### 2019　Data Analysis

Font size  SML

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
2019
Offered quarter
4Q
Syllabus updated
2019/7/11
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.

### 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

### 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 discriminant analysis, classification Application of discriminant analysis, classification
Class 4 Principal component analysis, autoencoder Principal component analysis, autoencoder
Class 5 factor analysis, latent variable Application of factor analysis, latent variable
Class 6 cluster analysis, normal mixture Application of cluster analysis, normal mixture
Class 7 time series analysis, convolutional neural network Application of time series analysis, convolutional neural network
Class 8 Summary and applications Summary of data analysis
Class 9 Bayes estimation, generalization and training losses Application of Bayesian estimation, generalization and training losses
Class 10 Hierarchical Bayes Application of Hierarchical Bayes, hyperparameter optimization
Class 11 Hypothesis test Application of hypothesis test
Class 12 Problems of Hypothesis test Problem of hypothesis test
Class 13 information criteria information criteria
Class 14 application of theoretical and mathematical physics to information criteria Application of theoretical and mathematical physics to free energy analysis
Class 15 Summary Summary

None.

None.

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.