Total Variation Distance for Product Distributions is $\#\mathsf{P}$-Complete
Computational Complexity
2024-05-15 v1
Abstract
We show that computing the total variation distance between two product distributions is -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.
Keywords
Cite
@article{arxiv.2405.08255,
title = {Total Variation Distance for Product Distributions is $\#\mathsf{P}$-Complete},
author = {Arnab Bhattacharyya and Sutanu Gayen and Kuldeep S. Meel and Dimitrios Myrisiotis and A. Pavan and N. V. Vinodchandran},
journal= {arXiv preprint arXiv:2405.08255},
year = {2024}
}
Comments
5 pages. An extended version of this paper appeared in the proceedings of IJCAI 2023, under the title "On approximating total variation distance" (see https://www.ijcai.org/proceedings/2023/387 and arXiv:2206.07209)