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Emmanuel J. Candès

  1. How well can we estimate a sparse vector?.

    Fri, 04/29/2011 - 15:01 — SomNambul
    Authors: Emmanuel J. Candès, Mark A. Davenport
    Subjects: Information Theory
    Abstract

    The estimation of a sparse vector in the linear model is a fundamental
    problem in signal processing, statistics, and compressive sensing. This paper
    establishes a lower bound on the mean-squared error, which holds regardless of
    the sensing/design matrix being used and regardless of the estimation
    procedure. This lower bound very nearly matches the known upper bound one gets
    by taking a random projection of the sparse vector followed by an $\ell_1$
    estimation procedure such as the Dantzig selector. In this sense, compressive
    sensing techniques cannot essentially be improved.

  2. Templates for Convex Cone Problems with Applications to Sparse Signal Recovery.

    Mon, 09/13/2010 - 15:01 — SomNambul
    Authors: Emmanuel J. Candès, Stephen R. Becker, Michael Grant
    Subjects: Optimization and Control
    Abstract

    This paper develops a general framework for solving a variety of convex cone
    problems that frequently arise in signal processing, machine learning,
    statistics, and other fields. The approach works as follows: first, determine a
    conic formulation of the problem; second, determine its dual; third, apply
    smoothing; and fourth, solve using an optimal first-order method. A merit of
    this approach is its flexibility: for example, all compressed sensing problems
    can be solved via this approach.

  3. Global Testing under Sparse Alternatives: ANOVA, Multiple Comparisons and the Higher Criticism.

    Fri, 07/09/2010 - 15:01 — SomNambul
    Authors: Emmanuel J. Candès, Yaniv Plan, Ery Arias-Castro
    Subjects: Statistics
    Abstract

    Testing for the significance of a subset of regression coefficients in a
    linear model, a staple of statistical analysis, goes back at least to the work
    of Fisher who introduced the analysis of variance (ANOVA). We study this
    problem under the assumption that the coefficient vector is sparse, a common
    situation in modern high-dimensional settings. Suppose the regression vector is
    of dimension p with S non-zero coefficients with S = p^{1 -alpha}. Under
    moderate sparsity levels, i.e. alpha <= 1/2, we show that ANOVA is essentially
    optimal under some conditions on the design.

  4. Near-ideal model selection by $\ell_1$ minimization.

    Mon, 08/24/2009 - 13:10 — SomNambul
    Authors: Emmanuel J. Cand&#xe8;s, Yaniv Plan
    Subjects: gr. Statistics
    Abstract

    We consider the fundamental problem of estimating the mean of a vector
    $y=X\beta+z$, where $X$ is an $n\times p$ design matrix in which one can have
    far more variables than observations, and $z$ is a stochastic error term--the
    so-called "$p>n$" setup. When $\beta$ is sparse, or, more generally, when there
    is a sparse subset of covariates providing a close approximation to the unknown
    mean vector, we ask whether or not it is possible to accurately estimate
    $X\beta$ using a computationally tractable algorithm.

Math-arch

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