The course addresses advanced methods in machine learning. The primal focus of the course are Bayesian methods for solving various machine learning problems (classification, regression, clustering, etc).
Bayesian approach to probability theory allows to take into account user’s preferences in decision rule construction. Besides, it offers efficient framework for model selection. In particular, one may perform automatic feature selection, adjust the number of clusters, estimate the dimension of latent subspace, set the regularization coefficients in an efficient way.
In the Bayesian framework the probability is interpreted as an ignorance measure rather than objective randomness. Simple rules for operating with probabilities such as the law of total probability and Bayes rule allow one to make inference under uncertainty conditions. In this sense Bayesian framework can be regarded as a generalization of Boolean logic.
Numerical Linear Algebra