Refined Pinsker's and reverse Pinsker's inequalities for probability distributions of different dimensions

2022/03/01 by Michele Caprio, Caprio, Michele
Mathematics · #60E15 #60E99 #Advanced Statistical Methods and Models #FOS: Mathematics #Mathematical Inequalities and Applications #Probability (math.PR) #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2203.00500

openalex publication_date 2022/03/01 · openalex created_date 2022/09/28 · openalex updated_date 2026/07/28

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.

Related

• On Reverse Pinsker Inequalities
• Pinsker's inequality for adapted total variation
• Minimum KL-divergence on complements of L₁ balls
• Generalised Pinsker Inequalities
• A short note on an inequality between KL and TV