A fast algorithm for particle simulations
Journal of Computational Physics
Convex optimization techniques for fitting sparse Gaussian graphical models
ICML '06 Proceedings of the 23rd international conference on Machine learning
Multiscale Gaussian Graphical Models and Algorithms for Large-Scale Inference
SSP '07 Proceedings of the 2007 IEEE/SP 14th Workshop on Statistical Signal Processing
Embedded trees: estimation of Gaussian Processes on graphs with cycles
IEEE Transactions on Signal Processing
Gaussian multiresolution models: exploiting sparse Markov and covariance structure
IEEE Transactions on Signal Processing
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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 uncorrelated with 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.