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# Online and Distributed Bayesian Moment Matching for Parameter Learning in Sum-Product Networks

*Proceedings of the 19th International Conference on Artificial Intelligence and Statistics*, PMLR 51:1469-1477, 2016.

#### Abstract

Probabilistic graphical models provide a general and flexible framework for reasoning about complex dependencies in noisy domains with many variables. Among the various types of probabilistic graphical models, 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. However, existing parameter learning algorithms for SPNs operate in batch mode and do not scale easily to large datasets. In this work, we explore online algorithms to ensure that parameter learning can also be done tractably with respect to the amount of data. More specifically, we propose a new Bayesian moment matching (BMM) algorithm that operates naturally in an online fashion and that can be easily distributed. We demonstrate the effectiveness and scalability of BMM in comparison to online extensions of gradient descent, exponentiated gradient and expectation maximization on 20 classic benchmarks and 4 large scale datasets.