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— Peer-to-peer distributed storage systems provide reliable access to data through redundancy spread over nodes across the Internet. A key goal is to minimize the amount of bandwidth used to maintain that redundancy. Storing a file using an erasure code, in fragments spread across nodes, promises to require less redundancy and hence less maintenance… (More)

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)

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)

—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… (More)

—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, combinato-rial enumeration, statistical decision theory, and large-deviations bounds. Our derivation is based on concepts from… (More)

The problem of consistently estimating the sparsity pattern of a vector β * ∈ R p based on observations contaminated by noise arises in various contexts, including subset selection in regression, structure estimation in graphical models, sparse approximation, and signal denoising. We analyze the behavior of ℓ 1-constrained quadratic programming (QP), also… (More)

—We develop and analyze methods for computing prov-ably 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)

—The problem of sparsity pattern or support set recovery refers to estimating the set of nonzero coefficients of an unknown vector 3 2 p based on a set of n noisy observations. It arises in a variety of settings, including subset selection in regression , graphical model selection, signal denoising, compressive sensing, and constructive approximation. The… (More)

—We present a tree-based reparameterization (TRP) framework that provides a new conceptual view of a large class of algorithms for computing approximate marginals in graphs with cycles. This class includes the belief propagation (BP) or sum-product algorithm as well as variations and extensions of BP. Algorithms in this class can be formulated as a sequence… (More)