Computational Explorations of Total Variation Distance
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917868036161536 |
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| author | Bhattacharyya, Arnab Gayen, Sutanu Meel, Kuldeep S. Myrisiotis, Dimitrios Pavan, A. Vinodchandran, N. V. |
| author_facet | Bhattacharyya, Arnab Gayen, Sutanu Meel, Kuldeep S. Myrisiotis, Dimitrios Pavan, A. Vinodchandran, N. V. |
| contents | We investigate some previously unexplored (or underexplored) computational aspects of total variation (TV) distance. First, we give a simple deterministic polynomial-time algorithm for checking equivalence between mixtures of product distributions, over arbitrary alphabets. This corresponds to a special case, whereby the TV distance between the two distributions is zero. Second, we prove that unless $\mathsf{NP} \subseteq \mathsf{RP}$, it is impossible to efficiently estimate the TV distance between arbitrary Ising models, even in a bounded-error randomized setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_10370 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Computational Explorations of Total Variation Distance Bhattacharyya, Arnab Gayen, Sutanu Meel, Kuldeep S. Myrisiotis, Dimitrios Pavan, A. Vinodchandran, N. V. Data Structures and Algorithms Computational Complexity We investigate some previously unexplored (or underexplored) computational aspects of total variation (TV) distance. First, we give a simple deterministic polynomial-time algorithm for checking equivalence between mixtures of product distributions, over arbitrary alphabets. This corresponds to a special case, whereby the TV distance between the two distributions is zero. Second, we prove that unless $\mathsf{NP} \subseteq \mathsf{RP}$, it is impossible to efficiently estimate the TV distance between arbitrary Ising models, even in a bounded-error randomized setting. |
| title | Computational Explorations of Total Variation Distance |
| topic | Data Structures and Algorithms Computational Complexity |
| url | https://arxiv.org/abs/2412.10370 |