Name
Abstract | ||
|---|---|---|
We present new MCMC algorithms for com- puting the posterior distributions and expec- tations of the unknown variables in undi- rected graphical models with regular struc- ture. For demonstration purposes, we fo- cus on Markov Random Fields (MRFs). By partitioning the MRFs into non-overlapping trees, it is possible to compute the posterior distribution of a particular tree exactly by conditioning on the remaining tree. These exact solutions allow us to construct e- cient blocked and Rao-Blackwellised MCMC algorithms. We show empirically that tree sampling is considerably more ecien t than other partitioned sampling schemes and the naive Gibbs sampler, even in cases where loopy belief propagation fails to converge. We prove that tree sampling exhibits lower variance than the naive Gibbs sampler and other naive partitioning schemes using the theoretical measure of maximal correlation. We also construct new information theory tools for comparing dieren t MCMC schemes and show that, under these, tree sampling is more ecien t. |
Year | Venue | Keywords |
|---|---|---|
2012 | UAI '04 Proceedings of the 20th conference on Uncertainty in artificial intelligence | naive partitioning scheme,partitioned sampling scheme,tree sampling,particular tree,rao-blackwellised mcmc algorithm,non-overlapping tree,different mcmc scheme,remaining tree,posterior distribution,naive gibbs sampler,graphical model,exact solution,gibbs sampler,information theory,loopy belief propagation |
Field | DocType | Volume |
Information theory,Markov chain Monte Carlo,Computer science,Markov chain,Posterior probability,Artificial intelligence,Sampling (statistics),Graphical model,Machine learning,Gibbs sampling,Belief propagation | Journal | abs/1207.4149 |
ISBN | Citations | PageRank |
0-9749039-0-6 | 20 | 1.49 |
References | Authors | |
7 | 2 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Firas Hamze | 1 | 131 | 14.05 |
| Nando De Freitas | 2 | 3284 | 273.68 |