Name
Abstract | ||
|---|---|---|
Variational methods are frequently used to approximate or bound the partition or likelihood function of a Markov random field. Methods base d on mean field theory are guaranteed to provide lower bounds, whereas certain types of convex relaxations provide upper bounds. In general, loopy belief propagation (BP) pro- vides often accurate approximations, but not bounds. We prove that for a class of attractive binary models, the so-called Bethe approximation associated with any fixed point of loopy BP always lower bounds the true likelihoo d. Empirically, this bound is much tighter than the naive mean field bound, and requires no fur- ther work than running BP. We establish these lower bounds using a loop series expansion due to Chertkov and Chernyak, which we show can be derived as a consequence of the tree reparameterization characterization of BP fixed points. |
Year | Venue | DocType |
|---|---|---|
2007 | NIPS | Conference |
Citations | PageRank | References |
8 | 0.68 | 16 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Erik B. Sudderth | 1 | 1420 | 119.04 |
| Martin J. Wainwright | 2 | 7398 | 533.01 |
| Alan S. Willsky | 3 | 7466 | 847.01 |