Dena Asta – Carnegie Mellon University

Title: Geometric methods for the statistical analysis of non-Euclidean data and networks. Abstract: In this talk, I will describe applications of geometry to large-scale data analysis. An overriding theme is that an understanding of the relevant geometric structure in the data is useful for efficient and large-scale statistical analyses. In the first part, I will discuss geometric methods for non-parametrics methods for non-Euclidian space. With tools from differential geometry, I develop a general kernel density estimator, for a large class of symmetric spaces, and then derive minimax rate for this estimator comparable to the Euclidean case. In the second part, I will discuss a geometric approach to network inference, joint work with Cosma Shalizi, that uses the above estimator on hyperbolic spaces. We propose a more general, principled statistical approach to network comparison, based on the non-parametric inference and comparison of densities on hyperbolic manifolds from sample networks.