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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

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 (Stanford, Google Research)
Sanmi Koyejo

Sanmi Koyejo an Assistant Professor in the Department of Computer Science at Stanford University. Koyejo also spends time at Google as a part of the Brain team. Koyejo's research interests are in developing the principles and practice of trustworthy machine learning. Additionally, Koyejo focuses on applications to neuroscience and healthcare. Koyejo has been the recipient of several awards, including a best paper award from the conference on uncertainty in artificial intelligence (UAI), a Skip Ellis Early Career Award, and a Sloan Fellowship. Koyejo serves as the president of the Black in AI organization.

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

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