TV distance estimation for graphical models

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

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)