Stat 202 C

Markov Chain Monte Carlo and Optimization

MWF 11:00-11:50 am, Spring 2011,     PAB 2748.
 
www.stat.ucla.edu/~yuille/Courses/UCLA/Stat_231/Stat_231.html.
 

Course Description

This course describes MCMC sampling techniques with emphasis on optimization and statistical estimation. Topics covered include Gibbs samplers, Metropolis-Hastings, importance sampling, and simulated annealing. In addition, the course covers alternative optimization techniques including Newton-Raphson, dynamic programming, belief propagation, and variational methods.
Note: course will be very similar to Spring 2010, there will be small changes to the lecture notes.

Textbook

Instructors

Grading Plan: 4 units, letter grades. 4 homework assignments. 1 final exam.
Homework 1:
Homework 2:
Homework 3:
Homework 4:

Tentative Schedule.

Lecture

Date

Topics

Reading Materials

Handouts

Roberts & Casella

1

3-28

Introduction to Sampling and Monte Carlo:
 Issues, Applications, and Examples.

Ch 1

2011lecture1.pdf
  Ch 2

2

3-30

Basic Monte Carlo:
Inversion Method, Gaussians, Mixtures

Ch 2.1

2011lecture2.pdf
  Ch 2.2
     3
   4-1
Basic Monte Carlo:
Rejection Methods.
            Ch 2.2
2011lecture3.pdf
  Ch 2.3, 2.4

4

4-4

Basic Monte Carlo:
Rao-Blackwellization and Exact Methods.

Ch 2

2011lecture4.pdf
 Ch  4.2

5

4-6

Basic Monte Carlo:
Importance Sampling

Ch 2.5

2011lecture5.pdf
  Ch 3.1-3.3
     6
   4-8
Basic Monte Carlo:
Importance Sampling, 
           Ch 2.5 2011lecture6.pdf
  Ch 3.1-3.3

7

4-11

Basic Monte Carlo
Weighted Sampling.

Ch 2.6

2011lecture7.pdf
 Ch 3.1-3.3

8

4-13

Exact Monte Carlo
Dynamic Programming
            Ch 2.4


2011lecture8.pdf


     9
  4-15
Exact Monte Carlo (cont)
Dynamic Programming
            Ch 2.4
2011lecture9.pdf

10

4-18

Structured Probability Distributions
Examples.    
  GYtics.pdf
2011lecture10.pdf

11

4-20

Kalman Filters: 
Filtering and Tracking Examples.
            Ch 3.2   2011lecture11.pdf

    12
   4-22
Particle (Boostrap) Filters: (Cont)
Filtering and Tracking Examples.
    Ch 3.2-3.3, 4.5
2011lecture12.pdf

13

4-25

 
Particle (Boostrap) Filters: (Cont)
Filtering and Tracking Examples
    Ch 3.2-3.3, 4.5   2011lecture13.pdf

14

4-27

Particle (Boostrap) Filters: (Cont)
Filtering and Tracking Examples
  Ch 3.2-3.3, 4.5

 

  2011lecture14.pdf

    15
   4-29
Sequential Importance Sampling
Saw Examples
Ch 3.2-3.3, 4.5  2011lecture15.pdf

16

   5-2
Markov Chain Monte Carlo: 
Introduction

Ch 5.0, 5.1

  2011lecture16.pdf

17

5-4

Markov Chain Monte Carlo:

 Example: Ising Model

 

Ch 5.2, 5.3

2011lecture17.pdf

    18
   5-6
Markov Chain Monte Carlo: 
Metropolis-Hastings 
          Ch 5.3  2011lecture18.pdf

19

5-9

Gibbs Sampler
Data Augmentation

Ch 6.1,6.2

2011lecture19.pdf

20

5-11

Gibbs Sampler
Data Augmentation (Cont)
        Ch 6.3
  Previous Lecture

    21
  5-13
Reversible Jumps and Multiple Try MH
 Hybrid Monte Carlo
         Ch 5.5,5.6 2011lecture20.pdf

22

  5-16

Convergence of MCMC
        Ch 12  2011lecture21.pdf

    23

5-18


            Hybrid Monte Carlo 
Ch 9.1,9.2,9.3   2011lecture22.pdf

    24
  5-20
Genetic Algorithms
        GA Handout  2011lecture23.pdf
ga_tutorial.pdf
    25

5-23

Population Methods and Simulated Annealing
  Ch 11.1-11.3   Previous Lecture

26

5-25

 
Swenson-Wang  

Ch 7

 2011lecture24.pdf

    27
  5-27
Deterministic Methods

 2010lecture25.pdf

   
  5-30
Memorial Day Holiday  



28

  6-1
Deterministic Methods  
 

Reading List

Previous Lecture


29

6-3

Overview:

 

2010lecture26.pdf