Name: ———————-
Practice Quiz - 1
CS 591Q/791V - Pattern Recognition
Posted on: February 26, 2008
Note:
Univariate normal density: N(µ, σ2)=1
√2πσ eh−
1
2(x−µ
σ)2i.
1. [6 points] Briefly describe the following terms: (a) Bayes Risk; (b) Minimum Distance Classifier.
2. [8 points] Consider a two-category one-feature classification problem with the following Gaussian
class-conditional densities:
p(x|ω1)∼N(0,1),
p(x|ω2)∼N1
2,4.
Assume P(ω1) = P(ω2) = 1/2and a 0-1 loss function. Derive the Bayes decision boundary.
3. [6 points] Let ωmax (x)be the state of nature for which P(ωmax|x)≥P(ωi|x)for all i= 1,2,...c.
Show that for the minimum error-rate decision rule, the average probability of error is given by
P(error) = 1 −ZP(ωmax|x)p(x)dx.
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