TV Distance Estimation for General Log-Concave Distributions

Develop efficient algorithms to estimate the total variation distance between two general log-concave probability distributions in R^n with provable guarantees (e.g., relative-error approximation), extending beyond the Gaussian case studied in this work.

Background

The paper provides relative-error approximation algorithms for the TV distance between multivariate Gaussians, via reductions to discrete product distributions. As a broader direction, the authors point out that moving beyond Gaussians to general log-concave distributions remains unresolved.

Log-concave distributions encompass many important models in statistics and machine learning; extending TV-distance estimation to this class would significantly broaden applicability of the computational framework.