TV Distance Estimation for Gaussian-Perturbed Distributions

Develop efficient algorithms to estimate the total variation distance between Gaussian-perturbed distributions, where base distributions are perturbed by additive Gaussian noise, with rigorous accuracy and runtime guarantees.

Background

Beyond pure Gaussian models, the authors note Gaussian-perturbed distributions as an open area for TV-distance estimation. Such settings arise in noisy measurements and robust modeling.

Addressing this problem would require extending the paper's reduction and discretization framework or developing new tools that exploit the structure of Gaussian perturbations.