### 2018　Data Analysis

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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
2018
Offered quarter
4Q
Syllabus updated
2018/3/20
Lecture notes updated
-
Language used
Japanese
Access Index

### Course description and aims

The goal of this lecture is that students understand basic data analysis with applications to practical problems. Both practical tools and basic concepts are introduced, however, students should not choose academic lecture according to practicality. The true study based on mathematics gives you the wide viewpoints and deep insights. In this lecture, we learn modern data analysis based on algebraic geometry, differential geometry, and theoretical physics.

### Student learning outcomes

Let's study and understand basic points of data analysis with applications to practical problems. Then you understand the limit of data analysis. You should understand that algebraic geometry, differential geometry, and theoretical physics are necessary in modern data analysis.

### Keywords

data analysis, real world, tool, the limit of data analysis, and true study, importance of mathematics and theoretical physics

### Competencies that will be developed

 Specialist skills Intercultural skills Communication skills Critical thinking skills ✔ Practical and/or problem-solving skills

### Class flow

For data analysis methods, their mathematical foundations and applications to practical problems are explained. Data analysis is a set of tools, which should be employed in a correct manner.

### Course schedule/Required learning

Course schedule Required learning
Class 1 True distribution is different from any statistical model. Data analysis is a set of tools, which is not the real world.
Class 2 regression analysis, layered neural networks Application of regression analysis, layered neural networks
Class 3 discriminant analysis, classification Application of discriminant analysis, classification
Class 4 factor analysis, latent variable Application of factor analysis, latent variable
Class 5 Principal component analysis, autoencoder Application of principal component analysis, autoencoder
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, hyperparameter optimization 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 algebraic geometry and differential geometry, information criteria Application of algebraic and differential geometry to 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 Real world and data analysis.

None.

None.

Reports.

### Related courses

• MCS.T223 ： Mathematical Statistics

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

Probability theory and statistics are necessary. Algebraic geometry, differential geometry, and theoretical physics are bases of this lecture. Practical data analysis is introduced based on pure mathematics and theoretical physics.