Statistical Learning Theory 2020


Sumio Watanabe


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Lecture in Department of Mathematical and Computing Science, Tokyo Institute of Technology.


Statistical Learning Theory (MCS.T403)


We have mathematical theory which holds for an arbitrary triple of a true distribution, a statistical model, and a prior. Thus we can apply them to the real wold even if we do not know the true distribution.


Statistical Learning Theory 01 Outline
Statistical Learning Theory 02 Probability Theory (1)
Statistical Learning Theory 03 Probability Theory (2)
Statistical Learning Theory 04 Algebraic Geometry
Statistical Learning Theory 05 Resolution of Singularities
Statistical Learning Theory 06 Zeta function
Statistical Learning Theory 07 Schwartz distribution
Statistical Learning Theory 08 Empirical Process
Statistical Learning Theory 09 Free Energy
Statistical Learning Theory 10 Generalization Loss
Statistical Learning Theory 11 Cross Validation and Information Criterion
Statistical Learning Theory 12 Model Evaluation
Statistical Learning Theory 13 Phase Transition and Prior Effect
Statistical Learning Theory 14 Application to Statistics


mp4 files
Norml mixture in Gibbs Sampler
Norml mixture H=2, H0=3
Norml mixture H=3, H0=3
Norml mixture H-5, H0=3
Neural Network in Langevin MCMC
Neural Network : Ge, Cv, Waic.






If you need more information, please find the following books.

Sumio Watanabe, Algebraic Geometry and Statistical Learning Theory, Cambridge Univesity Press, 2009.
Sumio Watanabe, Mathematical Theory of Bayesian Statistics, CRC Press. 2018.