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TV distance estimation for Gaussian-perturbed distributions

Develop algorithms to estimate the total variation distance between two Gaussian-perturbed probability distributions.

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Background

Beyond pure Gaussians, many practical models involve Gaussian perturbations of underlying distributions. The paper identifies this as a distinct open direction for TV distance estimation, suggesting potential extensions of the presented framework.

References

Several directions remain open; including TV distance estimation for general log-concave distributions, graphical models, and Gaussian-perturbed distributions; and approximations for other notions of distance such as the Wasserstein distance.

— Approximating the Total Variation Distance between Gaussians (2503.11099 - Bhattacharyya et al., 14 Mar 2025) in Section 5 (Conclusion)