[Ml-stat-talks] ORFE Colloquium: Martin Wainwright, Mar. 13 at 4:30pm, Computer Science 104
Philippe Rigollet
rigollet at Princeton.EDU
Thu Mar 7 09:00:59 EST 2013
> === ORFE Colloquium Announcement ===
>
> DATE: Wednesday, March 13, 2013
>
> TIME: 4:30pm
>
> LOCATION: Computer Science room 104
>
> SPEAKER: Martin Wainwright, Dept. of Electrical Engineering & Computer Science, University of California, Berkeley
>
> TITLE: Graphical Model Selection and Missing Data: Generalized Covariance Matrices and Non-convex Programs
>
> ABSTRACT: Graphical models are based on a combination between graph theory and probability theory, and are widely studied in statistics, applied mathematics and computer science. The problem of graphical model selection is simply stated: how to recover the structure of the graph based on a collection of observed samples? It has applications to
> computational biology, social network analysis, and recommender systems.
> In this talk, we begin by investigating a curious relationship between the structure of a discrete graphical model and the support of the inverse of a generalized covariance matrix. Our work extends results that have previously been established in the context of multivariate Gaussian graphical models, thereby addressing an open question about the significance of the inverse covariance matrix of a non-Gaussian distribution. The proof exploits a combination of ideas from the geometry of exponential families, junction tree theory, and convex analysis. We then discuss some consequences for graph selection methods, including a novel method for structure estimation for missing or corrupted observations. Interestingly, the method involves solving a non-convex program for which polynomial-time algorithms can be shown to compute a near global
> optimum with high probability.
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