|Stochastic Systems Group|
Gaussian Multiscale Modeling with Sparse In-scale Conditional Covariance
Myung Jin Choi
We consider the problem of learning Gaussian multiscale models in which coarser, hidden variables serve both to capture long-distance dependencies and to provide statistical structure that leads to new, efficient inference algorithms. These models are aimed at overcoming the limitations of tree-structured multiscale models. Instead of constraining variables at each scale to be independent to each other conditioned on other scales as in tree models, we require that variables at each scale be locally correlated conditioned on other scales. Thus, our multiscale model consists of sparse graphical structure (an embedded tree) for dependencies across scales and sparse structure for the in-scale conditional covariance. We demonstrate the modeling and inference advantages of our approach over methods that use multiscale tree models, and single-scale approximation methods that do not use hidden variables.
Joint work with Venkat Chandrasekaran and Alan Willsky.
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