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Unformatted text preview: CSE 555 Spring 2010 Homework 1: Bayesian Decision Theory Jason J. Corso Computer Science and Engineering SUNY at Buffalo SUNY [email protected] Date Assigned 13 Jan 2010 Date Due 1 Feb 2010 Homework must be submitted in class. No late work will be accepted. Problem 1: Bayesian Decision Rule (30%) Suppose the task is to classify the input signal x into one of K classes ω ∈ { 1 , 2 , . . . , K } such that the action α ( x ) = i means classifying x into class i . The Bayesian decision rule is to maximize the posterior probability α Bayes ( x ) = ω * = arg max ω p ( ω  x ) . Suppose we replace it by a randomized decision rule , which classifies x to class i following the posterior probability p ( ω = i  x ) , i.e., α rand ( x ) = ω ∼ p ( ω  x ) . 1. What is the overall risk R rand for this decision rule? Derive it in terms of the posterior probability using the zeroone loss function....
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This note was uploaded on 01/31/2010 for the course CSE 500 taught by Professor Aisdjapow during the Winter '08 term at SUNY Albany.
 Winter '08
 aisdjapow
 Computer Science

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