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- Martin J. Wainwright, Michael I. Jordan
- Foundations and Trends in Machine Learning
- 2008

The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building large-scale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fields, including bioinformatics, communication theory,… (More)

- Alexandros G. Dimakis, Brighten Godfrey, Yunnan Wu, Martin J. Wainwright, Kannan Ramchandran
- IEEE Transactions on Information Theory
- 2007

Distributed storage systems provide reliable access to data through redundancy spread over individually unreliable nodes. Application scenarios include data centers, peer-to-peer storage systems, and storage in wireless networks. Storing data using an erasure code, in fragments spread across nodes, requires less redundancy than simple replication for the… (More)

- Javier Portilla, Vasily Strela, Martin J. Wainwright, Eero P. Simoncelli
- IEEE Trans. Image Processing
- 2003

We describe a method for removing noise from digital images, based on a statistical model of the coefficients of an overcomplete multiscale oriented basis. Neighborhoods of coefficients at adjacent positions and scales are modeled as the product of two independent random variables: a Gaussian vector and a hidden positive scalar multiplier. The latter… (More)

- John C. Duchi, Alekh Agarwal, Martin J. Wainwright
- IEEE Trans. Automat. Contr.
- 2012

The goal of decentralized optimization over a network is to optimize a global objective formed by a sum of local (possibly nonsmooth) convex functions using only local computation and communication. It arises in various application domains, including distributed tracking and localization, multiagent co-ordination, estimation in sensor networks, and… (More)

We consider the problem of estimating the graph associated with a binary Ising Markov random field. We describe a method based on 1-regularized logistic regression, in which the neighborhood of any given node is estimated by performing logistic regression subject to an 1-constraint. The method is analyzed under high-dimensional scaling in which both the… (More)

High-dimensional statistical inference deals with models in which the the number of parameters p is comparable to or larger than the sample size n. Since it is usually impossible to obtain consistent procedures unless p/n → 0, a line of recent work has studied models with various types of low-dimensional structure, including sparse vectors, sparse and… (More)

The problem of consistently estimating the sparsity pattern of a vector based on observations contaminated by noise arises in various contexts, including signal denoising, sparse approximation, compressed sensing, and model selection. We analyze the behavior of -constrained quadratic programming (QP), also referred to as the Lasso, for recovering the… (More)

- John C. Duchi, Michael I. Jordan, Martin J. Wainwright
- 2013 IEEE 54th Annual Symposium on Foundations of…
- 2013

Working under local differential privacy-a model of privacy in which data remains private even from the statistician or learner-we study the tradeoff between privacy guarantees and the utility of the resulting statistical estimators. We prove bounds on information-theoretic quantities, including mutual information and Kullback-Leibler divergence, that… (More)

- Sahand Negahban, Martin J. Wainwright
- ICML
- 2010

We study an instance of high-dimensional inference in which the goal is to estimate a matrix Θ ∈ R12 on the basis of N noisy observations. The unknown matrix Θ is assumed to be either exactly low rank, or “near” low-rank, meaning that it can be wellapproximated by a matrix with low rank. We consider a standard M -estimator based on regularization by the… (More)

- Yuchen Zhang, John C. Duchi, Martin J. Wainwright
- Journal of Machine Learning Research
- 2012

We study two communication-efficient algorithms for distributed statistical optimization on large-scale data. The first algorithm is an averaging method that distributes the N data samples evenly to m machines, performs separate minimization on each subset, and then averages the estimates. We provide a sharp analysis of this average mixture algorithm,… (More)