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TV distance estimation for general log-concave distributions

Develop algorithms to estimate the total variation distance between two general log-concave probability distributions on R^n.

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Background

The paper provides relative-error algorithms for the total variation distance between multivariate Gaussians by reducing to discrete product distributions and leveraging new analysis tools. Extending such TV distance estimation beyond Gaussians to the broader class of log-concave distributions is identified as an explicit open direction.

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)