This is the program for the 2010 Joint Statistical Meetings in Vancouver, British Columbia.

Abstract Details

Activity Number: 560
Type: Invited
Date/Time: Wednesday, August 4, 2010 : 2:00 PM to 3:50 PM
Sponsor: IMS
Abstract - #306249
Title: A Unified Framework for High-Dimensional Analysis of M-estimators with Decomposable Regularizers
Author(s): Pradeep Ravikumar*+ and Sahand Negahban and Martin Wainwright and Bin Yu
Companies: The University of Texas at Austin and University of California, Berkeley and University of California, Berkeley and University of California, Berkeley
Address: 1 University Station C0500, Austin, TX, 78712, United States
Keywords: M-estimators ; High-dimensional ; Regularization ; Consistency ; Convergence Rates ; Sparsity
Abstract:

A line of recent work on high-dimensional statistical inference has studied models with various types of structure (e.g., sparse vectors; block-structured matrices; low-rank matrices, Markov assumptions). A general approach to estimation in such settings is to use a regularized M-estimator which combines a loss function (measuring goodness-of-fit of the models to the data) with some regularization function that encourages the assumed structure. Our goal is to provide a unified framework for establishing consistency and convergence rates for such regularized M-estimation procedures under high-dimensional scaling. We state one main theorem and show how it can be used to re-derive several existing results, and also to obtain several new results on consistency and convergence rates.


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