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.
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.
probability theory and mathematical statistics are necessary, practicability is not only measure, mathematics is the most important.
Intercultural skills | Communication skills | Specialist skills | Critical thinking skills | ✔ Practical and/or problem-solving skills |
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 | |
---|---|---|
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 |
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Reports.
Two lectures, both 'Fundamentals of Probability (MCS.T212)' and 'Mathematical Statistics (MCS.T223)' are necessary for this lecture.