Relative-Error TV Distance Approximation for Gaussian-Perturbed Distributions

Develop polynomial-time algorithms that approximate, to a prescribed relative error, the total variation distance between distributions obtained by perturbing arbitrary distributions with Gaussian noise in R^n.

Background

While the paper provides algorithms for Gaussians, many practical models arise as Gaussian-perturbed versions of other distributions (e.g., additive Gaussian noise).

The authors explicitly list TV distance estimation for Gaussian-perturbed distributions as an open direction, suggesting the challenge of extending their techniques to these noisy, potentially non-Gaussian settings.