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# Learning Markov Networks With Arithmetic Circuits

*Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics*, PMLR 31:406-414, 2013.

#### Abstract

Markov networks are an effective way to represent complex probability distributions. However, learning their structure and parameters or using them to answer queries is typically intractable. One approach to making learning and inference tractable is to use approximations, such as pseudo-likelihood or approximate inference. An alternate approach is to use a restricted class of models where exact inference is always efficient. Previous work has explored low treewidth models, models with tree-structured features, and latent variable models. In this paper, we introduce ACMN, the first ever method for learning efficient Markov networks with arbitrary conjunctive features. The secret to ACMN’s greater flexibility is its use of arithmetic circuits, a linear-time inference representation that can handle many high treewidth models by exploiting local structure. ACMN uses the size of the corresponding arithmetic circuit as a learning bias, allowing it to trade off accuracy and inference complexity. In experiments on 12 standard datasets, the tractable models learned by ACMN are more accurate than both tractable models learned by other algorithms and approximate inference in intractable models.