Kernel approaches in global statistical distances, local measure detection, and active learning

In this talk, we’ll discuss the problem of constructing meaningful distances between probability distributions given only finite samples from each distribution.  We approach this through the use of data-adaptive and localized kernels, and in a variety of contexts.  First, we construct locally adaptive kernels to define fast pairwise distances between distributions, with applications to unsupervised clustering.  Then, we construct localized kernels to determine a statistical framework for determining where two distributions differ, with applications to measure detection for generative models.  Finally, we’ll begin to address the question of measure detection without a priori known labels of which distribution a point came from.  This is addressed through active learning, in which one can choose a small number of points at which to query a label.  This is ongoing work with Xiuyuan Cheng (Duke) and Hrushikesh Mhaskar (CGU), among others.