Stochastic Systems Group  

Gaussian Multiscale Modeling with Sparse Inscale Conditional Covariance
Myung Jin Choi
SSG, MIT
We consider the problem of learning Gaussian multiscale models in which coarser, hidden variables serve both to capture longdistance dependencies and to provide statistical structure that leads to new, efficient inference algorithms. These models are aimed at overcoming the limitations of treestructured 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 inscale conditional covariance. We demonstrate the modeling and inference advantages of our approach over methods that use multiscale tree models, and singlescale approximation methods that do not use hidden variables.
Joint work with Venkat Chandrasekaran and Alan Willsky.
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