Relative-Error TV Distance Approximation for Graphical Models

Develop polynomial-time algorithms that approximate, to a prescribed relative error, the total variation distance between two probability distributions specified as graphical models.

Background

The current work resolves relative-error TV distance approximation for multivariate Gaussians via reduction and discretization techniques. Graphical models (e.g., Bayesian networks and Markov random fields) are pervasive representations of high-dimensional distributions.

The authors explicitly identify efficient relative-error TV distance approximation for graphical models as an open direction, indicating the need for algorithmic techniques that can handle structured dependencies beyond the product or Gaussian settings.