CANCELED--Kernel Approaches in Global Statistical Distances, Local Measure Detection, and Active Learning

Tuesday, March 24, 2020 - 1:25pm - 2:25pm
Lind 305
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.

Alex Cloninger is an Assistant Professor in the Mathematics Department and the Halıcıoğlu Data Science Institute at UCSD. He received his PhD in Applied Mathematics and Scientific Computation from the University of Maryland in 2014, and was then an NSF Postdoc and Gibbs Assistant Professor of Mathematics at Yale University until 2017, when he joined UCSD. Alex researches problems around the analysis of high dimensional data. He focuses on approaches that model the data as being locally lower dimensional, including data concentrated near manifolds or subspaces. These types of problems arise in a number of scientific disciplines, including imaging, medicine, and artificial intelligence, and the techniques developed relate to a number of machine learning and statistical algorithms, including deep learning, network analysis, and measuring distances between probability distributions.