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 …

Abstract Sparse Principal Component Analysis (SPCA) and Sparse Linear Regression
(SLR) have a wide range of applications and have attracted a tremendous amount of …

In the past decade, sparse principal component analysis has emerged as an archetypal
problem for illustrating statistical-computational tradeoffs. This trend has largely been driven …

Sparse linear regression is a fundamental problem in high-dimensional statistics, but
strikingly little is known about how to efficiently solve it without restrictive conditions on the …

We study the meta-learning for support (ie the set of non-zero entries) recovery in high-
dimensional Principal Component Analysis. We reduce the sufficient sample complexity in a …

The Sparse Principal Component Analysis (Sparse PCA) problem is a variant of the
classical PCA problem. The goal of Sparse PCA is to achieve a trade-off between the …

Principal component analysis (PCA) is a widely used dimension reduction technique in
machine learning and multivariate statistics. To improve the interpretability of PCA, various …

It is well-known that the statistical performance of Lasso can suffer significantly when the
covariates of interest have strong correlations. In particular, the prediction error of Lasso …

Sparse Principal Component Analysis is a cardinal technique for obtaining combinations of
features, or principal components (PCs), that explain the variance of high-dimensional …

In sparse principal component analysis we are given noisy observations of a low-rank matrix
of dimension n× p and seek to reconstruct it under additional sparsity assumptions. In …