Lecture 1: Introduction to PGMs and Parsimonious Modeling

- See lecture slides on piazza.

Lecture 2: Bayesian Networks (BNs), Representation, Conditional Independencies

Lecture 3: Markov Random Fields (MRFs), Representation, Conditional Independencies, Converting BNs to MRFs

Lecture 4: Log-Linear Models, Metric MRFs, Inference in PGMs, Variable Elimination Algorithm

- Chapters 4 and 9 from KF book.

Lecture 5: Variable Elimination Algorithm, Message Passing Algorithm, Cluster Graphs

- Chapters 9 and 10 from KF book.

Lecture 6: Cluster Graphs, Belief Propagation Algorithm, Cluster (Junction) Trees

Lecture 7: Cluster (Junction) Trees, Conditional Independencies, Loopy Belief Propagation, Calibration, Scheduling and Convergence

Lecture 8: MAP Estimation, Max Product Variable Elimination, Max Product Belief Propagation, Factor Graphs

Lecture 9: Particle-Based Sampling: Forward Sampling in Bayesian Nets, Conditional Probability Queries, Sampling Bounds, Rejection Sampling

Lecture 10: Particle-Based Sampling: Markov Chain, Invariant Distribution, Regularity, Markov Chain Monte Carlo (MCMC) Sampling

Lecture 11: Particle-Based Sampling: Metropolis-Hastings Algorithm, Gibbs Sampling

Lecture 12: Learning in PGMs: Density Estimation, Prediction, Bias-Variance Trade-off, MLE, Sufficient Statistics

- Chapters 16 and 17 from KF book.

Lecture 13: Learning in PGMs: MLE in BNs and MRFs, MLE in Log-Linear Models

- Chapters 16 and 17 from KF book.

Lecture 14: PGM Paper Presentations

- See Piazza for Detailed Information.

Lecture 15: PGM Paper Presentations

- See Piazza for Detailed Information.

Lecture 16: PGM Paper Presentations

- See Piazza for Detailed Information.

Lecture 17: PGM Paper Presentation, Introduction to Sparse Recovery

- See Piazza for Detailed Information.

Lecture 18: Sparse Recovery Problem: Formulation, Applications, Greedy Methods, Optimization-Based Methods

Lecture 19: Sparse Recovery Algorithm: L0 minimization, Convex Envelope, L1 Relaxation, Geometric Properties of Lp-norm Recovery

Lecture 20: Sparse Recovery Theory: Uniqueness, Exact Recovery via L1, Spark and Coherence of Dictionaries

Lecture 21: Sparse Recovery Extensions and Applications: Dealing with Corrupted Data, Sparse Dictionary Learning, Method of Optimal Directions, KSVD

Lecture 22: Affine Rank Minimization Problem: Formulation, Application Examples, Relationships to Sparse Recovery

Lecture 23: Affine Rank Minimization Theory: Uniqueness, Exact Recovery, Rank-RIPS, Matrix Completion