Exploiting Sparse Markov and Covariance Structure in Multiresolution Models
Abstract
We consider Gaussian multiresolution (MR) models in which coarser, hidden variables serve to capture statistical dependencies among the finest scale variables. Tree-structured MR models have limited modeling capabilities, as variables at one scale are forced to be independent of each other conditioned on other scales. We propose a new class of Gaussian MR models that capture the residual correlations within each scale using sparse covariance structure. Our goal is to learn a tree-structured graphical model connecting variables across different scales, while at the same time learning sparse structure for the conditional covariance 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.
Cite
Text
Choi et al. "Exploiting Sparse Markov and Covariance Structure in Multiresolution Models." International Conference on Machine Learning, 2009. doi:10.1145/1553374.1553397Markdown
[Choi et al. "Exploiting Sparse Markov and Covariance Structure in Multiresolution Models." International Conference on Machine Learning, 2009.](https://mlanthology.org/icml/2009/choi2009icml-exploiting/) doi:10.1145/1553374.1553397BibTeX
@inproceedings{choi2009icml-exploiting,
title = {{Exploiting Sparse Markov and Covariance Structure in Multiresolution Models}},
author = {Choi, Myung Jin and Chandrasekaran, Venkat and Willsky, Alan S.},
booktitle = {International Conference on Machine Learning},
year = {2009},
pages = {177-184},
doi = {10.1145/1553374.1553397},
url = {https://mlanthology.org/icml/2009/choi2009icml-exploiting/}
}