Optimization Online


Nonparametric Estimation via Convex Programming

Anatoli Juditsky (Anatoli.Juditsky***at***imag.fr)
Arkadi Nemirovski (nemirovs***at***isye.gatech.edu)

Abstract: In the paper, we focus primarily on the problem of recovering a linear form g'*x of unknown ``signal'' x known to belong to a given convex compact set X in R^n from N independent realizations of a random variable taking values in a finite set, the distribution p of the variable being affinely parameterized by x. With no additional assumptions on X and the dependence of p on x, we develop minimax optimal, within an absolute constant factor, and computationally efficient estimation routine. We then apply this routine to recovering x itself in the Euclidean norm.

Keywords: density estimation, inverse problems, convex optimization

Category 1: Applications -- Science and Engineering (Statistics )

Category 2: Convex and Nonsmooth Optimization (Convex Optimization )


Download: [PDF]

Entry Submitted: 08/23/2007
Entry Accepted: 08/23/2007
Entry Last Modified: 10/11/2007

Modify/Update this entry

  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository


Coordinator's Board
Classification Scheme
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Programming Society