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Expand-and-sparsify representations are a class of theoretical models that capture sparse representation phenomena observed in the sensory systems of many animals. At a high level, these representations map an input $x \in \mathbb{R}^d$ to…

This article considers the problem of multi-group classification in the setting where the number of variables $p$ is larger than the number of observations $n$. Several methods have been proposed in the literature that address this problem,…

We consider the estimation problem in high-dimensional semi-supervised learning. Our goal is to investigate when and how the unlabeled data can be exploited to improve the estimation of the regression parameters of linear model in light of…

When training an estimator such as a neural network for tasks like image denoising, it is often preferred to train one estimator and apply it to all noise levels. The de facto training protocol to achieve this goal is to train the estimator…

This paper studies the computation of robust deterministic policies for Markov Decision Processes (MDPs) in the Lightning Does Not Strike Twice (LDST) model of Mannor, Mebel and Xu (ICML '12). In this model, designed to provide robustness…

This paper gives a theoretical analysis of high dimensional linear discrimination of Gaussian data. We study the excess risk of linear discriminant rules. We emphasis on the poor performances of standard procedures in the case when…

In this paper we consider regression problems subject to arbitrary noise in the operator or design matrix. This characterization appropriately models many physical phenomena with uncertainty in the regressors. Although the problem has been…

Linear discriminant analysis (LDA) is a classical method for dimensionality reduction, where discriminant vectors are sought to project data to a lower dimensional space for optimal separability of classes. Several recent papers have…

Statistical inference from high-dimensional data with low-dimensional structures has recently attracted lots of attention. In machine learning, deep generative modeling approaches implicitly estimate distributions of complex objects by…

We consider the stochastic contextual bandit problem under the high dimensional linear model. We focus on the case where the action space is finite and random, with each action associated with a randomly generated contextual covariate. This…

We consider the problem of decomposing a higher-order tensor with binary entries. Such data problems arise frequently in applications such as neuroimaging, recommendation system, topic modeling, and sensor network localization. We propose a…

We consider the problem of fitting the parameters of a high-dimensional linear regression model. In the regime where the number of parameters $p$ is comparable to or exceeds the sample size $n$, a successful approach uses an…

Given a large number of covariates $Z$, we consider the estimation of a high-dimensional parameter $\theta$ in an individualized linear threshold $\theta^T Z$ for a continuous variable $X$, which minimizes the disagreement between…

We consider statistical methods which invoke a min-max distributionally robust formulation to extract good out-of-sample performance in data-driven optimization and learning problems. Acknowledging the distributional uncertainty in learning…

The best subset selection (or "best subsets") estimator is a classic tool for sparse regression, and developments in mathematical optimization over the past decade have made it more computationally tractable than ever. Notwithstanding its…

This paper develops a framework for the design of scoring rules to optimally incentivize an agent to exert a multi-dimensional effort. This framework is a generalization to strategic agents of the classical knapsack problem (cf. Briest,…

An important yet challenging problem in numerical linear algebra is finding a principal submatrix with maximum determinant from a given symmetric positive semidefinite matrix. This problem arises in experimental design, statistics, and…

We consider a linear model where the coefficients - intercept and slopes - are random with a law in a nonparametric class and independent from the regressors. Identification often requires the regressors to have a support which is the whole…

This paper compares a family of methods for characterizing neural feature selectivity with natural stimuli in the framework of the linear-nonlinear model. In this model, the neural firing rate is a nonlinear function of a small number of…

We consider the high-dimensional discriminant analysis problem. For this problem, different methods have been proposed and justified by establishing exact convergence rates for the classification risk, as well as the l2 convergence results…