Mathematical forecasting

This course joins two parts of the problem statements in Machine Learning. The first part comes from the structure of the measured data. The data come from Physics, Chemistry and Biology and have intrinsic algebraic structure. This stricture is part of the theory that stands behind the measurement. The second part comes from errors of the measurement. The stochastic nature errors request the statistical methods of analysis. So this course joins algebra and statistics. It is devoted to the problem of predictive model selection.

The course holds two semesters: Fall 2020 and Spring 2021. It contains lectures and practical works. The scoring:

1. Questionnaires during lectures
2. Two application projects
3. The final exam

Topics

• Forward and inverse problems, kernel regularisation
• Karhunen–Lo`eve theorem, FPCA
• Parametric and non-parametric models
• Reproductive kernel Hilbert space
• Integral operators and Mercer theorem Convolution theorem
• Graph convolution
• Manifolds and local models

L3 courses towards machine learning

• Functional analysis
• Differential geometry

References

1. FDA by T. Hsiing, R. Eubank
2. FDA by J. Ramsay, B. Silverman