Statistical Learning Theory

Academic unit or major

Graduate major in Mathematical and Computing Science

Instructor(s)

Sumio Watanabe

Class Format

Lecture (Livestream)

Media-enhanced courses

-

Day of week/Period
(Classrooms)

3-4 Tue / 3-4 Fri

Class

-

Course Code

MCS.T403

Number of credits

200

Course offered

2022

Offered quarter

2Q

Syllabus updated

Jul 10, 2025

Language

English

Syllabus

Course overview and goals

This lecture is for studying mathematics in graduate course, which is not suitable for those who have not studied mathematics sufficiently. This lecture is neither an easy introduction nor practical use of machine learning or statistics. This is the lecture on mathematical learning theory based on algebraic geometry, hyperfunctions and central limit theorem on function space. The aim is to be able to understand and make the mathematical structure of modern mathematics and learning theory. You should understand the purpose of this lecture if you want to attend.

Course description and aims

This lecture is neither an easy introduction nor practical use of machine learning or statistics. The purpose is to understand the mathematical structure of modern mathematics and learning theory based on algebraic geometry, hyperfunctions and central limit theorem on functional space.

Student learning outcomes

実務経験と講義内容との関連 (又は実践的教育内容)

The lecturer worked in the company for eight years, but realized that what was said to be practical in the world was useless at all. The truly useful things for constructing new theory were modern mathematics, such as algebraic geometry, algebraic analysis, and hyperfunction theory, and the mathematical mind which cannot be acquired without giving proofs of mathematics one by one. This course is not suitable for anyone seeking easy practical use.

Keywords

Algebraic Geometry, Hyperfunction theory, Central Limit Theorem on Function Space, Information Criterion, Not an easy introduction

Competencies

• Specialist skills
• Intercultural skills
• Communication skills
• Critical thinking skills
• Practical and/or problem-solving skills
• The purpose is to understand the mathematical structure of modern mathematics and learning theory.

Class flow

This is a lecture for constructing new theory of statistics and machine learning.

Course schedule/Objectives

Study advice (preparation and review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.

Textbook(s)

None.

Reference books, course materials, etc.

Sumio Watanabe. Alegebraic geometry and statistical learning theory, Cambridge University Press, 2009
Sumio Watanabe. Mathematical theory of Bayesian statistics, CRC Press,2018.

Evaluation methods and criteria

Reports. Mathematics is necessary to answer the problems. In order to take the credit, you need mathematical proof and heavy calculation. This lecture is not an easy introduction or practical use of machine learning or statistics.

Related courses

• MCS.T507 ： Theory of Statistical Mathematics
• ART.T458 ： Machine Learning

Prerequisites

Differential and integral analysis, complex function theory, probability theory are necessary. This is the lecture of mathematics. Those who understand this lecture is neither an easy introduction nor practical use of machine learning and statistics may attend this lecture.

Other

Remark that this lecture is not an easy introduction or practical use of machine learning or statistics.