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.
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.
data analysis, real world, tool, the limit of data analysis, and true study, importance of mathematics and theoretical physics
Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | ✔ Practical and/or problem-solving skills |
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 | |
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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. |
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Reports.
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.