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- 工学院，物質理工学院，環境・社会理工学院共通科目
- Liberal arts and basic science courses
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School of Environment and Society
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- Common courses
- Liberal arts and basic science courses
- Academic unit or major
- Undergraduate major in Mathematical and Computing Science
- Instructor(s)
- Watanabe Sumio
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Tue3-4(W834) Fri3-4(W834)
- Group
- -
- Course number
- MCS.T332
- Credits
- 2
- Academic year
- 2021
- Offered quarter
- 4Q
- Syllabus updated
- 2021/10/14
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
-
Course description and aims
Both Fundamentals of Probability (MCS.T212) and Mathematical Statistics (MCS.T223) are necessary. Based on probability theory and mathematical statistics, mathematical structure of data analysis is introduced. Student should not measure this subject by practicability. True data analysis, which is based on mathematics, enables us to have wide viewpoints and deep insight. Nowadays, data analysis requires not only classical tools but also algebraic geometry, manifold theory, and stochastic process theory on functional space.
Student learning outcomes
Using probability theory and mathematical statistics, let's study and understand basic points of data analysis with applications to practical problems. You should understand that algebraic geometry, manifold theory, and stochastic process theory on functional space are necessary in modern data analysis.
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 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. |
Keywords
probability theory and mathematical statistics are necessary, practicability is not only measure, mathematics is the most important.
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | ✔ Critical thinking skills | ✔ Practical and/or problem-solving skills |
| ✔ To do mathematical work, you need to learn mathematics. Easy introduction of machine learning and statistics is useless in the real world. | ||||
Class flow
Both Fundamentals of Probability (MCS.T212) and Mathematical Statistics (MCS.T223) are necessary for attending this lecture. In data analysis, their mathematical foundations and applications to practical problems are explained.
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | True distribution is different from any statistical model. | A statistical model only a tools, which is not the real world. |
| Class 2 | regression analysis, layered neural networks | regression analysis, layered neural networks |
| Class 3 | regression analysis, layered neural networks | regression analysis, layered neural networks |
| Class 4 | classification | classification |
| Class 5 | Principal component analysis, autoencoder | Principal component analysis, autoencoder |
| Class 6 | latent variable | latent variable |
| Class 7 | normal mixture | normal mixture |
| Class 8 | time series analysis, convolutional neural network | Application of time series analysis, convolutional neural network |
| Class 9 | Bayes estimation, generalization and training losses | Application of Bayesian estimation, generalization and training losses |
| Class 10 | Bayesian method and | hyperparameter optimization |
| Class 11 | information criteria and cross validation | information criteria |
| Class 12 | marginal likelihood | marginal likelihood |
| Class 13 | Hypothesis test | hypothesis test |
| Class 14 | Hypothesis test (2) | hypothesis test |
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.
They should do so by referring to textbooks and other course material.
Textbook(s)
None.
Reference books, course materials, etc.
You need basic probability theory (MCS.T212) and mathematical statistics (MCS.T223).
Assessment criteria and methods
Reports.
Related courses
- MCS.T212 ： Fundamentals of Probability
- MCS.T223 ： Mathematical Statistics
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Two lectures, both 'Fundamentals of Probability (MCS.T212)' and 'Mathematical Statistics (MCS.T223)' are necessary for this lecture.
Other
Both Fundamentals of Probability (MCS.T212) and Mathematical Statistics (MCS.T223) are necessary. This lecture is mainly suitable for students of 3rd year undergraduate.
