Introduction to Bayesian Learning

Topics that will be covered include: the Bayesian learning paradigm: prior and posterior distributions, Bayesian point estimation, credible intervals, hypothesis testing, linear and logistic regression. Bayesian Approaches in Machine Learning with specific emphasis on Bayesian optimization, Bayesian Neural Network and Bayesian AB testing.

On the more computational aspects we will cover: Monte Carlo integration, Markov chains, Markov chain Monte Carlo (MCMC) methods, Adaptive MCMC, MCMC convergence diagnostics, Approximate Bayesian Computation.

Prerequisites. Introduction to statistical inference: notion of population, sample, point estimator, confidence interval, hypothesis testing, linear regression. Having taken the course “Introduction to Data Science” or a similar course covering the basics of Statistical inference is very beneficial.

The students will understand the main differences between the Bayesian and the frequentist approach to statistical learning.

Will be able to estimate a Bayesian model and to provide corresponding uncertainty quantifications. They will also learn how some Machine Learning algorithms can be embedded and/or interpreted in a Bayesian framework.

In presence

Weekly lectures will be complemented with tutorials and practicals (with R / Python notebooks)

Class participation is an important component of the course grade (10% of final grade). There will be a final exam that will comprise 90% of the final grade. The exam will consist on a project comprising a statistical data analysis performed using the inferential tools introduced in the course. The students have to turn in the R or Python code, a PPT presentation and the final report (pdf) where the data are described together with the research questions, the analysis, the conclusions and possible further research directions. The project will be presented and discussed with possible questions ranging on the topics covered in class.