产品分布的总变异距离是 $\#\mathsf{P}$ 完整的

arXiv - CS - Computational Complexity Pub Date : 2024-05-14 DOI:arxiv-2405.08255

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

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引用次数: 0

摘要

我们证明，计算两个乘积分布之间的总变异距离是$\#\mathsf{P}$-complete的。这与 Kullback-Leibler、Chi-square 和 Hellinger 等其他距离度量形成了鲜明对比，这些度量会对边际进行张量，从而产生高效算法。

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

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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arXiv - CS - Computational Complexity

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