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Total Variation Distance for Product Distributions is $\#\mathsf{P}$-Complete
Published 14 May 2024 in cs.CC | (2405.08255v1)
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.
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