Fundamentals of Bayesian Networks (directed graphical models): representation, semantics, learning and inference [11 Lectures]
- Introduction to the class
- Representation, semantics
- MLE parameter learning
- Structure learning for BNs - complete data
- Constraint-based
- Chow-Liu
- Fixed-order
- Structure search
- Exact inference
- Variable elimination
- Junction trees
- Context-specific independence
Mon., Sept. 08:
- Introduction
[Slides] [Annotated]
- JavaBayes Applet
Wed., Sept. 10:
- NO CLASS
Mon., Sept. 15:
- BN Semantics
[Slides] [Annotated]
Wed., Sept. 17:
- BN Semantics 2 - Representation Theorem, d-Separation
[Slides]
[Annotated]
Mon., Sept. 22:
- BN Semantics 3 - d-Separation, minimal I-map, perfect maps
[Slides]
[Annotated]
Wed., Sept. 24:
- Perfect maps, Parameter Learning
[Slides]
[Annotated]
Mon., Sept. 29:
- NO CLASS
Wed., Oct. 1:
- Parameter Learning (MLE), Structure learning (The Good)
[Slides]
[Annotated]
Mon., Oct. 6:
- Bayesian Parameter Learning, Bayesian Structure learning
[Slides]
[Annotated]
Wed., Oct. 8:
- Structure learning: The Good, The Bad, The Ugly
A little inference too
[Slides]
[Annotated]
Mon., Oct. 13:
- Structure learning: The Good, The Bad, The Ugly (conclusion)
Inference
[Slides]
[Annotated]
Wed., Oct. 15:
- Variable Elimination
[Slides]
[Annotated]
Mon., Oct. 20:
- Variable Elimination Complexity, MPE Inference, Junction Trees
[Slides]
[Annotated]
Wed., Oct. 22:
- Junction Trees 2
[Slides]
[Top]
Representation revisited [3 Lectures]
- Undirected models, Markov Random Fields
- Factor graphs - unifying representation
- Exponential family
Mon., Oct. 27:
- Junction Trees 3, Undirected Graphical Models
[Slides]
[Annotated]
Wed., Oct. 29:
- Undirected Graphical Models
[Slides]
[Annotated]
[Top]
Inference revisited:approximate inference [3 Lectures]
- Sampling
- importance sampling
- MCMC, Gibbs
- Variational inference
- Loopy belief propagation
- Generalized belief propagation
- Kikuchi
Mon., Nov. 3:
- Undirected Graphical Models, Variational Inference
[Slides]
[Annotated]
Wed., Nov. 5:
- Variational Inference, Loopy BP
[Slides]
[Annotated]
Mon., Nov. 10:
- Sampling
[Slides]
Wed., Nov. 12:
- Generalized Belief Propagation
Parameter learning in Markov networks
[Slides]
[Annotated]
[Top]
Learning revisited [3 Lectures]
- Parameter estimation in BNs with missing data
- EM
- Gradient descent
- Structure learning for BNs - missing data
- Learning undirected graphical models
- Gradient algorithms
- IPF for tabular MRFs
- Structure Learning
Mon., Nov. 17:
-
Parameter learning in Markov networks
Conditional random fields
EM
[Slides]
[Annotated]
Mon., Nov. 24:
-
EM for BNs
Gaussians
[Slides]
[Annotated]
[Top]
Special graphical models / Applications [6 Lectures]
- Gaussian
- Multivariate Gaussians
- Gaussian graphical models
- Inference in Gaussian models
- Hybrid models
- discrete and continuous variables
- Hidden Markov Models
- Representation
- Inference
- Forwards-Backwards
- Viterbi
- Baum-Welch
- Kalman filter
- representation
- linearization
- switching Kalman filter
- assumed density filtering
- DBNs
- Representation
- Inference
- BK
Mon., Dec. 1:
-
Gaussians, Kalman Filters, Gaussian MNs
[Slides]
[Annotated]
[Top]
Advanced Topics [3 Lectures]
- Causality
- Relational probabilistic models
- Template models
Mon., Dec. 3:
-
DBNs, Overview
[Slides]
[Annotated]
[Top]
Project Poster Session
3-6pm, Monday, Dec 1st
NSH Atrium
[Top]
Project Paper Due
Wednesday, Dec. 3rd by 3pm by email to the instructors list
[Top]
Final Exam
[Top]