10-602 CALD
15-802 Computer Science
36-712 Statistics
80-802 Philosophy
Statistical Approaches to Learning and Discovery

Course Web Page


Time: Mondays and Wednesdays 1:00 pm - 2:20 pm

Location:  Wean Hall 4615A

Instructors:  Zoubin Ghahramani  (zoubin@cs.cmu.edu) and Teddy Seidenfeld (teddy@stat.cmu.edu)

Textbook:  Tanner's "Tools for Statistical  Inference", supplemented by readings.

Additional Reference Material:  G.Casella and R.Berger, "Statistical Inference." and  J.O.Berger, "Statistical Decision Theory" 1st ed. (only).  Both books are on "Reserve" in the E&S Library. The 2nd  edition of Berger is better, but was not in the library yesterday.  We'll try to get  the 2nd ed. on reserve once it shows up.

Written Requirements:  There will be approximately 5 homework assignments, a mid-term  examination, and a final examination.

Tentative Topic List and Schedule

Here is a schedule of class meetings and a preliminary choice of topics to be covered.
We emphasize that the selection of topics and their order of appearance is tentative.
Week 1 (Jan 14 and 16)
Introduction, information theory and statistics
  • Supervised vs Unsupervised vs Reinforcement Learning
  • Statistics and Information theory
  • Maximum Likelihood 
  • Bayesian learning
Lecture Slides
Week 2 (Jan 23)
Some asymptotics of Bayesian inference
  • Asymptotic certainty
  • Asymptotic consensus
Lecture Slides (corrected)
Tanner Chapter 2
Week 3 (Jan 28 and 30)
Normal and other approximations to Bayesian inference
  • Symmetry and independence assumptions
  • Data reduction
  • Asymptotic Normality
Tanner Chapter 2
Lecture Slides (Monday)
Lecture Slides (Wednesday)
Week 4 (Feb 4 and 6)
Latent variable models
  • Mixture of Gaussians (MoG) and k-means
  • Factor Analysis (FA) and PCA
  • Relation to Neural Networks
Lecture Slides(revised)
Homework 1 (revised, due Wed Feb 13)
Text data for Beta-binomial problem
Matlab minimize function
Matlab digamma function
Week 5 (Feb 11  and 13)
The EM algorithm
  • General theory
  • Missing data 
  • Exponential Family
  • Bayesian and non-Bayesian form
  • Applications to MoG and FA
Lecture Slides (Mon)
Extended Remarks on Improper Priors
Slide on KL Inequality
Lecture Slides (Wed)
Tanner Chapter 4
Week 6 (Feb 18 and 20)
MCMC methods
  • Simple Monte Carlo
  • Rejection Sampling
  • Importance Sampling
  • Gibbs Sampling 
  • Relation between Gibbs, MCMC and EM
Lecture Slides (Mon)
Gibbs sampling demo (needs plot_gaussian)
Tanner Chapter 6 and additional readings
Lecture Slides (Wed)
Radford Neal's Technical Report
Week 7 (Feb 25 and 27)
MCMC methods
  • EM as MM, a counterexample
  • Metropolis
  • Hybrid Monte Carlo and other topics in sampling
EM as MM with an EM counterexample (Mon / Teddy)
metropolis demos: one and two
hybrid Monte Carlo demo
Week 8 (March 4 and 6)
Variational Methods and
Probabilistic Graphical Models
  • Variational Methods
  • Conditional Independence
  • Bayesian Networks (directed graphical models)
  • d-Separation
Lecture Slides (Mon)
Jordan et al Variational Tutorial
Homework 2 (part 1)
Homework 2 (part 2)
Data for Hw 2: images.jpg
Data generating code: genimages.m
Week 9 (March 11 and 13)
Probabilistic Graphical Models and
Causal Inference
  • Markov Networks (undirected graphical models)
  • Hammersley-Clifford Theorem
  • Belief Propagation 
  • Causal Inference
Lecture Slides (Mon)

Lecture Slides (Scheines) [pdf] [ppt][html][html - yellow teeth]

Scheines, R. An Introduction to Causal Inference.

Spirtes, P., Richardson, T., Meek, C., Scheines, R., and Glymour, C. 
(1997). Using Path Diagrams as a Structural Equation Modelling Tool
(Sociological Methods and Research)

Scheines, R., Spirtes, P., Glymour, C., Meek, C., and Richardson, T. 
(forthcoming). The TETRAD Project: Constraint Based Aids to Causal Model Specification (Multivariate Behavioral Research)

Tetrad Software Project Homepage

Week 10 /11 (March 18, 20, 25, 27)
Latent Variable Time Series Models
  • Hidden Markov Models (HMMs)
  • Forward-Backward and Viterbi
  • Linear Dynamical Systems
  • Kalman Filtering (KF) and Extended KF
  • Particle Filters
  • Hybrid and Nonlinear Time Series Models
  • Dynamic Bayesian Networks
Paper on Learning Dynamic Bayesian Networks[pdf] [ps]
Lecture Slides (Wed 20, Mon 25)

Week 12 (April 8 and 10)
Sample Reuse Techniques
  • Jackknife
  • Bootstrap
Lecture Slides (Sample Reuse Techniques)
Homework 3 (part 1)
Week 13/14 (April 15, 17, 22)
Reinforcement Learning and Sequential Decisions
  • Decisions
  • Active Learning
  • Experiment Design
  • Reinforcement Learning
  • Markov Decision Problems
  • The Bellman Equation
  • Temporal Difference and Q-learning
  • Relation to Optimal Control and Influence Diagrams
Lecture Slides (Sequential Decision Making)
Lecture Slides (Reinforcement Learning)
Sutton and Barto Textboook
Kaelbling, Littman and Moore Review Paper
Week 14/15 (April 24, 29, May 1)
Model Selection
  • Bayes Factors
  • Multiple Testing
  • Laplace Approximation and Variational Methods
  • Cross Validation
Lecture Slides (Bayesian Model Selection)
Lecture Slides (Cross Validation)

Other topics we would have liked to cover:

Additive Models
Iterative Scaling

Exact Sampling Methods

Hierarchical and Nonlinear Latent-Variable Models:

Nonparametric Inference Loopy Belief Propagation, Bethe Approximations, and Kikuchi Approximations

Expectation Propagation