In this lecture, a graphical model representing a probability distribution is treated. We will learn basics such as defining a graph and interpreting a graph as a conditional probability and practical topics such as inference of a graph and inference on a graphical model. In addition, we will treat related topics on statistics and machine learning to learn inference methods using a graphical model.
The student will acquire the basics of graphical models by learning the following:
1. Basic concepts of Bayesian networks and Markov networks
2. Inference methods on graphs such as structure learning and inference of conditional probabilities
3. Effective calculations on graphs represented by belief propagation
4. Applications of a graphical model to various problems
5. Sufficient knowledge to learn advanced topics such as causal inference
Bayesian networks, Markov networks, Structure learning, Belief propagation
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
The student will learn each topic as lectures (in japanese).
Course schedule | Required learning | |
---|---|---|
Class 1 | Basics of graphical model and Bayesian network 12/9(Fri) 8:50-10:30 at W833 | Understanding the contents covered by the course. |
Class 2 | Markov network 12/9(Fri) 10:45-12:25 at W833 | Understanding the contents covered by the course. |
Class 3 | Inference of conditional probability 12/16(Fri) 8:50-10:30 at W833 | Understanding the contents covered by the course. |
Class 4 | Strucurture learning 12/16(Fri) 10:45-12:25 at W833 | Understanding the contents covered by the course. |
Class 5 | Variable deletion on graphical model 12/23(Fri) 8:50-10:30 at W833 | Understanding the contents covered by the course. |
Class 6 | Junction tree algorithm 12/23(Fri) 10:45-12:25 at W833 | Understanding the contents covered by the course. |
Class 7 | Belief propagation on tree 1/6(Fri) 8:50-10:30 at W833 | Understanding the contents covered by the course. |
Class 8 | Approximate inference by belief propagation 1/6(Fri) 10:45-12:25 at W833 | Understanding the contents covered by the course. |
Class 9 | Approximate message passing for regression and sparse recovery 1/20(Fri) 8:50-10:30 at W833 | Understanding the contents covered by the course. |
Class 10 | Density evolution 1/20(Fri) 10:45-12:25 at W833 | Understanding the contents covered by the course. |
Class 11 | Information criterion and cross validation 1/27(Fri) 8:50-10:30 at W833 | Understanding the contents covered by the course. |
Class 12 | Active learning 1/27(Fri) 10:45-12:25 at W833 | Understanding the contents covered by the course. |
Class 13 | Decision theory 2/3(Fri) 8:50-10:30 at TBA | Understanding the contents covered by the course. |
Class 14 | Reserved 2/3(Fri) 10:45-12:25 at TBA | Understanding the contents covered by the course. |
None.
Koller & Friedman, “Probabilistic Graphical Models” MIT Press (2009)
Mézard and Montanari, “Information, Physics, and Computation,” Oxford University Press (2009).
Evaluate understanding by a report assignment.
None.
Lecturer: Ayaka Sakata (The Institute of Statistical Mathematics) ayaka[at]ism.ac.jp
Contact professor: Satoshi Takabe (TiTech) takabe[at]c.titech.ac.jp
Be sure to the lecture day.