The 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 structure 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.
- Autoregressive models.
- Correlation and Convergence Analysis.
- Tensor decompositions.
- Neural differential equations.
- Continuous time and streams.
- Metric methods and tensors.
- Spectral methods.
- Spectral graph models.
- Geometric data analysis.
Two personal labworks on brain data analysis include the problem statement and the computational experiment. The delivery is a two-page report with the problem and experimental results, a code and a talk.
Questionnaires during lectures (3), two labworks (2+2), the final exam: topics and problems with discussion (3).
Algebra, analysis and physics at the graduate level.