[Colloquium] TTIC Colloquium: Martin Wainwright, UC Berkeley

[Julia MacGlashan]

When:             *Monday, Feb 1 @ 1:00pm*

Where:           * TTIC Conference Room #526*, 6045 S Kenwood Ave


Who:              * **Martin Wainwright*, UC Berkeley


Title:          *      **Statistical inference in high-dimensional settings:
A unified analysis of regularized estimators***



 Classical asymptotics, in which the sample size increases as the model
remains fixed, do not provide useful predictions for many modern scientific
problems, in which the data dimension may be of the same size or
substantially larger than the sample size.  With this motivation, an
on-going line of work seeks to develop theory allowing the sample size, data
dimension, and other structural parameters of the model to tend to infinity
simultaneously.  Many researchers have analyzed the behavior of different
estimators under high-dimensional scaling, including sparse linear
regression, multivariate regression, and structured matrix models.

In this talk, we present a single theorem that isolates some properties
common to much high-dimensional analysis, and yields optimal rates for a
large class of regularized $M$-estimators.  The result depends on two
intuitive conditions: the regularizer needs suitably constrain the parameter
space via the notion of decomposability, and the loss function needs to be
sufficiently curved, formalized via the notion of restricted strong
convexity. When applied to specific high-dimensional models, we recover
various results (some known and some new), including rates for estimating
sparse (generalized) linear models, structured covariance matrices, and near
low-rank matrices.  As we discuss, many of these rates are
information-theoretically optimal.

Based on joint work with Sahand Negahban (UC Berkeley), Pradeep Ravikumar
(UT Austin), and Bin Yu (UC Berkeley).
*
*Host:              David McAllester, mcallester at ttic.edu
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