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On Prior Distributions and Approximate Inference for Structured Variables
Sanmi Koyejo · Rajiv Khanna · Joydeep Ghosh · Russell Poldrack

Thu Dec 11 11:00 AM -- 03:00 PM (PST) @ Level 2, room 210D #None

We present a general framework for constructing prior distributions with structured variables. The prior is defined as the information projection of a base distribution onto distributions supported on the constraint set of interest. In cases where this projection is intractable, we propose a family of parameterized approximations indexed by subsets of the domain. We further analyze the special case of sparse structure. While the optimal prior is intractable in general, we show that approximate inference using convex subsets is tractable, and is equivalent to maximizing a submodular function subject to cardinality constraints. As a result, inference using greedy forward selection provably achieves within a factor of (1-1/e) of the optimal objective value. Our work is motivated by the predictive modeling of high-dimensional functional neuroimaging data. For this task, we employ the Gaussian base distribution induced by local partial correlations and consider the design of priors to capture the domain knowledge of sparse support. Experimental results on simulated data and high dimensional neuroimaging data show the effectiveness of our approach in terms of support recovery and predictive accuracy.

Author Information

Sanmi Koyejo (University of Illinois at Urbana-Champaign & Google Research)

Sanmi (Oluwasanmi) Koyejo an Assistant Professor in the Department of Computer Science at the University of Illinois at Urbana-Champaign. Koyejo's research interests are in the development and analysis of probabilistic and statistical machine learning techniques motivated by, and applied to various modern big data problems. He is particularly interested in the analysis of large scale neuroimaging data. Koyejo completed his Ph.D in Electrical Engineering at the University of Texas at Austin advised by Joydeep Ghosh, and completed postdoctoral research at Stanford University with a focus on developing Machine learning techniques for neuroimaging data. His postdoctoral research was primarily with Russell A. Poldrack and Pradeep Ravikumar. Koyejo has been the recipient of several awards including the outstanding NCE/ECE student award, a best student paper award from the conference on uncertainty in artificial intelligence (UAI) and a trainee award from the Organization for Human Brain Mapping (OHBM).

Rajiv Khanna (University of California at Berkeley)
Joydeep Ghosh (UT Austin)
Russell Poldrack (University of Texas)

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