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.
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.
✔ 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. |
Algebraic Geometry, Hyperfunction theory, Central Limit Theorem on Function Space, Information Criterion, Not an easy introduction
✔ 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. |
This is a lecture for constructing new theory of statistics and machine 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 |
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.
None.
Sumio Watanabe. Alegebraic geometry and statistical learning theory, Cambridge University Press, 2009
Sumio Watanabe. Mathematical theory of Bayesian statistics, CRC Press,2018.
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.
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.
Remark that this lecture is not an easy introduction or practical use of machine learning or statistics.