Approximate Inference based on Convex Set Sampling
Juan K. Lin · AIP conference proceedings · 2004
We address the approximate inference problem by considering the set of all probability measures which satisfy the marginal and conditional constraints specified in a graphical model. The structure of this convex set is elucidated through the explicit enumeration of its extreme points for a number of important cases. This result generalizes the Birkhoff‐von Neumann theorem. For approximate inference calculations of marginals of interest, we present two non‐iterative algorithms based on sampling from this convex set. Results from numerical experiments support the accuracy of these approximations.