Markov chain Monte Carlo (MCMC) is one of the most widely used methods for sampling from high-dimensional probability distributions, with applications in machine learning, statistics, and data science. Understanding the convergence rate of MCMC algorithms, which is captured by the concept of mixing time, is a central topic in MCMC theory. In this 3-day mini-course, I will introduce several classical and modern techniques for analyzing the mixing time of standard MCMC algorithms.
| Lecture | Date | Time | Topic | Materials |
|---|---|---|---|---|
| 1 | Jan 15 | 4:00 PM | Markov chains, mixing times, and coupling analysis | Lecture Notes |
| 2 | Jan 16 | 2:00 PM | Spectral gaps and comparisons of Markov chains | Lecture Notes |
| 3 | Jan 17 | 9:30 AM | Down-up walks and spectral independence | Lecture Notes |
For further reading, I recommend the following books and lecture notes. For classical techniques such as coupling and spectral analysis, one can refer to the following three books.
For the more recent developments on spectral independence, one can refer to the following lecture notes.
There are many excellent courses on Markov chains and sampling algorithms. Here are some of them.