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2022　Topics on Mathematical and Computing Science A

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Academic unit or major
Graduate major in Mathematical and Computing Science
Instructor(s)
Sakata Ayaka 
Class Format
Lecture    (Face-to-face)
Media-enhanced courses
Day/Period(Room No.)
Intensive ()  
Group
-
Course number
MCS.T414
Credits
2
Academic year
2022
Offered quarter
3-4Q
Syllabus updated
2022/12/19
Lecture notes updated
-
Language used
Japanese
Access Index

Course description and aims

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.

Student learning outcomes

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

Keywords

Bayesian networks, Markov networks, Structure learning, Belief propagation

Competencies that will be developed

✔ Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

Class flow

The student will learn each topic as lectures (in japanese).

Course schedule/Required learning

  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.

Textbook(s)

None.

Reference books, course materials, etc.

Koller & Friedman, “Probabilistic Graphical Models” MIT Press (2009)
Mézard and Montanari, “Information, Physics, and Computation,” Oxford University Press (2009).

Assessment criteria and methods

Evaluate understanding by a report assignment.

Related courses

  • MCS.T212 ： Fundamentals of Probability
  • MCS.T223 ： Mathematical Statistics

Prerequisites (i.e., required knowledge, skills, courses, etc.)

None.

Contact information (e-mail and phone)    Notice : Please replace from "[at]" to "@"(half-width character).

Lecturer: Ayaka Sakata (The Institute of Statistical Mathematics) ayaka[at]ism.ac.jp
Contact professor: Satoshi Takabe (TiTech) takabe[at]c.titech.ac.jp

Other

Be sure to the lecture day.

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