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arXiv · 2412.10370

Computational Explorations of Total Variation Distance

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

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.

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Arnab Bhattacharyya, Sutanu Gayen, Kuldeep S. Meel, Dimitrios Myrisiotis, A. Pavan, N. V. Vinodchandran. 2024-12-13. Computational Explorations of Total Variation Distance. https://arxiv.org/abs/2412.10370

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