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pRavikumar-FACULTYCANDIDATE

Type of Talk:  UTCS FACULTY CANDID

ATE

Speaker/Affiliation:   Pradeep Ravikumar/University of Cali

fornia-Berkeley

Date/Time:  Tuesday, March 31, 2009  11

:00 a.m.

Location:  ACES 2.302

Host:  Inderjit Dhi

llon

Talk Title:  "Sparse Model Estimation: Parametric an

d Nonparametric Settings"

Talk Abstract:

 A common

approach in settings with high-dimensional data has been to estimate models
that are "sparse," in the sense that an index set of relevant
model components has small cardinality. In this talk I will cover two inst

ances, one parametric and the other nonparametric, of sparse model estima

tion.

The first part of the talk considers the task of estimatin

g the covariance and inverse covariance or concentration matrices of a rand

om vector from i.i.d. observations. We study an estimator based on minimizi

ng an l1-penalized log-determinant Bregman divergence, that is equivalent

to the usual l1-regularized maximum likelihood estimator when the random ve

ctor is multivariate Gaussian. We analyze the performance of this estimator
under high-dimensional scaling, in which the number of variables and othe

r model parameters are allowed to grow as a function of the sample size.&nb

sp; Our analysis identifies key players affecting the convergence rates of
the estimator in various norms as well as its success in recovering the tr

ue sparsity pattern (its "sparsistency").

The second
part of the talk considers the task of encoding fMRI signals from the prim

ary visual cortex, also called area V1, of the brain in response to natur

al image stimuli; as well as identifying potential features of images that
drive the neural activity. Our method is based on the understanding that t

he fMRI signal reflects the pooled, and potentially nonlinearly transforme

d output of a large population of neurons in area V1. Our class of models,
which we call the V-SPAM framework, mimics this with an initial hierarchi

cal filtering stage that consists of three layers of artificial neuronal ce

lls, and a final nonparametric pooling stage which learns nonparametric tr

ansformations of a sparse set of neuronal filters.

This is joint
work with Garvesh Raskutti, Vincent Vu, Martin Wainwright, Bin Yu, and
the Jack Gallant lab at UC Berkeley; Kendrick Kay, Thomas Naselaris and

Jack Gallant.