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Consider input X being 1-D, and Y belongs to two classes, which have equal priors and the class- conditional densities of X are shifted versions of each other, as shown in the plot below. Each within-class density of X is a mixture of two normal distributions: Class 1 (red): 0.6N(-2, %4) + 0.4N(0, 1). Class 2 (blue): 0.6N(0, %) + 0.4N(2, 1). (a) Describe the classifier obtained by LDA when the number of samples/observations goes to infinity. Justify your answer. (b) Assume instead that the prior of class 1 is twice of that the prior of class 2. