Statistical learning with applications - 4MMASA

Goal(s)

The goal of this course is to introduce students to classical approaches of statistical learning. The information age has resulted in masses of multivariate data in many fields: finance, marketing, economy, biology, environmental sciences, and the knowledge to handle them in a rigorous and self-critical manner is of great importance in research and industry. We will give equal importance to theoretical and practical aspects of statistical learning, showing several applications in class and proposing practical sessions in which the student has to perform actual data analysis using Python software.

This course is intended for students from IF, ISI, and MMIS, as well as those form the M1AM master.

Content(s)

Review of multivariate statistics. Simple and multivariate linear regression. Cross-validation, model selection, bias-variance. Principal component analysis. Linear classification: discriminative and generative approaches. Decision trees. Ensemble methods: bagging and boosting. Performance metrics and overfitting. Introduction to network analysis and community detection in graphs.

Notions of probability theory: probability distribution, joint probability density function for random vectors, conditional distribution, expectation, variance, covariance, Gaussian distribution

Notions of mathematical statistics: estimator, confidence interval, statistical tests.

Notions of linear algebra: matrix reductions, eigenvalue decomposition.

Bonus: Elementary notions of Python programming, writing Rmd files, and typesetting equations in LaTeX.