In recent years, studies such as \cite{carmon2019unlabeled,gowal2021improving,xing2022artificial} have demonstrated that incorporating additional real or generated data with pseudo-labels can enhance adversarial training through a two-stage training approach. In this paper, we perform a theoretical analysis of the asymptotic behavior of this method in high-dimensional linear regression. While a double-descent phenomenon can be observed in ridgeless training, with an appropriate $\mathcal{L}_2$ regularization, the two-stage adversarial training achieves a better performance. Finally, we derive a shortcut cross-validation formula specifically tailored for the two-stage training method.

Being able to predict the remaining useful life (RUL) of an engineering system is an important task in prognostics and health management. Recently, data-driven approaches to RUL predictions are becoming prevalent over model-based approaches since no underlying physical knowledge of the engineering system is required. Yet, this just replaces required expertise of the underlying physics with machine learning (ML) expertise, which is often also not available. Automated machine learning (AutoML) promises to build end-to-end ML pipelines automatically enabling domain experts without ML expertise to create their own models. This paper introduces AutoRUL, an AutoML-driven end-to-end approach for automatic RUL predictions. AutoRUL combines fine-tuned standard regression methods to an ensemble with high predictive power. By evaluating the proposed method on eight real-world and synthetic datasets against state-of-the-art hand-crafted models, we show that AutoML provides a viable alternative to hand-crafted data-driven RUL predictions. Consequently, creating RUL predictions can be made more accessible for domain experts using AutoML by eliminating ML expertise from data-driven model construction.

Understanding the effect of a feature vector $x \in \mathbb{R}^d$ on the response value (label) $y \in \mathbb{R}$ is the cornerstone of many statistical learning problems. Ideally, it is desired to understand how a set of collected features combine together and influence the response value, but this problem is notoriously difficult, due to the high-dimensionality of data and limited number of labeled data points, among many others. In this work, we take a new perspective on this problem, and we study the question of assessing the difference of influence that the two given features have on the response value. We first propose a notion of closeness for the influence of features, and show that our definition recovers the familiar notion of the magnitude of coefficients in the parametric model. We then propose a novel method to test for the closeness of influence in general model-free supervised learning problems. Our proposed test can be used with finite number of samples with control on type I error rate, no matter the ground truth conditional law $\mathcal{L}(Y |X)$. We analyze the power of our test for two general learning problems i) linear regression, and ii) binary classification under mixture of Gaussian models, and show that under the proper choice of score function, an internal component of our test, with sufficient number of samples will achieve full statistical power. We evaluate our findings through extensive numerical simulations, specifically we adopt the datamodel framework (Ilyas, et al., 2022) for CIFAR-10 dataset to identify pairs of training samples with different influence on the trained model via optional black box training mechanisms.

Correlated time series analysis plays an important role in many real-world industries. Learning an efficient representation of this large-scale data for further downstream tasks is necessary but challenging. In this paper, we propose a time-step-level representation learning framework for individual instances via bootstrapped spatiotemporal representation prediction. We evaluated the effectiveness and flexibility of our representation learning framework on correlated time series forecasting and cold-start transferring the forecasting model to new instances with limited data. A linear regression model trained on top of the learned representations demonstrates our model performs best in most cases. Especially compared to representation learning models, we reduce the RMSE, MAE, and MAPE by 37%, 49%, and 48% on the PeMS-BAY dataset, respectively. Furthermore, in real-world metro passenger flow data, our framework demonstrates the ability to transfer to infer future information of new cold-start instances, with gains of 15%, 19%, and 18%. The source code will be released under the GitHub https://github.com/bonaldli/Spatiotemporal-TS-Representation-Learning

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.