This article reviews recent progress in high-dimensional bootstrap. We first review high-
dimensional central limit theorems for distributions of sample mean vectors over the …

Boolean functions are perhaps the most basic objects of study in theoretical computer
science. They also arise in other areas of mathematics, including combinatorics, statistical …

In a sparse-representation-based face recognition scheme, the desired dictionary should
have good representational power (ie, being able to span the subspace of all faces) while …

This paper derives central limit and bootstrap theorems for probabilities that sums of
centered high-dimensional random vectors hit hyperrectangles and sparsely convex sets …

Abstract Slepian and Sudakov–Fernique type inequalities, which compare expectations of
maxima of Gaussian random vectors under certain restrictions on the covariance matrices …

We study the problem of agnostic learning under the Gaussian distribution in the Statistical
Query (SQ) model. We develop a method for finding hard families of examples for a wide …

This article is a survey of developments in algorithmic convex geometry over the past
decade. These include algorithms for sampling, optimization, integration, rounding and …

A remarkable recent paper by Rubinfeld and Vasilyan (2022) initiated the study of testable
learning, where the goal is to replace hard-to-verify distributional assumptions (such as …

We consider the problem of learning an unknown ReLU network with respect to Gaussian
inputs and obtain the first nontrivial results for networks of depth more than two. We give an …

We give a new algorithm for learning mixtures of $ k $ Gaussians (with identity covariance in
$\mathbb {R}^ n $) to TV error $\varepsilon $, with quasi-polynomial ($ O (n^{\text {poly …