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arXiv · 2405.08255

Total Variation Distance for Product Distributions is $\#\mathsf{P}$-Complete

Arnab Bhattacharyya·Sutanu Gayen·Kuldeep S. Meel·Dimitrios Myrisiotis·A. Pavan·N. V. Vinodchandran
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Abstract

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.

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Arnab Bhattacharyya, Sutanu Gayen, Kuldeep S. Meel, Dimitrios Myrisiotis, A. Pavan, N. V. Vinodchandran. 2024-05-14. Total Variation Distance for Product Distributions is $\#\mathsf{P}$-Complete. https://arxiv.org/abs/2405.08255

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