Bayesian Learning

Aim

The course gives a solid introduction to Bayesian learning, with special emphasis on theory, models and methods used in machine learning applications. The student will learn about the basic ideas and concepts in Bayesian analysis from detailed analysis of simple probability models. The course presents simulation algorithms typically used in practical Bayesian work, and course participants will learn how to apply those algorithms to analyze complex machine learning models. After completing the course the student should be able to:

• derive the posterior distribution for a number of basic probability models
• use simulation algorithms to perform a Bayesian analysis of more complex models
• perform Bayesian prediction and decision making
• perform Bayesian model inference.

Content

Likelihood, Subjective probability, Bayes theorem, Prior and posterior distribution, Bayesian analysis of the following models: Bernoulli, Normal, Multinomial, Multivariate normal, Linear and nonlinear regression, Binary regression, Mixture models; Regularization priors, Classification, Naïve Bayes, Marginalization, Posterior approximation, Prediction, Decision theory, Markov Chain Monte Carlo, Gibbs sampling, Bayesian variable selection, Model selection, Model averaging.