This talk will provide an overview of a personal perspective on inference and learning for graphical models, one that began with work on multi-resolution models for signals and images but that has evolved into a more general look at inference and learning especially for graphical models for which these tasks are tractable and scalable to large problems.
The talk will begin with a brief introduction to Markov models on undirected graphs and message-passing algorithms, often known as Belief Propagation, that exactly solve inference problems on a very special set of graphs, namely those without loops or cycles, i.e., trees. We’ll then turn to building or learning models on such graphs, including ones that explicitly have hierarchical structure and will comment on some of the differences between the questions that have typically been addressed in very different communities (namely machine learning and system theory). We’ll then provide a new method for learning models on trees with hidden nodes.
The rest of the talk will deal with a look at what happens if one considers graphs with loops. We first look at what is known as Loopy Belief Propagation and provide, for the Gaussian case, an explicit picture of what it does and when and why it works and when it doesn’t based on what we call walk-sum analysis. We then use these ideas to describe another new set of algorithms based on the graph-theoretic concept of a feedback vertex set (i.e., a set of nodes in the graph that, if removed, leave a cycle-free graph). As time allows we’ll discuss the learning of several other classes of graphical models, where in each case, the objective is to learn models for which both the learning of these models as well as exact or nearly exact inference using these models is computationally feasible.
Alan S. Willsky is the Edwin Sibley Webster Professor of Electrical Engineering and Computer Science and Director of the Laboratory for Information and Decision Systems at MIT. Dr. Willsky was a founder, member of the Board of Directors, and Chief Scientific Consultant of Alphatech, Inc. Dr. Willsky has held visiting positions at several institutions in England and France. He has authored more than 200 journal papers and 350 conference papers, as well as two books, including the widely used undergraduate text Signals and Systems. Prof. Willsky has received numerous awards, including the 1975 American Automatic Control Council Donald P. Eckman Award, the 1980 IEEE Browder J. Thompson Memorial Award, the 2004 IEEE Donald G. Fink Prize Paper Award, a number of other best paper awards, and an honorary doctorate from Université de Rennes. Prof. Willsky received the 2009 Technical Achievement Award from the IEEE Signal Processing Society and in 2010 was elected to the National Academy of Engineering.
Prof. Willsky is the leader of MIT’s Stochastic Systems Group. His early work on methods for failure detection in dynamic systems is still widely cited and used in practice, and his more recent research on multiresolution methods for large-scale data fusion and assimilation has found application in fields including target tracking, object recognition, oil exploration, oceanographic remote sensing, and groundwater hydrology. Dr. Willsky’s present research interests are in problems involving multidimensional and multiresolution estimation and imaging, inference algorithms for graphical and relational models, statistical image and signal processing, data fusion and estimation for complex systems, image reconstruction, discovery of models for complex interacting phenomena, and computer vision.