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A common belief in high-dimensional data analysis is that data are concentrated on a low-dimensional manifold. This motivates simultaneous dimension reduction and regression on manifolds. We provide an algorithm for learning gradients on…

Learning with label dependent label noise has been extensively explored in both theory and practice; however, dealing with instance (i.e., feature) and label dependent label noise continues to be a challenging task. The difficulty arises…

We study high-dimensional distribution learning in an agnostic setting where an adversary is allowed to arbitrarily corrupt an $\varepsilon$-fraction of the samples. Such questions have a rich history spanning statistics, machine learning…

We study convex empirical risk minimization for high-dimensional inference in binary models. Our first result sharply predicts the statistical performance of such estimators in the linear asymptotic regime under isotropic Gaussian features.…

The automated construction of coarse-grained models represents a pivotal component in computer simulation of physical systems and is a key enabler in various analysis and design tasks related to uncertainty quantification. Pertinent methods…

The literature on "benign overfitting" in overparameterized models has been mostly restricted to regression or binary classification; however, modern machine learning operates in the multiclass setting. Motivated by this discrepancy, we…

Policymakers in resource-constrained settings require experimental designs that satisfy strict budget limits while ensuring precise estimation of treatment effects. We propose a framework that applies a dependent randomized rounding…

We introduce estimation and test procedures through divergence minimization for models satisfying linear constraints with unknown parameter. Several statistical examples and motivations are given. These procedures extend the empirical…

"All models are wrong, but some are useful", wrote George E. P. Box (1979). Machine learning has focused on the usefulness of probability models for prediction in social systems, but is only now coming to grips with the ways in which these…

Numerous studies have shown that label noise can lead to poor generalization performance, negatively affecting classification accuracy. Therefore, understanding the effectiveness of classifiers trained using deep neural networks in the…

Although recent provable methods have been developed to compute preimage bounds for neural networks, their scalability is fundamentally limited by the #P-hardness of the problem. In this work, we adopt a novel probabilistic perspective,…

Why are classifiers in high dimension vulnerable to "adversarial" perturbations? We show that it is likely not due to information theoretic limitations, but rather it could be due to computational constraints. First we prove that, for a…

Performative prediction is a framework accounting for the shift in the data distribution induced by the prediction of a model deployed in the real world. Ensuring rapid convergence to a stable solution where the data distribution remains…

The study of a machine learning problem is in many ways is difficult to separate from the study of the loss function being used. One avenue of inquiry has been to look at these loss functions in terms of their properties as scoring rules…

While the expected calibration error (ECE), which employs binning, is widely adopted to evaluate the calibration performance of machine learning models, theoretical understanding of its estimation bias is limited. In this paper, we present…

We study the regret guarantee for risk-sensitive reinforcement learning (RSRL) via distributional reinforcement learning (DRL) methods. In particular, we consider finite episodic Markov decision processes whose objective is the entropic…

We consider a deep neural network estimator based on empirical risk minimization with l_1-regularization. We derive a general bound for its excess risk in regression and classification (including multiclass), and prove that it is adaptively…

In most machine learning applications, classification accuracy is not the primary metric of interest. Binary classifiers which face class imbalance are often evaluated by the $F_\beta$ score, area under the precision-recall curve, Precision…

Exponential tilting is a technique commonly used in fields such as statistics, probability, information theory, and optimization to create parametric distribution shifts. Despite its prevalence in related fields, tilting has not seen…

Label Proportion Learning (LLP) addresses the classification problem where multiple instances are grouped into bags and each bag contains information about the proportion of each class. However, in practical applications, obtaining precise…