific exploration across interdisciplinary domains. To this end, we introduce a parallelized tree search (PTS) model to efficiently distill generic mathematical expressions from limited data. Through a series of extensive experiments, we demonstrate the superior accuracy and efficiency of PTS for equation discovery, which greatly outperforms the state-of-the-art baseline models on over 80 synthetic and experimental datasets (e.g., lifting its performance by up to 99% accuracy improvement and one-order of magnitude speed up). PTS represents a key advance in accurate and efficient data-driven discovery of symbolic, interpretable models (e.g., underlying physical laws) and marks a pivotal transition towards scalable symbolic learning.

Gradients can be employed for sensitivity analysis. Here, we leverage the advantages of the Loss Landscape to comprehend which independent variables impact the dependent variable. We seek to grasp the loss landscape by utilizing first, second, and third derivatives through automatic differentiation. we know that Spearman's rank correlation coefficient can detect the monotonic relationship between two variables. However, I have found that second-order gradients, with certain configurations and parameters, provide information that can be visualized similarly to Spearman results, In this approach, we incorporate a loss function with an activation function, resulting in a non-linear pattern. Each exploration of the loss landscape through retraining yields new valuable information. Furthermore, the first and third derivatives are also beneficial, as they indicate the extent to which independent variables influence the dependent variable.

In this paper, we introduce the idea of decomposing the residuals of regression with respect to the data instances instead of features. This allows us to determine the effects of each individual instance on the model and each other, and in doing so makes for a model-agnostic method of identifying instances of interest. In doing so, we can also determine the appropriateness of the model and data in the wider context of a given study. The paper focuses on the possible applications that such a framework brings to the relatively unexplored field of instance analysis in the context of Explainable AI tasks.

Small language models (SLMs) are more efficient, cost-effective, and customizable than large language models (LLMs), though they often underperform in specific areas like reasoning. Past methods for enhancing SLMs' reasoning, such as supervised fine-tuning and distillation, often depend on costly external signals, resulting in SLMs being overly confident with limited supervision signals, thus limiting their abilities. Therefore, this study enables SLMs to learn to reason from self-iterative feedback. By combining odds ratio preference optimization (ORPO), we fine-tune and align SLMs using positive and negative signals generated by themselves. Additionally, we introduce process supervision for rewards in preference alignment by sampling-based inference simulation and process reward models. Compared to Supervised Fine-Tuning (SFT), our method improves the performance of Gemma-2B by 12.43 (Acc) on GSM8K and 3.95 (Pass@1) on MBPP. Furthermore, the proposed method also demonstrated superior out-of-domain generalization capabilities on MMLU_Math and HumanEval.

Motivated by a wide variety of applications, ranging from stochastic optimization to dimension reduction through variable selection, the problem of estimating gradients accurately is of crucial importance in statistics and learning theory. We consider here the classic regression setup, where a real valued square integrable r.v. Y is to be predicted upon observing a (possibly high dimensional) random vector X by means of a predictive function f(X) as accurately as possible in the mean-squared sense and study a nearest-neighbour-based pointwise estimate of the gradient of the optimal predictive function, the regression function m(x)=E[Ymid X=x]. Under classic smoothness conditions combined with the assumption that the tails of Y-m(X) are sub-Gaussian, we prove nonasymptotic bounds improving upon those obtained for alternative estimation methods. Beyond the novel theoretical results established, several illustrative numerical experiments have been carried out. The latter provide strong empirical evidence that the estimation method proposed works very well for various statistical problems involving gradient estimation, namely dimensionality reduction, stochastic gradient descent optimization and quantifying disentanglement.

It is well known that accurate probabilistic predictors can be trained through empirical risk minimisation with proper scoring rules as loss functions. While such learners capture so-called aleatoric uncertainty of predictions, various machine learning methods have recently been developed with the goal to let the learner also represent its epistemic uncertainty, i.e., the uncertainty caused by a lack of knowledge and data. An emerging branch of the literature proposes the use of a second-order learner that provides predictions in terms of distributions on probability distributions. However, recent work has revealed serious theoretical shortcomings for second-order predictors based on loss minimisation. In this paper, we generalise these findings and prove a more fundamental result: There seems to be no loss function that provides an incentive for a second-order learner to faithfully represent its epistemic uncertainty in the same manner as proper scoring rules do for standard (first-order) learners. As a main mathematical tool to prove this result, we introduce the generalised notion of second-order scoring rules.

