Stat 232B: Stat Modeling and Learning

     Stat 232B-CS266B: 
 Statistical Computing and Inference
      in Vision and Image Science

                MW 2-3:20 pm Spring 2011, Math Sci. Bldg 5203

                            [syllabus.pdf]

Course Description

This graduate level course introduces a broad range of advanced algorithms for statistical inference and learning on graphical structures. These algorithms could be used in vision, pattern recognition, speech, bio-informatics and data mining. Topics include Markov chain Monte Carlo computing, Sequential Monte Carlo methods, heuristic search and parsing algorithms, and stochastic partial differential equations. We organize these algorithms in three methods according to their underlying representations.

1. Descriptive methods: algorithms working on various graphs where the nodes/vertices represent states of the same semantic level. E.g, dynamic programming, Viterbi, belief propagation, constraint-satisfaction, relaxation-labeling, Gibbs sampler, Sequential Monte Carlo, Swendsen-Wang, and Swendsen-Wang Cut).

2. Generative methods: algorithms working on hierarchic graph representations where one level of vertices semantically generate the nodes at the level below. E.g. matching pursuit, heuristic search (A*), language parsing (Earley, Inside-Outside), search on And-Or graphs, Data-Driven Markov Chain Monte Carlo, and compositional inference.

The MCMC methods can be used in both descriptive and generative graphs. Metropolis-Hastings, Markov chain Monte Carlo, reversible jumps etc.

Prerequisites

Basic statistics, linear algebra, MCMC, Stat232A or equivalence, programming skills (matlab, C++) for a project.
Knowledge and experience on images will be a plus.

Reference books
   The lectures will be based on papers and book chapters.

J.S. Liu, Monte Carlo Strategies in Scientific Computing, Springer, 2001.
P. Bremaud, Markov Chains: Gibbs Fields, Monte Carlo Simulation and Queues, Springer, 1999.
Pattern Theory: the stochastic Analysis of Real-World Signal, by Mumford and Desolneux, 2010.
W. R. Gilks et al (eds) Markov Chain Monte Carlo in Practice, Chapman & Hall, 1996
J. Pearl, Heuristics:Intelligent Search Strategies for Computer Problem Solving, 1984.
J. Pearl, Probabilistic Reasoning in Intelligent Systems, 1988.

Instructors

Prof. Song-Chun Zhu, sczhu@stat.ucla.edu, 310-206-8693, office BH 9404. Office Hours: Monday 3:30pm-5:00pm

Grading Plan: 4 units, letter grades

    The grade will be based on four parts
        2 homework                                       20%
        4 small projects                                  40%
             Project 1:  Importance sampling for counting the number of SAWs in a lattice (10%) 
             Project 2:  Exact sampling of Potts model with Gibbs sampler    (10%)
             Project 3:  Cluster sampling for Potts model using Swerndsen-Wang method (10%)
             Project 4:  C4 for line drawing intepretation with positive and negative edges (10%)
        Final exam                                         40%

Tentative List of Topics [zip file for the reading_materials, 210M]

  Chapter 1   Introduction (1 lecture) (Pearl 84 Ch1,  Liu Ch1)     [introduction.pdf]
   1. Problems, objectives, and applications 
           Search, simulation,  integration, optimization and learning 
   2. Basic search techniques and heuristics
           Spaces, representations, operators, constraints, metrics and heuristics.
   3. Introduction to search algorithms on various graphical structures.
          
 Chapter 2  Search, matching and parsing techniques in Computer Science  (2 lectures)
   1. Heuristic searches (Pearl 84, 2.3-2.4)                 [part1_search.pdf]
   2. *More on heuristics (Pearl 84, Ch.4)
   3. Matching pursuit for image coding (Mallat Ch 9 basis pursuit and match pursuit)
   4. Relaxation-Labeling with line drawing example (Winston_AI, Ch12) [part2_relaxation.pdf]
   ----- * Topics won't be discussed in class, read the list materials.  

Chapter 3.   Backgrounds on Markov chains  (2 lectures)       [MCMC_basics.pdf]
   1. The transition matrix  (Bremaud, Ch 2.1)
   2. Topology of transition matrix: communication and period (Bremaud, Ch 2.4)
   3. Positive recurrence and invariant measures (Bremaud, Ch 3.3)
   4. Ergodic theorem (Bremaud, Ch 3.4)

Chapter 4. Markov chain Monte Carlo computing (4 lectures)   [MCMC_Design_tricks.pdf]
   1. Gibbs sampler and variants    (Liu, Ch 6, )
        (multi-grid, generalized Gibbs, Metropolized Gibbs,
         data association, slice sampling, data augmentation) 
   2. Metrolopis-Hastings and variants (Liu, Ch 5) 
   3. Swendsen-Wang and clustering sampling (Liu, Ch 5)  [SW_interpretation.pdf]
   4. Two exact sampling techniques (papers) (Coupling from the past CFTP, Bounding chain) 
   5. Swendsen-Wang cut and variants (paper)     [SW-cut.pdf]
      special cases:
      6. Belief propagation on chain, tree and poly-trees (Pearl 88, Ch4)
   7. Dynamic programming on chains: Viterbi and Beam search on HMM 

  Chapter 5: Convergence analysis (option, 2 lectures)
   1. Contraction coefficient (Winkler, Ch 4.2)
   2. Puskin's order (Liu, Ch 13.3)
   3. Eigen-structures of the transition matrix (Bremaud, Ch 6.1, 6.2)
         (Perron-Frobenius theorem, spectral theorem)
   4. Geometric bounds (Bremaud, Ch 6.4)
   5. Exact analysis on independence Metropolised Sampler (IMS) (Liu, 13.4)
   6. First hitting time analysis and bounds for IMS (paper) 
   7. Path coupling techniques. Bounds for Gibbs sampler and Swendson-Wang algorithm (paper).
        
  Chapter 6.  Sequential Monte Carlo   (option, 2 lectures)
      1. Importance sampling and weighted samples (Liu, Ch 2.5)
   2. Advanced importance sampling techniques (Liu, Ch 2.6)
   3. Framework for sequential Monte Carlo (Liu, Ch 3.4)
         (selection, pruning, resampling, ...)
   4. Particle filtering (paper)
   
  Chapter 7 Hashing techniques  (option, 1 lectures)
   1. RANSAC
   2. Geometric hashing (2 papers)
      
 Chapter 8   Integrated methods     (2 lectures)
   1. Reversible jumps and trans-dimensional MCMC
   2. stochastic diffusion and Langevins
   3. Jump-diffusion (Paper)
   4. Data-driven Markov chain Monte Carlo (image segmentation and parsing)   [DDMCMC.pdf]
   5. Computing multiple distinct solutions:  C4_ppt.pdf  C4_draft.pdf 

 Chapter 9  Parsing methods     (3 lectures)
   1. Grammar parsing algorithms (Earley and Inside-Outside) [Event parsing by Earley.pdf]           
   2. Top-down / bottom-up image parsing with attribute grammar 
   3. Recent advances in image parsing and grammar inference:
        alpha-beta-gamma [papers]   [grammar_parsing.pdf]