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Total Variation Distance for Product Distributions is $\#\mathsf{P}$-Complete (2405.08255v1)
Published 14 May 2024 in cs.CC
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.
- On approximating total variation distance. In Proc. of IJCAI, 2023.
- Efficient distance approximation for structured high-dimensional distributions via learning. In Proc. of NeurIPS, 2020.
- Lpsubscriptđżđ{L}_{p}italic_L start_POSTSUBSCRIPT italic_p end_POSTSUBSCRIPT distance and equivalence of probabilistic automata. Int. J. Found. Comput. Sci., 18(4):761â779, 2007.
- Perfect zero knowledge: New upperbounds and relativized separations. In Proc. of TCC, 2020.
- A simple polynomial-time approximation algorithm for the total variation distance between two product distributions. TheoretiCS, 2, 2023.
- On deterministically approximating total variation distance. In David P. Woodruff, editor, Proc. of SODA, 2024.
- Can statistical zero knowledge be made non-interactive? or On the relationship of SZK and NISZK. In Proc. of CRYPTO, 1999.
- Stefan Kiefer. On computing the total variation distance of hidden Markov models. In Proc. of ICALP, 2018.
- Rune B. Lyngsø and Christian N. S. Pedersen. The consensus string problem and the complexity of comparing hidden Markov models. J. Comput. Syst. Sci., 65(3):545â569, 2002.
- Lior Malka. How to achieve perfect simulation and a complete problem for non-interactive perfect zero-knowledge. J. Cryptol., 28(3):533â550, 2015.
- Testing probabilistic circuits. In Proc. of NeurIPS, 2021.
- A complete problem for statistical zero knowledge. J. ACM, 50(2):196â249, 2003.