Many real-world machine learning applications are characterized by a huge number of features, leading to computational and memory issues, as well as the risk of overfitting. Ideally, only relevant and non-redundant features should be considered to preserve the complete information of the original data and limit the dimensionality. Dimensionality reduction and feature selection are common preprocessing techniques addressing the challenge of efficiently dealing with high-dimensional data. Dimensionality reduction methods control the number of features in the dataset while preserving its structure and minimizing information loss. Feature selection aims to identify the most relevant features for a task, discarding the less informative ones. Previous works have proposed approaches that aggregate features depending on their correlation without discarding any of them and preserving their interpretability through aggregation with the mean. A limitation of methods based on correlation is the assumption of linearity in the relationship between features and target. In this paper, we relax such an assumption in two ways. First, we propose a bias-variance analysis for general models with additive Gaussian noise, leading to a dimensionality reduction algorithm (NonLinCFA) which aggregates non-linear transformations of features with a generic aggregation function. Then, we extend the approach assuming that a generalized linear model regulates the relationship between features and target. A deviance analysis leads to a second dimensionality reduction algorithm (GenLinCFA), applicable to a larger class of regression problems and classification settings. Finally, we test the algorithms on synthetic and real-world datasets, performing regression and classification tasks, showing competitive performances.

In this research, we investigate the high-dimensional linear contextual bandit problem where the number of features $p$ is greater than the budget $T$, or it may even be infinite. Differing from the majority of previous works in this field, we do not impose sparsity on the regression coefficients. Instead, we rely on recent findings on overparameterized models, which enables us to analyze the performance the minimum-norm interpolating estimator when data distributions have small effective ranks. We propose an explore-then-commit (EtC) algorithm to address this problem and examine its performance. Through our analysis, we derive the optimal rate of the ETC algorithm in terms of $T$ and show that this rate can be achieved by balancing exploration and exploitation. Moreover, we introduce an adaptive explore-then-commit (AEtC) algorithm that adaptively finds the optimal balance. We assess the performance of the proposed algorithms through a series of simulations.

We consider the problem of model building for rare events prediction in longitudinal follow-up studies. In this paper, we compare several resampling methods to improve standard regression models on a real life example. We evaluate the effect of the sampling rate on the predictive performances of the models. To evaluate the predictive performance of a longitudinal model, we consider a validation technique that takes into account time and corresponds to the actual use in real life.

We give the first result for agnostically learning Single-Index Models (SIMs) with arbitrary monotone and Lipschitz activations. All prior work either held only in the realizable setting or required the activation to be known. Moreover, we only require the marginal to have bounded second moments, whereas all prior work required stronger distributional assumptions (such as anticoncentration or boundedness). Our algorithm is based on recent work by [GHK$^+$23] on omniprediction using predictors satisfying calibrated multiaccuracy. Our analysis is simple and relies on the relationship between Bregman divergences (or matching losses) and $\ell_p$ distances. We also provide new guarantees for standard algorithms like GLMtron and logistic regression in the agnostic setting.

Supervised machine learning (ML) and deep learning (DL) algorithms excel at predictive tasks, but it is commonly assumed that they often do so by exploiting non-causal correlations, which may limit both interpretability and generalizability. Here, we show that this trade-off between explanation and prediction is not as deep and fundamental as expected. Whereas ML and DL algorithms will indeed tend to use non-causal features for prediction when fed indiscriminately with all data, it is possible to constrain the learning process of any ML and DL algorithm by selecting features according to Pearl's backdoor adjustment criterion. In such a situation, some algorithms, in particular deep neural networks, can provide near unbiased effect estimates under feature collinearity. Remaining biases are explained by the specific algorithmic structures as well as hyperparameter choice. Consequently, optimal hyperparameter settings are different when tuned for prediction or inference, confirming the general expectation of a trade-off between prediction and explanation. However, the effect of this trade-off is small compared to the effect of a causally constrained feature selection. Thus, once the causal relationship between the features is accounted for, the difference between prediction and explanation may be much smaller than commonly assumed. We also show that such causally constrained models generalize better to new data with altered collinearity structures, suggesting generalization failure may often be due to a lack of causal learning. Our results not only provide a perspective for using ML for inference of (causal) effects but also help to improve the generalizability of fitted ML and DL models to new data.

