Big Data bring new opportunities to modern society and challenges to data scientists. On the
one hand, Big Data hold great promises for discovering subtle population patterns and …

We give an overview of random matrix theory (RMT) with the objective of highlighting the
results and concepts that have a growing impact in the formulation and inference of …

A suitable feature representation that can both preserve the data intrinsic information and
reduce data complexity and dimensionality is key to the performance of machine learning …

Statistical Foundations of Data Science gives a thorough introduction to commonly used
statistical models, contemporary statistical machine learning techniques and algorithms …

We provide a unified analysis of the predictive risk of ridge regression and regularized
discriminant analysis in a dense random effects model. We work in a high-dimensional …

We prove bounds on the population risk of the maximum margin algorithm for two-class
linear classification. For linearly separable training data, the maximum margin algorithm has …

This is an expository paper that reviews recent developments on optimal estimation of
structured high-dimensional covariance and precision matrices. Minimax rates of …

It is often of interest to understand how the structure of a genetic network differs between two
conditions. In this paper, each condition-specific network is modelled using the precision …

High-throughput metabolomics investigations, when conducted in large human cohorts,
represent a potentially powerful tool for elucidating the biochemical diversity underlying …

We survey optimization problems that involve the cardinality of variable vectors in
constraints or the objective function. We provide a unified viewpoint on the general problem …