Scalable Variational Inference in Log-supermodular Models
This work addresses the challenge of efficient inference in complex probabilistic models for applications like computer vision, though it is incremental as it builds on existing variational methods.
The paper tackles the problem of approximate Bayesian inference in log-supermodular models, which are intractable for existing methods, by showing that a variational approach reduces to a minimum norm problem, enabling orders of magnitude faster solutions and demonstrating scalability and high-quality marginals in image segmentation tasks.
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 minimization. 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 Rényi 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.