New Outer Bounds on the Marginal Polytope
Abstract
We give a new class of outer bounds on the marginal polytope, and propose a cutting-plane algorithm for efficiently optimizing over these constraints. When combined with a concave upper bound on the entropy, this gives a new variational inference algorithm for probabilistic inference in discrete Markov Random Fields (MRFs). Valid constraints on the marginal polytope are derived through a series of projections onto the cut polytope. As a result, we obtain tighter upper bounds on the log-partition function. We also show empirically that the approximations of the marginals are significantly more accurate when using the tighter outer bounds. Finally, we demonstrate the advantage of the new constraints for finding the MAP assignment in protein structure prediction.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 06, 2007
- Accession Number
- AD1007221
Entities
People
- David A Sontag
- Tommi S. Jaakkola
Organizations
- Massachusetts Institute of Technology