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Scalable Variational Inference in Log-supermodular Models
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<span title="2015-02-24">2015</span>
<i >
arXiv
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<span class="release-stage" >pre-print</span>
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<span title="2015-02-23">2015</span>
<span class="release-stage" >pre-print</span>
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1502.06531v1">arXiv:1502.06531v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/rdiwt2mpb5ewhorykwepqnpixi">fatcat:rdiwt2mpb5ewhorykwepqnpixi</a> </span>
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We consider the problem of approximate Bayesian inference in log-supermodular models. These models encompass regular pairwise MRFs with binary variables, but allow to capture high-order interactions, which are intractable for existing approximate inference techniques such as belief propagation, mean field, and variants. We show that a recently proposed variational approach to inference in log-supermodular models -L-FIELD- reduces to the widely-studied minimum norm problem for submodular
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... tion. This insight allows to leverage powerful existing tools, and hence to solve the variational problem orders of magnitude more efficiently than previously possible. We then provide another natural interpretation of L-FIELD, demonstrating that it exactly minimizes a specific type of R\'enyi divergence measure. This insight sheds light on the nature of the variational approximations produced by L-FIELD. Furthermore, we show how to perform parallel inference as message passing in a suitable factor graph at a linear convergence rate, without having to sum up over all the configurations of the factor. Finally, we apply our approach to a challenging image segmentation task. Our experiments confirm scalability of our approach, high quality of the marginals, and the benefit of incorporating higher-order potentials.
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