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Learning a Small Mixture of Trees
M. Pawan Kumar · Daphne Koller

Mon Dec 07 07:00 PM -- 11:59 PM (PST) @
The problem of approximating a given probability distribution using a simpler distribution plays an important role in several areas of machine learning, e.g. variational inference and classification. Within this context, we consider the task of learning a mixture of tree distributions. Although mixtures of trees can be learned by minimizing the KL-divergence using an EM algorithm, its success depends heavily on the initialization. We propose an efficient strategy for obtaining a good initial set of trees that attempts to cover the entire observed distribution by minimizing the $\alpha$-divergence with $\alpha = \infty$. We formulate the problem using the fractional covering framework and present a convergent sequential algorithm that only relies on solving a convex program at each iteration. Compared to previous methods, our approach results in a significantly smaller mixture of trees that provides similar or better accuracies. We demonstrate the usefulness of our approach by learning pictorial structures for face recognition.

Author Information

M. Pawan Kumar (Stanford University)
Daphne Koller (insitro)

Daphne Koller is the Rajeev Motwani Professor of Computer Science at Stanford University and the co-founder and co-CEO of Coursera, a social entrepreneurship company that works with the best universities to connect anyone around the world with the best education, for free. Coursera is the leading MOOC (Massive Open Online Course) platform, and has partnered with dozens of the world’s top universities to offer hundreds of courses in a broad range of disciplines to millions of students, spanning every country in the world. In her research life, she works in the area of machine learning and probabilistic modeling, with applications to systems biology and personalized medicine. She is the author of over 200 refereed publications in venues that span a range of disciplines, and has given over 15 keynote talks at major conferences. She is the recipient of many awards, which include the Presidential Early Career Award for Scientists and Engineers (PECASE), the MacArthur Foundation Fellowship, the ACM/Infosys award, and membership in the US National Academy of Engineering. She is also an award winning teacher, who pioneered in her Stanford class many of the ideas that underlie the Coursera user experience. She received her BSc and MSc from the Hebrew University of Jerusalem, and her PhD from Stanford in 1994.

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