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

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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Veröffentlicht in:arXiv.org 2024-05
Hauptverfasser: Bhattacharyya, Arnab, Gayen, Sutanu, Meel, Kuldeep S, Myrisiotis, Dimitrios, Pavan, A, Vinodchandran, N V
Format: Artikel
Sprache:eng
Schlagworte:
Algorithms
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Zusammenfassung: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.
ISSN:2331-8422