In this course we will study several techniques developed in the last 30 years to sample from sophisticated probability distributions of exponential size. Approximately half of the course will focus on techniques based on Markov Chain Monte Carlo techniques. In the rest of the course we will see more modern results based on Correlation decay and geometry of Polynomials. ## Administrative Information- Instructor: Shayan Oveis Gharan
- Office Hours: By appointment, email me at shayan at cs dot washington dot edu.
- Lectures: Wednesday - Friday 3:00 - 4:20 at Low 116
## Assignments- Problem Set 1, due October 27th in canvas. solution
- Problem Set 2, due December 9th in canvas.
## List of Reading- Dyer: Approximate counting by dynamic programming
- Peters, Regts On a conjecture of Sokal concerning roots of the independence polynomial
- Barvinok: Concentration of the Mixed Discriminant of well-conditioned Matrcies
- Efthymiou, Hayes, Stefankovic, Vigoda, Yin: Convergence of MCMC and Loopy BP in the Tree Uniqueness Region for the Hard-Core Model
- Barvinok, Luria, Samorodnitsky, Yong: An approximation algorithm for counting contingency tables
- Cryan, Dyer, Goldberg, Jerrum, Martin: RAPIDLY MIXING MARKOV CHAINS FOR SAMPLING CONTINGENCY TABLES WITH A CONSTANT NUMBER OF ROWS
- Bezakova, Galanis, Goldberg, Guo, Stefankovic: Approximation via Correlation Decay when Strong Spatial Mixing Fails
- Hayes, Vigoda: A Non-Markovian Coupling for Randomly Sampling Colorings
- Moitra: Approximate Counting, the Lovasz Local Lemma and Inference in Graphical Models
- Jerrum, Sinclair, Vigoda: An FPRAS for Permanent of Nonnegative Matrices
## Related Courses## Related Books/Monographs- Persi Diaconis's Monograph on the mathematics of mixing things up
- Persi's Monograph on The Markov Chain Monte Carlo Revolution
- Markov Chains and Mixing Times by David Levin, Yuval Peres, and Elizabeth Wilmer. Also, take a look at the 2nd edition
- Combinatorics and Complexity of Partition Functions by Sasha Barvinok
- Algebraic Combinatorics by Chris Godsil
Several of the notes on analysis of Markov chains are heavily borrowed from Sinclair's Courese Notes. |