Bayesian Estimation and Stochastic Optimization

Catalog description

Covers essential topics in high dimensional statistical inference, stochastic optimization, Bayesian statistical signal processing and Markov Chain Monte-Carlo stochastic simulation. The course is four inter-related parts. Part 1 covers the basics of probabilistic models, Markov chain Monte-Carlo simulation and regression with sparsity constraints. Part 2 covers Bayesian filtering including the Kalman filter, Hidden Markov Model filter and sequential Markov chain Monte-Carlo methods such as the particle filter. Part 3 covers maximum likelihood estimation and numerical methods such as the Expectation Maximization algorithm. Part 4 covers stochastic gradient algorithms and stochastic optimization. The course focuses on the deep fundamental ideas that underpin signal processing, data science and machine learning. The discussion sections will focus on more advanced aspects in statistical inference.