Locality information is crucial in datasets where each variable corresponds to a measurement in a manifold (silhouettes, motion trajectories, 2D and 3D images). Although these datasets are typically under-sampled and high-dimensional, they often need to be represented with low-complexity statistical models, which are comprised of only the important probabilistic dependencies in the datasets. Most methods attempt to reduce model complexity by enforcing structure sparseness. However, sparseness cannot describe inherent regularities in the structure. Hence, in this paper we first propose a new class of Gaussian graphical models which, together with sparseness, imposes local constancy through ${\ell}_1$-norm penalization. Second, we propose an efficient algorithm which decomposes the strictly convex maximum likelihood estimation into a sequence of problems with closed form solutions. Through synthetic experiments, we evaluate the closeness of the recovered models to the ground truth. We also test the generalization performance of our method in a wide range of complex real-world datasets and demonstrate that it can capture 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. Our method outperforms the state-of-the-art structure learning techniques for Gaussian graphical models both for small and large datasets.

Functional Magnetic Resonance Imaging (fMRI) has enabled scientists to look into the active brain. However, interactivity between functional brain regions, is still little studied. In this paper, we contribute a novel framework for modeling the interactions between multiple active brain regions, using Dynamic Bayesian Networks (DBNs) as generative models forbrain activation patterns. This framework is applied to modeling of neuronal circuits associated with reward. The novelty of our framework froma Machine Learning perspective lies in the use of DBNs to reveal the brain connectivity and interactivity.