Predicting sets of outcomes -- instead of unique outcomes -- is a promising solution to uncertainty quantification in statistical learning. Despite a rich literature on constructing prediction sets with statistical guarantees, adapting to unknown covariate shift -- a prevalent issue in practice -- poses a serious unsolved challenge. In this paper, we show that prediction sets with finite-sample coverage guarantee are uninformative and propose a novel flexible distribution-free method, PredSet-1Step, to efficiently construct prediction sets with an asymptotic coverage guarantee under unknown covariate shift. We formally show that our method is \textit{asymptotically probably approximately correct}, having well-calibrated coverage error with high confidence for large samples. We illustrate that it achieves nominal coverage in a number of experiments and a data set concerning HIV risk prediction in a South African cohort study. Our theory hinges on a new bound for the convergence rate of the coverage of Wald confidence intervals based on general asymptotically linear estimators.

This paper investigates an interesting weakly supervised regression setting called regression with interval targets (RIT). Although some of the previous methods on relevant regression settings can be adapted to RIT, they are not statistically consistent, and thus their empirical performance is not guaranteed. In this paper, we provide a thorough study on RIT. First, we proposed a novel statistical model to describe the data generation process for RIT and demonstrate its validity. Second, we analyze a simple selection method for RIT, which selects a particular value in the interval as the target value to train the model. Third, we propose a statistically consistent limiting method for RIT to train the model by limiting the predictions to the interval. We further derive an estimation error bound for our limiting method. Finally, extensive experiments on various datasets demonstrate the effectiveness of our proposed method.

Estimating heterogeneous treatment effects is crucial for informing personalized treatment strategies and policies. While multiple studies can improve the accuracy and generalizability of results, leveraging them for estimation is statistically challenging. Existing approaches often assume identical heterogeneous treatment effects across studies, but this may be violated due to various sources of between-study heterogeneity, including differences in study design, confounders, and sample characteristics. To this end, we propose a unifying framework for multi-study heterogeneous treatment effect estimation that is robust to between-study heterogeneity in the nuisance functions and treatment effects. Our approach, the multi-study R-learner, extends the R-learner to obtain principled statistical estimation with modern machine learning (ML) in the multi-study setting. The multi-study R-learner is easy to implement and flexible in its ability to incorporate ML for estimating heterogeneous treatment effects, nuisance functions, and membership probabilities, which borrow strength across heterogeneous studies. It achieves robustness in confounding adjustment through its loss function and can leverage both randomized controlled trials and observational studies. We provide asymptotic guarantees for the proposed method in the case of series estimation and illustrate using real cancer data that it has the lowest estimation error compared to existing approaches in the presence of between-study heterogeneity.

Numerous solutions for yield estimation are either based on data-driven models, or on crop-simulation models (CSMs). Researchers tend to build data-driven models using nationwide crop information databases provided by agencies such as the USDA. On the opposite side of the spectrum, CSMs require fine data that may be hard to generalize from a handful of fields. In this paper, we propose a comprehensive approach for yield forecasting that combines data-driven solutions, crop simulation models, and model surrogates to support multiple user-profiles and needs when dealing with crop management decision-making. To achieve this goal, we have developed a solution to calibrate CSMs at scale, a surrogate model of a CSM assuring faster execution, and a neural network-based approach that performs efficient risk assessment in such settings. Our data-driven modeling approach outperforms previous works with yield correlation predictions close to 91\%. The crop simulation modeling architecture achieved 6% error; the proposed crop simulation model surrogate performs predictions almost 100 times faster than the adopted crop simulator with similar accuracy levels.

Machine learning techniques paired with the availability of massive datasets dramatically enhance our ability to explore the chemical compound space by providing fast and accurate predictions of molecular properties. However, learning on large datasets is strongly limited by the availability of computational resources and can be infeasible in some scenarios. Moreover, the instances in the datasets may not yet be labelled and generating the labels can be costly, as in the case of quantum chemistry computations. Thus, there is a need to select small training subsets from large pools of unlabelled data points and to develop reliable ML methods that can effectively learn from small training sets. This work focuses on predicting the molecules atomization energy in the QM9 dataset. We investigate the advantages of employing domain knowledge-based data sampling methods for an efficient training set selection combined with informed ML techniques. In particular, we show how maximizing molecular diversity in the training set selection process increases the robustness of linear and nonlinear regression techniques such as kernel methods and graph neural networks. We also check the reliability of the predictions made by the graph neural network with a model-agnostic explainer based on the rate distortion explanation framework.