Total Variation Distance for Product Distributions is #P-Complete
Total Variation Distance for Product Distributions is #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.
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)
- University of Iowa United States
- University of Nebraska System United States
- Iowa State University United States
- University of Toronto Canada
- Indian Institute of Technology Kanpur India
FOS: Computer and information sciences, Computer Science - Computational Complexity, Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.), Probability distributions: general theory, Computational Complexity (cs.CC), Approximations to statistical distributions (nonasymptotic)
FOS: Computer and information sciences, Computer Science - Computational Complexity, Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.), Probability distributions: general theory, Computational Complexity (cs.CC), Approximations to statistical distributions (nonasymptotic)
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