Name
Abstract | ||
|---|---|---|
In this paper, we consider the problem of learning Gaussian multiresolution (MR) models in which data are only available at the finest scale, and the coarser, hidden variables serve to capture long-distance dependencies. Tree-structured MR models have limited modeling capabilities, as variables at one scale are forced to be uncorrelated with each other conditioned on other scales. We propose a new class of Gaussian MR models in which variables at each scale have sparse conditional covariance structure conditioned on other scales. Our goal is to learn a tree-structured graphical model connecting variables across scales (which translates into sparsity in inverse covariance), while at the same time learning sparse structure for the conditional covariance (not its inverse) within each scale conditioned on other scales. This model leads to an efficient, new inference algorithm that is similar to multipole methods in computational physics. We demonstrate the modeling and inference advantages of our approach over methods that use MR tree models and single-scale approximation methods that do not use hidden variables. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1109/TSP.2009.2036042 | IEEE Transactions on Signal Processing |
Keywords | Field | DocType |
sparse markov,gaussian multiresolution models,hidden variables,graphical model connecting variables,trees (mathematics),single-scale approximation methods,graphical models,gauss–markov random fields,sparse conditional covariance structure,gaussian multiresolution model,covariance matrices,inverse covariance,multipole methods,gaussian multiresolution,multiresolution (mr) models,tree models,inference advantage,mr tree model,gaussian mr model,tree-structured mr model,conditional covariance,computational physics,covariance structure,hidden variable,signal resolution,markov processes,finest scale | Variable-order Bayesian network,Pattern recognition,Markov model,Markov chain,Gaussian,Variable-order Markov model,Artificial intelligence,Graphical model,Hidden variable theory,Mathematics,Covariance | Journal |
Volume | Issue | ISSN |
58 | 3 | 1053-587X |
Citations | PageRank | References |
9 | 0.63 | 19 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Myung Jin Choi | 1 | 342 | 13.21 |
| Venkat Chandrasekaran | 2 | 716 | 37.92 |
| Alan S. Willsky | 3 | 7466 | 847.01 |