Yaniv Plan
Robust 1-bit compressed sensing and sparse logistic regression: A convex programming approach.
Tue, 02/07/2012 - 15:01 — SomNambulAuthors: Yaniv Plan, Roman Vershynin
Subjects: Information Theory
AbstractThis paper develops theoretical results regarding noisy 1-bit compressed
sensing and sparse binomial regression. We show that a single convex program
gives an accurate estimate of the signal, or coefficient vector, for both of
these models. We demonstrate that an s-sparse signal in R^n can be accurately
estimated from m = O(slog(n/s)) single-bit measurements using a simple convex
program. This remains true even if almost half of the measurements are randomly
flipped.Unicity conditions for low-rank matrix recovery.
Wed, 03/30/2011 - 15:01 — SomNambulAuthors: Yaniv Plan, Yonina C. Eldar, Deanna Needell
Subjects: Numerical Analysis
AbstractLow-rank matrix recovery addresses the problem of recovering an unknown
low-rank matrix from few linear measurements. Nuclear-norm minimization is a
tractible approach with a recent surge of strong theoretical backing. Analagous
to the theory of compressed sensing, these results have required random
measurements. For example, m >= Cnr Gaussian measurements are sufficient to
recover any rank-r n x n matrix with high probability. In this paper we address
the theoretical question of how many measurements are needed via any method
whatsoever --- tractible or not.Global Testing under Sparse Alternatives: ANOVA, Multiple Comparisons and the Higher Criticism.
Fri, 07/09/2010 - 15:01 — SomNambulAuthors: Emmanuel J. Candès, Yaniv Plan, Ery Arias-Castro
Subjects: Statistics
AbstractTesting 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.Tight oracle bounds for low-rank matrix recovery from a minimal number of random measurements.
Tue, 01/05/2010 - 16:01 — SomNambulAuthors: Yaniv Plan, Emmanuel J. Candes
Subjects: Information Theory
AbstractThis paper presents several novel theoretical results regarding the recovery
of a low-rank matrix from just a few measurements consisting of linear
combinations of the matrix entries. We show that properly constrained
nuclear-norm minimization stably recovers a low-rank matrix from a constant
number of noisy measurements per degree of freedom; this seems to be the first
result of this nature.Accurate low-rank matrix recovery from a small number of linear measurements.
Mon, 10/05/2009 - 20:24 — SomNambulAuthors: Yaniv Plan, Emmanuel J. Candes
Subjects: Information Theory
AbstractWe consider the problem of recovering a lowrank matrix M from a small number
of random linear measurements. A popular and useful example of this problem is
matrix completion, in which the measurements reveal the values of a subset of
the entries, and we wish to fill in the missing entries (this is the famous
Netflix problem). When M is believed to have low rank, one would ideally try to
recover M by finding the minimum-rank matrix that is consistent with the data;
this is, however, problematic since this is a nonconvex problem that is,
generally, intractable.Accurate low-rank matrix recovery from a small number of linear measurements.
Mon, 10/05/2009 - 20:24 — SomNambulAuthors: Yaniv Plan, Emmanuel J. Candes
Subjects: Information Theory
AbstractWe consider the problem of recovering a lowrank matrix M from a small number
of random linear measurements. A popular and useful example of this problem is
matrix completion, in which the measurements reveal the values of a subset of
the entries, and we wish to fill in the missing entries (this is the famous
Netflix problem). When M is believed to have low rank, one would ideally try to
recover M by finding the minimum-rank matrix that is consistent with the data;
this is, however, problematic since this is a nonconvex problem that is,
generally, intractable.Near-ideal model selection by $\ell_1$ minimization.
Mon, 08/24/2009 - 13:10 — SomNambulAuthors: Emmanuel J. Candès, Yaniv Plan
Subjects: gr. Statistics
AbstractWe 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.
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