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TV distance estimation for graphical models

Develop algorithms to estimate the total variation distance between two probability distributions represented as graphical models.

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Background

The authors’ techniques address Gaussians via reductions and discretizations; they point to graphical models as a broader structured class where analogous TV distance estimation remains unresolved.

Graphical models are widely used in probabilistic modeling; efficient TV distance estimation could have significant implications for model comparison and validation.

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)