This first chapter formulates the objectives of compressive sensing. It introduces the
standard compressive problem studied throughout the book and reveals its ubiquity in many …

Divide-and-conquer based methods for Bayesian inference provide a general approach for
tractable posterior inference when the sample size is large. These methods divide the data …

Concentration inequalities form an essential toolkit in the study of high-dimensional
statistical methods. Most of the relevant statistics literature in this regard is, however, based …

We address the problem of learning the parameters of a stable linear time invariant (LTI)
system with unknown latent space dimension, or order, from a single time—series of noisy …

In this article, we introduce a new type of tree-based method, reinforcement learning trees
(RLT), which exhibits significantly improved performance over traditional methods such as …

We modify Talagrand's generic chaining method to obtain upper bounds for all p-th
moments of the supremum of a stochastic process. These bounds lead to an estimate for the …

We study how correlations in the design matrix influence Lasso prediction. First, we argue
that the higher the correlations, the smaller the optimal tuning parameter. This implies in …

Cross-validation is one of the most popular model and tuning parameter selection methods
in statistics and machine learning. Despite its wide applicability, traditional cross-validation …

We introduce and study the group square-root lasso (GSRL) method for estimation in high
dimensional sparse regression models with group structure. The new estimator minimizes …

In location estimation, we are given $ n $ samples from a known distribution $ f $ shifted by
an unknown translation $\lambda $, and want to estimate $\lambda $ as precisely as …