Refined Pinsker's and reverse Pinsker's inequalities for probability distributions of different dimensions
arXiv:2203.00500
Abstract
We provide optimal lower and upper bounds for the augmented Kullback-Leibler divergence in terms of the augmented total variation distance between two probability measures defined on two Euclidean spaces having different dimensions. We call them refined Pinsker's and reverse Pinsker's inequalities, respectively.