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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)

—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)

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)

- Pradeep Ravikumar, Martin J Wainwright, Garvesh Raskutti, Bin Yu
- 2008

Given i.i.d. observations of a random vector X ∈ R p , we study the problem of estimating both its covariance matrix Σ * , and its inverse covariance or concentration matrix Θ * = (Σ *) −1. We estimate Θ * by minimizing an ℓ1-penalized log-determinant Bregman divergence; in the multivariate Gaussian case, this approach corresponds to ℓ1-penalized maximum… (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 consistently estimating the sparsity pattern of a vector 3 2 p 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`1-constrained quadratic programming (QP), also referred to as the Lasso, for recovering… (More)