Bayesian Decision Theory: Utility, Risk, and Classification

This lecture introduces Bayesian decision theory, focusing on utility, risk, and classification. It covers the concept of cost functions, maximum expected utility, and the Bayes decision rule. The lecture contrasts empirical risk minimization with the Bayesian framework, emphasizing parameterizing distributions and minimizing expected loss. It discusses Bayes risk, decision rules, and classification using the Bayes decision rule. The lecture also explores different cost functions, such as the 0/1 cost, and their implications in binary classification problems. Finally, it delves into decision regions and the equivalence of the Bayes decision rule with decision by regions.