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- 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)

- 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)

- 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)

- Jon Feldman, Martin J. Wainwright, David R. Karger
- IEEE Transactions on Information Theory
- 2005

A new method is given for performing approximate maximum-likelihood (ML) decoding of an arbitrary binary linear code based on observations received from any discrete memoryless symmetric channel. The decoding algorithm is based on a linear programming (LP) relaxation that is defined by a factor graph or parity-check representation of the code. The resulting… (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)

- Martin J. Wainwright, Tommi S. Jaakkola, Alan S. Willsky
- IEEE Transactions on Information Theory
- 2005

We develop and analyze methods for computing provably optimal maximum a posteriori probability (MAP) configurations for a subclass of Markov random fields defined on graphs with cycles. By decomposing the original distribution into a convex combination of tree-structured distributions, we obtain an upper bound on the optimal value of the original problem… (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)

- Martin J. Wainwright, Tommi S. Jaakkola, Alan S. Willsky
- IEEE Transactions on Information Theory
- 2002

We introduce a new class of upper bounds on the log partition function of a Markov random field (MRF). This quantity plays an important role in various contexts, including approximating marginal distributions, parameter estimation, combinatorial enumeration, statistical decision theory, and large-deviations bounds. Our derivation is based on concepts from… (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)

- Martin J. Wainwright, Tommi Jaakkolay, Alan Willskyy
- 2002

We develop an approach for computing provably exact maximum a posteriori (MAP) configurations for a subclass of problems on graphs with cycles. By decomposing the original problem into a convex combination of tree-structured problems, we obtain an upper bound on the optimal value of the original problem (i.e., the log probability of the MAP assignment) in… (More)