[Ml-stat-talks] Thurs: Emily Fox on Bayesian covariance regression

David Mimno mimno at CS.Princeton.EDU
Mon Nov 14 13:35:42 EST 2011

This week we have Emily Fox from Penn, who does excellent
work in Bayesian non-parametric models. Note that we'll be meeting
on THURSDAY, in the usual place at the usual time.

Thurs, Nov 17, 12:30 in CS402.

Title: Bayesian Covariance Regression and Autoregression


Although there is a rich literature on methods for allowing the
variance in a univariate regression model to vary with predictors,
time and other factors, relatively little has been done in the
multivariate case.  A number of multivariate heteroscedastic time
series models have been proposed within the econometrics literature,
but are typically limited by lack of clear margins, computational
intractability, and curse of dimensionality.  In this talk, we first
introduce and explore a new class of time series models for covariance
matrices based on a constructive definition exploiting inverse Wishart
distribution theory.  The construction yields a stationary,
first-order autoregressive (AR) process on the cone of positive
semi-definite matrices.

We then turn our focus to more general predictor spaces and scaling to
high-dimensional datasets.  Our proposed Bayesian nonparametric
covariance regression framework harnesses a latent factor model
representation.  In particular, the predictor-dependent factor
loadings are characterized as a sparse combination of a collection of
unknown dictionary functions (e.g, Gaussian process random functions).
The induced predictor-dependent covariance is then a regularized
quadratic function of these dictionary elements. Our proposed
framework leads to a highly-flexible, but computationally tractable
formulation with simple conjugate posterior updates that can readily
handle missing data. Theoretical properties are discussed and the
methods are illustrated through an application to the Google Flu
Trends data and the task of word classification based on single-trial
MEG data.

Joint work with David Dunson and Mike West.

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