### 2022　Data Analysis

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Undergraduate major in Mathematical and Computing Science
Instructor(s)
Watanabe Sumio
Class Format
Lecture    (Face-to-face)
Media-enhanced courses
Day/Period(Room No.)
Tue3-4(W834)  Fri3-4(W834)
Group
-
Course number
MCS.T332
Credits
2
2022
Offered quarter
4Q
Syllabus updated
2022/9/12
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

How instructors' work experience benefits the course ✔ Applicable 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, 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 Evaluation hyperparameter optimization
Class 11 information criteria and cross validation information criteria and cross validation
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.

None.

### Reference books, course materials, etc.

You need basic probability theory (MCS.T212) and mathematical statistics (MCS.T223).

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. 'Lebesgure Integration(MCS.T3-4)' is recommended.

### 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.