Parameter and Structure Learning Techniques for Sum Product Networks

Abstract

Probabilistic graphical models (PGMs) provide a general and flexible framework for reasoning about complex dependencies in noisy domains with many variables. Among the various types of PGMs, sum-product networks (SPNs) have recently generated some interest because exact inference can always be done in linear time with respect to the size of the network. This is particularly attractive since it means that learning an SPN from data always yields a tractable model for inference. Learning the parameters and the structure for SPNs is being explored by various researchers, having algorithms that scale are essential in the era of big data. In this thesis, I present tractable parameter and structure learning techniques for SPNs. First, I propose a new Bayesian moment matching (BMM) algorithm to learn the parameters for SPNs generatively. BMM operates naturally in an online fashion and that can be easily distributed. I demonstrate the effectiveness and scalability of BMM in comparison to other online algorithms in the literature.

Second, I present a discriminative learning algorithm for SPNs based on the Extended Baum-Welch (EBW) algorithm. The experiments show that this algorithm performs better than both generative Expectation-Maximization, and discriminative gradient descent on a wide variety of applications. I also demonstrate the robustness of the algorithm in the case of missing features by comparing its performance to Support Vector Machines and Neural Networks.

Finally, I present the first online structure learning algorithm for recurrent SPNs. Recurrent SPNs were proposed by Mazen et. al to model sequential data. They also proposed a structure learning algorithm which is slow, and it only operates in batch mode. I present the first online algorithm to learn the structure of recurrent SPNs. I also show how the parameters can be learned simultaneously using a modified version of hard-EM algorithm. I compare the performance of the algorithm against different models on sequential data problems.