Core Concepts in Statistical Learning

Abstract

The course reviews the main concepts in statistical learning including statistical models, parametric and non-parametric inference, hypothesis testing and p-values, and classification. Additionally, it serves as a gentle introduction into some special topics such as the bootstrap, the EM-algorithm, causal inference and kernel estimation.

Objective

The main objects of the course are to first recall the foundations of sample spaces, random variables and their moments, joint distributions, concentration inequalities and modes of convergence. The second part of the course will dedicated to the foundations of statistical inference including the method of moments, maximum likelihood estimation, the EM-algorithm, hypothesis testing, p-values and corrections in multiple testing. In the third part, the focus will be put on estimation in regression models with the focus on linear and logistic links, testing independence of discrete outcomes, causal inference (introduction), non-parametric curve estimation (histograms and smooth kernel estimation for a probability density and a regression curve) and some chosen approaches in classification.

Resources