Observational studies require adjustment for confounding factors that are correlated with both the treatment and outcome. In the setting where the observed variables are tabular quantities such as average income in a neighborhood, tools have been developed for addressing such confounding. However, in many parts of the developing world, features about local communities may be scarce. In this context, satellite imagery can play an important role, serving as a proxy for the confounding variables otherwise unobserved. In this paper, we study confounder adjustment in this non-tabular setting, where patterns or objects found in satellite images contribute to the confounder bias. Using the evaluation of anti-poverty aid programs in Africa as our running example, we formalize the challenge of performing causal adjustment with such unstructured data -- what conditions are sufficient to identify causal effects, how to perform estimation, and how to quantify the ways in which certain aspects of the unstructured image object are most predictive of the treatment decision. Via simulation, we also explore the sensitivity of satellite image-based observational inference to image resolution and to misspecification of the image-associated confounder. Finally, we apply these tools in estimating the effect of anti-poverty interventions in African communities from satellite imagery.

We propose a novel Bayesian inference framework for distributed differentially private linear regression. We consider a distributed setting where multiple parties hold parts of the data and share certain summary statistics of their portions in privacy-preserving noise. We develop a novel generative statistical model for privately shared statistics, which exploits a useful distributional relation between the summary statistics of linear regression. Bayesian estimation of the regression coefficients is conducted mainly using Markov chain Monte Carlo algorithms, while we also provide a fast version to perform Bayesian estimation in one iteration. The proposed methods have computational advantages over their competitors. We provide numerical results on both real and simulated data, which demonstrate that the proposed algorithms provide well-rounded estimation and prediction.

Conventional supervised learning typically assumes that the learning task can be solved by learning a single function since the data is sampled from a fixed distribution. However, this assumption is invalid in open-ended environments where no task-level data partitioning is available. In this paper, we present a novel supervised learning framework of learning from open-ended data, which is modeled as data implicitly sampled from multiple domains with the data in each domain obeying a domain-specific target function. Since different domains may possess distinct target functions, open-ended data inherently requires multiple functions to capture all its input-output relations, rendering training a single global model problematic. To address this issue, we devise an Open-ended Supervised Learning (OSL) framework, of which the key component is a subjective function that allocates the data among multiple candidate models to resolve the "conflict" between the data from different domains, exhibiting a natural hierarchy. We theoretically analyze the learnability and the generalization error of OSL, and empirically validate its efficacy in both open-ended regression and classification tasks.

Patient recruitment is challenging for clinical trials. We introduce TrialGPT, an end-to-end framework for zero-shot patient-to-trial matching with large language models. TrialGPT comprises three modules: it first performs large-scale filtering to retrieve candidate trials (TrialGPT-Retrieval); then predicts criterion-level patient eligibility (TrialGPT-Matching); and finally generates trial-level scores (TrialGPT-Ranking). We evaluate TrialGPT on three cohorts of 183 synthetic patients with over 75,000 trial annotations. TrialGPT-Retrieval can recall over 90% of relevant trials using less than 6% of the initial collection. Manual evaluations on 1,015 patient-criterion pairs show that TrialGPT-Matching achieves an accuracy of 87.3% with faithful explanations, close to the expert performance. The TrialGPT-Ranking scores are highly correlated with human judgments and outperform the best-competing models by 43.8% in ranking and excluding trials. Furthermore, our user study reveals that TrialGPT can reduce the screening time by 42.6% in patient recruitment. Overall, these results have demonstrated promising opportunities for patient-to-trial matching with TrialGPT.

Many political science theories relate to latent variables, but such quantities cannot be observed directly and must instead be estimated from data with inherent uncertainty. In regression models, when a variable is measured with error, its slope coefficient is known to be biased toward zero. We show how measurement error interacts with unique aspects of latent variable estimation, identification restrictions in particular, and demonstrate how common error adjustment strategies can worsen bias. We introduce a method for adjusting coefficients on latent predictors, which reduces bias and typically increases the magnitude of estimated coefficients, often dramatically. We illustrate these dynamics using several different estimation strategies for the latent predictors. Corrected estimates using our proposed method show stronger relationships -- sometimes up to 50% larger -- than those from naive regression. Our findings highlight the importance of considering measurement error in latent predictors and the inadequacy of many commonly used approaches for dealing with this issue.