Lecture 7 Master.key

Review 2 Bayesian Classification For a given pattern x, classify it to the most probable class. 1 Probabilistic Classification Recall the problem with the MICD. The MICD always favours C 2. Instead, we ideally want it to favour the class with the highest probability: P (C i |x) C i ≷ C j P (C j |x) where P (C i |x) is the a posteriori (after measurement) probability of class C i given x. To get at P (C i |x) we need p(x|C i) and Bayes Theorem: P (C i |x) = p(x|C i)P (C i) p(x) where p(x|C i) is the class conditional probability density function (pdf)-which needs to be estimated from available samples or otherwise assumed. P (C i) is a priori (before measurement) probability of class C i. 1 Probabilistic Classification Recall the problem with the MICD. The MICD always favours C 2. Instead, we ideally want it to favour the class with the highest probability: P (C i |x) C i ≷ C j P (C j |x) where P (C i |x) is the a posteriori (after measurement) probability of class C i given x. To get at P (C i |x) we need p(x|C i) and Bayes Theorem: P (C i |x) = p(x|C i)P (C i) p(x) where p(x|C i) is the class conditional probability density function (pdf)-which needs to be estimated from available samples or otherwise assumed.