Relative-Error TV Distance Approximation for General Log-Concave Distributions

Develop polynomial-time algorithms that approximate, to a prescribed relative error, the total variation distance between two general log-concave probability distributions on R^n given in an explicit form.

Background

The paper provides relative-error approximation algorithms for the total variation distance between multivariate Gaussian distributions, leveraging reductions to product distributions and discretization techniques.

Extending such guarantees beyond Gaussians to the broad class of log-concave distributions remains explicitly identified as an open direction, reflecting both the statistical importance and algorithmic challenge of TV distance estimation in this general setting.