Computational Explorations of Total Variation Distance
Keywords: total variation distance, TV distance, mixtures of products, equivalence checking, Ising models, computational complexity, FPRAS
Abstract: We investigate some previously unexplored (or under-explored) computational aspects of total variation (TV) distance.
First, we give a simple deterministic polynomial-time algorithm for checking equivalence between mixtures of product distributions, over arbitrary alphabets.
This corresponds to a special case, whereby the TV distance between the two distributions is zero.
Second, we prove that unless $\mathsf{NP} \subseteq \mathsf{RP}$ it is impossible to efficiently estimate the TV distance between arbitrary Ising models, even in a bounded-error randomized setting.
Primary Area: learning theory
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Submission Number: 525
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