[Colloquium] TTI-C Talk: Pradeep Ravikumar, UC Berkeley

[Julia MacGlashan]

REMINDER

When:             Tuesday, April 14th @ 11:00am (lunch will be provided
after talk)

Where:            6045 S Kenwood Ave, TTI-C Conference Room #526 (5th Floor)

Who:               Pradeep Ravikumar, UC Berkeley

Title:                Sparse Model Estimation: Parametric and Nonparametric
Settings


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 instances, one parametric and the other nonparametric, of sparse model
estimation.

The first part of the talk considers the task of estimating the covariance
and inverse covariance or concentration matrices of a random vector from
i.i.d. observations. We study an estimator based on minimizing an
l1-penalized log-determinant Bregman divergence, that is equivalent to the
usual l1-regularized maximum likelihood estimator when the random vector is
multivariate Gaussian. We analyze the performance of this estimator under
high-dimensional scaling, in which the number of variables and other model
parameters are allowed to grow as a function of the sample size. Our
analysis identifies key players affecting the convergence rates of the
estimator in various norms as well as its success in recovering the true
sparsity pattern (its ``sparsistency'').

The second part of the talk considers the task of encoding fMRI signals from
the primary visual cortex, also called area V1, of the brain in response to
natural image stimuli; as well as identifying potential features of images
that drive the neural activity. Our method is based on the understanding
that the fMRI signal reflects the pooled, and potentially nonlinearly
transformed 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
hierarchical filtering stage that consists of three layers of artificial
neuronal cells, and a final nonparametric pooling stage which learns
nonparametric transformations 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. 

Contact:          Nati Srebro, TTI-C		nati at tti-c.org
834-7493



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