Structured sparsity is an important part of the modern statistical toolkit. We say a set of model
parameters has block diagonal sparsity up to permutations if its elements can be viewed as …

We study the problem of statistical estimation with a signal known to be sparse, spatially
contiguous, and containing many highly correlated variables. We take inspiration from the …

Two principles at the forefront of modern machine learning and statistics are sparse
modeling and robustness. Sparse modeling enables the construction of simpler statistical …

This paper studies the sparsistency and rates of convergence for estimating sparse
covariance and precision matrices based on penalized likelihood with nonconvex penalty …

In this dissertation, we study joint sparsity pursuit and its applications in variable selection in
high dimensional data. The first part of dissertation focuses on hierarchical variable …

In this thesis we study the interplay between theoretical computer science and machine
learning in three different directions. First, we make a connection between two ubiquitous …

Motivated by a sampling problem basic to computational statistical inference, we develop a
toolset based on spectral sparsification for a family of fundamental problems involving …

Covariance estimation for high-dimensional datasets is a fundamental problem in modern
day statistics with numerous applications. In these high dimensional datasets, the number of …

Statistical inference for sparse covariance matrices is crucial to reveal dependence structure
of large multivariate data sets, but lacks scalable and theoretically supported Bayesian …

Many popular statistical models, such as factor and random effects models, give arise a
certain type of covariance structures that is a summation of low rank and sparse matrices …