MURI Research
Topic: Stochastic Processes defined by Graphical Models
By: Martin Wainwright (MIT), Erik Sudderth (MIT), Alan S. Willsky (MIT), Tommi Jaakkola (MIT)
In broad overview, this research addresses stochastic processes defined by graphical models, and associated problems of modeling and estimation. The nodes of a singly-connected (i.e., tree) graph can be partially ordered in scale, which gives rise to powerful algorithms for many problems. In contrast, straightforward solution to these same problems are prohibitively complex for more general graphs of any substantial size. As a result, there is considerable interest in developing tractable techniques for graphs with loops. More specifically, we are interested in the following problems: (a) An embedded trees (ET) algorithm for exact estimation of Gaussian processes on graphs with cycles. [See Wainwright, Sudderth, and Willsky, 2000]. (b) Techniques for approximate estimation of discrete processes on graphs with cycles. Report in preparation. (c) Modeling natural image statistics with random cascades of Gaussian scale mixtures on graphical models, and their application to image processing problems. [See Wainwright, Simoncelli, and Willsky, 2000].

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