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2021　Statistical Learning Theory

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Academic unit or major
Graduate major in Mathematical and Computing Science
Instructor(s)
Watanabe Sumio 
Class Format
Lecture     
Media-enhanced courses
Day/Period(Room No.)
Tue3-4()  Fri3-4()  
Group
-
Course number
MCS.T403
Credits
2
Academic year
2021
Offered quarter
2Q
Syllabus updated
2021/3/19
Lecture notes updated
-
Language used
English
Access Index

Course description and aims

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.

Student learning outcomes

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.

Course taught by instructors with work experience

✔ Applicable How instructors' work experience benefits the course
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 that will be developed

✔ 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/Required learning

  Course schedule Required learning
Class 1 Advanced mathematics is necessary. This lecture is neither an easy introduction nor practical use of machine learning or statistics. Understanding the purpose of this lecture.
Class 2 Probability Theory Probability Theory
Class 3 Probability Theory Probability Theory
Class 4 foundation of algebraic geometry algebraic geometry
Class 5 foundation of algebraic geometry algebraic geometry
Class 6 foundation of hyperfunction hyperfunction
Class 7 foundation of hyperfunction hyperfunction
Class 8 probability theory of functional space probability theory of functional space
Class 9 probability theory of functional space probability theory of functional space
Class 10 mathematical learning theory likelihood
Class 11 mathematical learning theory partition function
Class 12 free energy free energy
Class 13 generalization loss generalization loss
Class 14 Application to mathematical Statistics Application to mathematical Statistics

Out-of-Class Study Time (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.

Assessment criteria and methods

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

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.

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