Description: This course will give a brief introduction to random matrix theory. Some topics we plan to cover are: Wigner semicircle law, the moment method, the resolvent method, invariant ensembles, Wigner matrices, sample covariance matrices, bulk universality, edge universality, rigidity of eigenvalues, Dyson Brownian motion, Tracy-Widom law, and free probability.Prerequisite:Probability, S...
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...