The variational approach provides a complementary alternative to Markov chain Monte Carlo as a general source of approximation methods for inference in large-scale statistical models.Expand

This paper shows how to optimally generate MDS fragments directly from existing fragments in the system, and introduces a new scheme called regenerating codes which use slightly larger fragments than MDS but have lower overall bandwidth use.Expand

The performance of this method for removing noise from digital images substantially surpasses that of previously published methods, both visually and in terms of mean squared error.Expand

A unified framework for establishing consistency and convergence rates for regularized M-estimators under high-dimensional scaling is provided and one main theorem is state and shown how it can be used to re-derive several existing results, and also to obtain several new results.Expand

This work analyzes the behavior of l1-constrained quadratic programming (QP), also referred to as the Lasso, for recovering the sparsity pattern of a vector beta* based on observations contaminated by noise, and establishes precise conditions on the problem dimension p, the number k of nonzero elements in beta*, and the number of observations n.Expand

This book provides a self-contained introduction to the area of high-dimensional statistics, aimed at the first-year graduate level, and includes chapters that are focused on core methodology and theory - including tail bounds, concentration inequalities, uniform laws and empirical process, and random matrices.Expand

Given i.i.d. observations of a random vector X 2 R p , we study the problem of estimating both its covariance matrix � ∗ , and its inverse covariance or concentration matrix � ∗ = (� ∗ ) −1 . We… Expand

Statistical Learning with Sparsity: The Lasso and Generalizations presents methods that exploit sparsity to help recover the underlying signal in a set of data and extract useful and reproducible patterns from big datasets.Expand

The definition of a pseudocodeword unifies other such notions known for iterative algorithms, including "stopping sets," "irreducible closed walks," "trellis cycles," "deviation sets," and "graph covers," which is a lower bound on the classical distance.Expand

This work develops and analyze distributed algorithms based on dual subgradient averaging and provides sharp bounds on their convergence rates as a function of the network size and topology, and shows that the number of iterations required by the algorithm scales inversely in the spectral gap of thenetwork.Expand