CSE 599: Counting and Sampling

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

List of Reading

Related Courses

Related Books/Monographs

Lecture Topic Notes Bonus Materials
Lecture 1 (09/27/17) Intro, Equivalence of Counting and Sampling pdf
Lecture 2 (09/29/17) DNF Counting and Karger's Algorithm for Network Reliability pdf Faster Algorithm
Lecture 3 (10/04/17) Markov chains Intro, Metropolis Rule, Glauber Dynamics, Fundamental Theorem of Markov Chains pdf Bayer-Diaconis
Lecture 4 (10/06/17) Introduction to Coupling pdf
Lecture 5 (10/11/17) Strong Stationary Time pdf Diaconis-Fill
Lecture 6 (10/13/17) Path Coupling: Graph Coloring pdf Vigoda's bound
Coupling for Partial Order
Lecture 7 (10/18/17) Advanced Coupling and Mixing Time via Eigenvalues pdf Hayes-Vigoda
Lecture 8 (10/20/17) Poincare Constant, bounding Mixing time by Flows pdf Mixing Time by Conductance curve
Lecture 9 (10/25/17) Counting Matchings pdf Heilman-Lieb: Theory of Monomer-Dimer
Lecture 10 (10/27/17) Counting Matchings/Conductance pdf Jerrum-Sinclair-Vigoda on Permanent
Lecture 11 (11/01/17) Lower Bounds on Mixing pdf Mixing of Ising above critical temperature
Lecture 12 (11/03/17) Correlation Decay for counting Matchings pdf Correlation Decay for Expanders
Lecture 13 (11/08/17) Weitz Algorithm for Counting Independent Sets pdf Inapprox above t_c
Indepdence Polyn in Shearer Region
(11/10/17) Veternas Day
Lecture 14 (11/15/17) Barvinok Polynomial Method, Approximating Permanent pdf Approximating Permanent of Real Matrices
Lecture 15 (11/17/17) Barvinok Strip Technique, Patel-Regts Result pdf Patel-Regts
Lecture 16 (11/22/17) More on Matching Polynomial, Roots, Moments of the Roots pdf Chapter 6 of Algebraic Combinatorics
(11/24/17) Thanksgiving day
Lecture 17 (11/29/17) D-stable Polynomials and Approximating Partition Functions of Ising Model pdf FPTAS for Ising on Bounded Degree Graphs
Lecture 18 (12/01/17) Permanent and Gurvits' technique pdf 2^n Approx to Permanent
Lecture 19 (12/06/17) Log Concavity in Counting and Optimization pdf
Lecture 20 (12/08/17) Stability Perservers, Matching Polynomial and Generalization of Gurvits's Technique Generalization of Gurvits' Technique H-stability and Nash-Welfare Problem

Several of the notes on analysis of Markov chains are heavily borrowed from Sinclair's Courese Notes.