NIPS Proceedingsβ

Counting the Optimal Solutions in Graphical Models

Part of: Advances in Neural Information Processing Systems 32 (NIPS 2019) pre-proceedings

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Authors

Conference Event Type: Poster

Abstract

We introduce #opt, a new inference task for graphical models which calls for counting the number of optimal solutions of the model. We describe a novel variable elimination based approach for solving this task, as well as a depth-first branch and bound algorithm that traverses the AND/OR search space of the model. The key feature of the proposed algorithms is that their complexity is exponential in the induced width of the model only. It does not depend on the actual number of optimal solutions. Our empirical evaluation on various benchmarks demonstrates the effectiveness of the proposed algorithms compared with existing depth-first and best-first search based approaches that enumerate explicitly the optimal solutions.