Geometry of Covariance Matrices, Covariance Operators, and Gaussian Processes

Explore the geometric aspects of covariance matrices, covariance operators, and Gaussian processes in this seminar series presented by Dr. Quang Minh Ha. Delve into the application of functional analysis and differential geometry in machine learning, statistics, computer vision, and signal processing. Examine recent generalizations of non-Euclidean distances between covariance matrices and Gaussian measures, focusing on the Fisher-Rao distance from Information Geometry and the Entropic Regularization of the 2-Wasserstein distance from Optimal Transport. Learn about closed-form expressions applicable in practice, particularly in the reproducing kernel Hilbert space (RKHS) setting. Gain insights into the importance of similarity functions between these objects and their applications in various domains. Witness the mathematical formulations complemented by numerical experiments in computer vision during this hour-long presentation by a distinguished researcher from the RIKEN Center for Advanced Intelligence Project.