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In this paper, we establish a novel connection between total variation (TV)distance estimation and probabilistic inference. In particular, we present anefficient, structure-preserving reduction from relative approximation of TVdistance to probabilistic inference over directed graphical models. Thisreduction leads to a fully polynomial randomized approximation scheme (FPRAS)for estimating TV distances between distributions over any class of Bayes netsfor which there is an efficient probabilistic inference algorithm. Inparticular, it leads to an FPRAS for estimating TV distances betweendistributions that are defined by Bayes nets of bounded treewidth. Prior tothis work, such approximation schemes only existed for estimating TV distancesbetween product distributions. Our approach employs a new notion of $partial$couplings of high-dimensional distributions, which might be of independentinterest.

Total Variation Distance Estimation Is as Easy as Probabilistic Inference