In this monograph, we have attempted to summarize the actively developing field of
statistical learning with sparsity. A sparse statistical model is one having only a small …

While Deep Neural Networks (DNNs) have achieved tremendous success for large
vocabulary continuous speech recognition (LVCSR) tasks, training of these networks is …

We establish theoretical results concerning all local optima of various regularized M-
estimators, where both loss and penalty functions are allowed to be nonconvex. Our results …

A Unified Framework for High-Dimensional Analysis of M-Estimators with Decomposable
Regularizers Page 1 Statistical Science 2012, Vol. 27, No. 4, 538–557 DOI: 10.1214/12-STS400 …

Good models require good training data. For overparameterized deep models, the causal
relationship between training data and model predictions is increasingly opaque and poorly …

The affine rank minimization problem, which consists of finding a matrix of minimum rank
subject to linear equality constraints, has been proposed in many areas of engineering and …

The R package partykit provides a flexible toolkit for learning, representing, summarizing,
and visualizing a wide range of tree-structured regression and classification models. The …

Estimation of (near) low-rank matrices with noise and high-dimensional scaling Page 1 The
Annals of Statistics 2011, Vol. 39, No. 2, 1069–1097 DOI: 10.1214/10-AOS850 © Institute of …

Many statistical $ M $-estimators are based on convex optimization problems formed by the
weighted sum of a loss function with a norm-based regularizer. We analyze the convergence …

We propose a procedure for constructing a sparse estimator of a multivariate regression
coefficient matrix that accounts for correlation of the response variables. This method, which …