Name: Seaworth 2011-09-22 13:57
Hey guys - I was wondering if anyone could help me with a few problems I have in my graduate level Pattern Classification class. Some hints, or resources would be awesome because I am really struggling. If you want to contact me feel free.
I will appreciate any help. Thanks again.
The problem is:
Consider the Neyman-Pearson criterion for two univariate normal distributions: p(x|w1) ~ N(ui, sigma^2i) and P(wi) = 1/2 for i = 1,2. Assume a zero-one error loss, and for convenience let u2>u1.
a) Suppose the maximum acceptable error rate for classifying a patter that is actually in w1 as if it were in w2 is E1. Determine the single-point decision boundary in terms of the variables given.
b) For this boundary, what is the error rate for classifying w2 as w1?
c) What is the overall error rate under zero-one loss?
d) Apply your results to the specific case p(x|w1) ~ N(-1,1) and p(x|w2) ~ N(1,1) and E1 = 0.05
e) Compare your result to the Bayes error rate (without Neyman-Pearson conditions)
I will appreciate any help. Thanks again.
The problem is:
Consider the Neyman-Pearson criterion for two univariate normal distributions: p(x|w1) ~ N(ui, sigma^2i) and P(wi) = 1/2 for i = 1,2. Assume a zero-one error loss, and for convenience let u2>u1.
a) Suppose the maximum acceptable error rate for classifying a patter that is actually in w1 as if it were in w2 is E1. Determine the single-point decision boundary in terms of the variables given.
b) For this boundary, what is the error rate for classifying w2 as w1?
c) What is the overall error rate under zero-one loss?
d) Apply your results to the specific case p(x|w1) ~ N(-1,1) and p(x|w2) ~ N(1,1) and E1 = 0.05
e) Compare your result to the Bayes error rate (without Neyman-Pearson conditions)