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A Unified Approach for Learning the Parameters of Sum-Product Networks
Han Zhao · Pascal Poupart · Geoffrey Gordon

Wed Dec 07 09:00 AM -- 12:30 PM (PST) @ Area 5+6+7+8 #117 #None

We present a unified approach for learning the parameters of Sum-Product networks (SPNs). We prove that any complete and decomposable SPN is equivalent to a mixture of trees where each tree corresponds to a product of univariate distributions. Based on the mixture model perspective, we characterize the objective function when learning SPNs based on the maximum likelihood estimation (MLE) principle and show that the optimization problem can be formulated as a signomial program. We construct two parameter learning algorithms for SPNs by using sequential monomial approximations (SMA) and the concave-convex procedure (CCCP), respectively. The two proposed methods naturally admit multiplicative updates, hence effectively avoiding the projection operation. With the help of the unified framework, we also show that, in the case of SPNs, CCCP leads to the same algorithm as Expectation Maximization (EM) despite the fact that they are different in general.

Author Information

Han Zhao (Carnegie Mellon University)
Pascal Poupart (University of Waterloo & RBC Borealis AI)
Geoffrey Gordon (MSR Montréal & CMU)

Dr. Gordon is an Associate Research Professor in the Department of Machine Learning at Carnegie Mellon University, and co-director of the Department's Ph. D. program. He works on multi-robot systems, statistical machine learning, game theory, and planning in probabilistic, adversarial, and general-sum domains. His previous appointments include Visiting Professor at the Stanford Computer Science Department and Principal Scientist at Burning Glass Technologies in San Diego. Dr. Gordon received his B.A. in Computer Science from Cornell University in 1991, and his Ph.D. in Computer Science from Carnegie Mellon University in 1999.

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