Computational Explorations of Total Variation Distance
Arnab Bhattacharyya Sutanu Gayen Kuldeep S. Meel Dimitrios Myrisiotis A. Pavan N. V. Vinodchandran
We investigate some previously unexplored (or underexplored) 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.
total variation distance, TV distance, mixtures of products, equivalence checking, Ising models, computational complexity, FPRAS