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Motivated by recent work on stochastic gradient descent methods, we develop two stochastic variants of greedy algorithms for possibly non-convex optimization problems with sparsity constraints. We prove linear convergence in expectation to…

The lasso and related sparsity inducing algorithms have been the target of substantial theoretical and applied research. Correspondingly, many results are known about their behavior for a fixed or optimally chosen tuning parameter specified…

Many problems in signal processing require finding sparse solutions to under-determined, or ill-conditioned, linear systems of equations. When dealing with real-world data, the presence of outliers and impulsive noise must also be accounted…

Microbiome data require statistical models that can simultaneously decode microbes' reaction to the environment and interactions among microbes. While a multiresponse linear regression model seems like a straight-forward solution, we argue…

Large spatial datasets are becoming ubiquitous in environmental sciences with the explosion in the amount of data produced by sensors that monitor and measure the Earth system. Consequently, the geostatistical analysis of these data…

Sampling from distributions play a crucial role in aiding practitioners with statistical inference. However, in numerous situations, obtaining exact samples from complex distributions is infeasible. Consequently, researchers often turn to…

There are many settings where researchers are interested in estimating average treatment effects and are willing to rely on the unconfoundedness assumption, which requires that the treatment assignment be as good as random conditional on…

Conformal predictors, introduced by Vovk et al. (2005), serve to build prediction intervals by exploiting a notion of conformity of the new data point with previously observed data. In the present paper, we propose a novel method for…

In this paper, we revisit the regret minimization problem in sparse stochastic contextual linear bandits, where feature vectors may be of large dimension $d$, but where the reward function depends on a few, say $s_0\ll d$, of these features…

Nonconvex penalty methods for sparse modeling in linear regression have been a topic of fervent interest in recent years. Herein, we study a family of nonconvex penalty functions that we call the trimmed Lasso and that offers exact control…

Bagging, a powerful ensemble method from machine learning, improves the performance of unstable predictors. Although the power of Bagging has been shown mostly in classification problems, we demonstrate the success of employing Bagging in…

Consider the standard Gaussian linear regression model $Y=X\theta+\epsilon$, where $Y\in R^n$ is a response vector and $ X\in R^{n*p}$ is a design matrix. Numerous work have been devoted to building efficient estimators of $\theta$ when $p$…

This paper considers generalized linear models in the presence of many controls. We lay out a general methodology to estimate an effect of interest based on the construction of an instrument that immunize against model selection mistakes…

We propose a residual randomization procedure designed for robust Lasso-based inference in the high-dimensional setting. Compared to earlier work that focuses on sub-Gaussian errors, the proposed procedure is designed to work robustly in…

In this work, we focus on the high-dimensional trace regression model with a low-rank coefficient matrix. We establish a nearly optimal in-sample prediction risk bound for the rank-constrained least-squares estimator under no assumptions on…

In a polynomial regression model, the divisibility conditions implicit in polynomial hierarchy give way to a natural construction of constraints for the model parameters. We use this principle to derive versions of strong and weak hierarchy…

We consider the problem of learning a graph modeling the statistical relations of the $d$ variables from a dataset with $n$ samples $X \in \mathbb{R}^{n \times d}$. Standard approaches amount to searching for a precision matrix $\Theta$…

All models may be wrong -- but that is not necessarily a problem for inference. Consider the standard $t$-test for the significance of a variable $X$ for predicting response $Y$ whilst controlling for $p$ other covariates $Z$ in a random…

A novel framework is introduced to formalize identifiability in well-specified but ill-posed linear regression models. The framework is distribution-free and accommodates highly correlated features that may or may not relate to the…

The prototypical high-dimensional statistics problem entails finding a structured signal in noise. Many of these problems exhibit an intriguing phenomenon: the amount of data needed by all known computationally efficient algorithms far…