Variational Inference on the Boolean Hypercube with the Quantum Entropy
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866915151550087168 |
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| author | Beyler, Eliot Bach, Francis |
| author_facet | Beyler, Eliot Bach, Francis |
| contents | In this paper, we derive variational inference upper-bounds on the log-partition function of pairwise Markov random fields on the Boolean hypercube, based on quantum relaxations of the Kullback-Leibler divergence. We then propose an efficient algorithm to compute these bounds based on primal-dual optimization. An improvement of these bounds through the use of ''hierarchies,'' similar to sum-of-squares (SoS) hierarchies is proposed, and we present a greedy algorithm to select among these relaxations. We carry extensive numerical experiments and compare with state-of-the-art methods for this inference problem. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_03759 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Variational Inference on the Boolean Hypercube with the Quantum Entropy Beyler, Eliot Bach, Francis Information Theory Machine Learning Optimization and Control In this paper, we derive variational inference upper-bounds on the log-partition function of pairwise Markov random fields on the Boolean hypercube, based on quantum relaxations of the Kullback-Leibler divergence. We then propose an efficient algorithm to compute these bounds based on primal-dual optimization. An improvement of these bounds through the use of ''hierarchies,'' similar to sum-of-squares (SoS) hierarchies is proposed, and we present a greedy algorithm to select among these relaxations. We carry extensive numerical experiments and compare with state-of-the-art methods for this inference problem. |
| title | Variational Inference on the Boolean Hypercube with the Quantum Entropy |
| topic | Information Theory Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/2411.03759 |