Description: This course introduces how to develop deep generative models (DGMs) by integrating probabilistic graphical models and deep learning to generate realistic data including images, texts, graphs, etc. Course contents include 1) basics of probabilistic graphical models, including Bayesian network and Markov random field; 2) posterior inference methods, including message passing, variat...
Abstract:Every horocycle in a closed hyperbolic surface is dense, and this has been known since the 1940's. We study the behavior of horocycle orbit closures in Z-covers of closed surfaces, and obtain a fairly complete classification of their topology and geometry. The main tool is a solution of a surprisingly delicate geometric optimization problem: finding an optimal Lipschitz map to the cir...