Geometry and Duality of Alternating Markov Chains
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866918003103236096 |
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| author | Mithal, Deven Orecchia, Lorenzo |
| author_facet | Mithal, Deven Orecchia, Lorenzo |
| contents | In this note, we realize the half-steps of a general class of Markov chains as alternating projections with respect to the reverse Kullback-Leibler divergence between convex sets of joint probability distributions. Using this characterization, we provide a geometric proof of an information-theoretic duality between the Markov chains defined by the even and odd half-steps of the alternating projection scheme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_12721 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Geometry and Duality of Alternating Markov Chains Mithal, Deven Orecchia, Lorenzo Probability Information Theory In this note, we realize the half-steps of a general class of Markov chains as alternating projections with respect to the reverse Kullback-Leibler divergence between convex sets of joint probability distributions. Using this characterization, we provide a geometric proof of an information-theoretic duality between the Markov chains defined by the even and odd half-steps of the alternating projection scheme. |
| title | Geometry and Duality of Alternating Markov Chains |
| topic | Probability Information Theory |
| url | https://arxiv.org/abs/2410.12721 |