Overview

Machine Learning is a powerful tool that is widely used today and is specified in computer science education, while Statistics and Probability are traditionally studied in mathematical departments. Nevertheless, there is a strong relationship between these theories, and it is desirable to be aware of both general principles and differences in approaches. Indeed, machine learning uses mathematical and/or statistical models to gain an overview of the data to make predictions.

The novel contributions in data mining are mostly informal and usually linked with the Bayesian point of view on statistics. But, probability theory itself is more than just Kolmogorov's axiomatic approach or Bayesian reasoning. For instance, the frequentist approach of R. von Mises coexists with novel contributions from quantum probabilities until now. Thus, the overcoming of the formal separation in theoretical understandings may help to avoid confusion and mistakes.

This course tries to show the existing diversity of approaches while staying within classical Kolmogorov's probability theory. The necessary classical theoretical material would be explained as well. We aim to consider several paradoxical situations that arise in practice.

Most examples would be taken from natural sciences and simple situations in data analysis. The outcome is expected to be the practical training in understanding the popular statistical models and the ability to critically read a professional text. A standard undergraduate course in calculus is required; the simple basic experience in PYTHON, or R or MATLAB (or OCTAVE --- the freeware clone of the MATLAB) would also be needed.