Total Variation Distance for Product Distributions is $\#\mathsf{P}$-Complete
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arXiv
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| Format: | Preprint |
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2024
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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 show that computing the total variation distance between two product distributions is $\#\mathsf{P}$-complete. This is in stark contrast with other distance measures such as Kullback-Leibler, Chi-square, and Hellinger, which tensorize over the marginals leading to efficient algorithms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_08255 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Total Variation Distance for Product Distributions is $\#\mathsf{P}$-Complete Bhattacharyya, Arnab Gayen, Sutanu Meel, Kuldeep S. Myrisiotis, Dimitrios Pavan, A. Vinodchandran, N. V. Computational Complexity We show that computing the total variation distance between two product distributions is $\#\mathsf{P}$-complete. This is in stark contrast with other distance measures such as Kullback-Leibler, Chi-square, and Hellinger, which tensorize over the marginals leading to efficient algorithms. |
| title | Total Variation Distance for Product Distributions is $\#\mathsf{P}$-Complete |
| topic | Computational Complexity |
| url | https://arxiv.org/abs/2405.08255 |