Sum-product networks (SPNs) are a recently developed class of deep probabilistic models where inference is tractable. We present two new structure learning algorithms for sum-product networks, in the generative and discriminative settings, that are based on recursively extracting rank-one submatrices from data. The proposed algorithms find the subSPNs that are the most coherent jointly in the instances and variables - that is, whose instances are most strongly correlated over the given variables. Experimental results show that SPNs learned using the proposed generative algorithm have better likelihood and inference results - and also much faster - than previous approaches. Finally, we apply the discriminative SPN structure learning algorithm to handwritten digit recognition tasks, where it achieves state-of-the-art performance for an SPN.
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