Learning Gaussian Graphical Models With Domain Specific Prior
Place: Large Lecture Room - CVC
Affiliation: Associate Professor Stony Brook University, NY. USA
Structure learning techniques are very useful for analyzing complex datasets for which probabilistic dependencies are not known apriori. For instance, these techniques allow for modeling interactions between brain regions, based on measured activation levels through imaging.
Locality information is crucial in datasets where each variable corresponds to a measurement in a manifold (silhouettes, motion trajectories, 2D and 3D images). We propose a "local constancy" prior which encourages finding connectivities between two (close or distant) clusters of variables, instead of between isolated variables. Suppose that we want to learn the structure of brain region interactions for one person. We can expect that the interaction patterns in the brains of two persons are not exactly the same. On the other hand, when learning the structure for one person, we would like to use evidence from other persons as a side information in our learning process. We propose "multi-task" learning, which allows for a more efficient use of training data which is available for multiple related tasks. We propose efficient algorithms which decompose the strictly convex maximum likelihood estimation into a sequence of problems with closed form solutions. We evaluate our methods in a wide range of complex real-world datasets and demonstrate that it captures useful structures such as the rotation and shrinking of a beating heart, motion correlations between body parts during walking and functional interactions of brain regions.