Total variation distance for product distributions is #P-complete

Arnab Bhattacharyya, Sutanu Gayen, Kuldeep S. Meel, Dimitrios Myrisiotis, A. Pavan, N. V. Vinodchandran

Abstract: Highlights•We show that computing the total variation distance between two product distributions is #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.