Topic

PART 0 - Introduction & Background

Week 1

• Introduction to Graphical Models and Applications

• Introduction to Probability Theory, discrete and continuous random variables, probability mass function, probability density function,

Week 2

• Joint distribution, marginalization, Conditional probabilities, Independence, conditional independence

• probabilistic modeling, basic problems: representation, sampling, inference, parameter learning

PART I - Representation

Week 3

• Directional graphs, bayesian networks, independence and factorization, examples: Markov Chains, Hidden Markov Models, Bayesian Filters, the Kalman Filter, Decision networks

• Undirected graphs, Markov Random Fields (MRF), Gibbs distribution, Hammersley–Clifford theorem and MRF-Gibbs equivalence.

Week 4

• Reasoning in bayesian networks, flow of influence, active trails

• More on independence & factorization in Bayesian Nets

Week 5

• More on Markov Nets, factorization and independence, potential functions, active trials in markov nets

• Conditional Random Fields (CRF)

Week 6

• Log-linear MRF models, features, energy function, shared features, Examples

PART II - Inference

Week 7

• Introduction to inference, Exact inference vs approximate inference, Map inference

• Variable Elimination and Its complexity, elimination ordering,

• Junction-Tree Algorithm

Week 8

• Message Passing & Belief propagation, Hidden Markov Models & Forward-Backward algorithm

• Loopy Belief Propagation

• Message Passing for MAP inference

Week 9

• Graph Cuts

• Bayesian Filtering, Kalman Filtering

PART III - Sampling

Week 10

• Introduction to Sampling, Monte Carlo Estimation, Discrete & continuous sampling, multivariable sampling, Forward sampling in Bayes Nets

• Markov Chain Monte Carlo

Week 11

• Sampling from Markov Networks

• Gibbs sampling

• Metropolis Hasting

PART IV - Learning

Week 12

• Introduction to Learning, Maximum-Likelihood Parameter Estimation, Sufficient Statistics

• Maximum-Likelihood for Bayes Nets

Week 13

• Maximum-Likelihood for MRFs,

• Maximum-Likelihood for CRFs,

Week 14

• Introduction to Structure Learning,

• Structure Learning in Bayes Nets

Week 15

• Partially Observed Data, Latent variables,

• incomplete Likelihood, optimization methods

Week 16

• Expectation Maximization