On the Equivalence of Statistical Distances for Isotropic Convex Measures

2021/12/16 by Arnaud Marsiglietti, Marsiglietti, Arnaud, Puja Pandey +1
Mathematics · Physics and Astronomy · #FOS: Mathematics #Point processes and geometric inequalities #Probability (math.PR) #Statistical Mechanics and Entropy

paper · pdf · doi:10.48550/arxiv.2112.09009

openalex publication_date 2021/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish quantitative comparisons between classical distances for probability distributions belonging to the class of convex probability measures. Distances include total variation distance, Wasserstein distance, Kullback-Leibler distance and more general Rényi divergences. This extends a result of Meckes and Meckes (2014).

Related

• A Note on Statistical Distances for Discrete Log-Concave Measures
• Distances between probability distributions of different dimensions
• Fisher information distance: a geometrical reading
• Limit laws of the empirical Wasserstein distance: Gaussian distributions
• Distance Metrics for Gamma Distributions