Total Variation Distance Estimation Is as Easy as Probabilistic
  Inference
Arnab Bhattacharyya Sutanu Gayen Kuldeep S. Meel Dimitrios Myrisiotis A. Pavan N. V. Vinodchandran
In this paper, we establish a novel connection between total variation (TV)
distance estimation and probabilistic inference. In particular, we present an
efficient, structure-preserving reduction from relative approximation of TV
distance to probabilistic inference over directed graphical models. This
reduction leads to a fully polynomial randomized approximation scheme (FPRAS)
for estimating TV distances between distributions over any class of Bayes nets
for which there is an efficient probabilistic inference algorithm. In
particular, it leads to an FPRAS for estimating TV distances between
distributions that are defined by Bayes nets of bounded treewidth. Prior to
this work, such approximation schemes only existed for estimating TV distances
between product distributions. Our approach employs a new notion of $partial$
couplings of high-dimensional distributions, which might be of independent
interest.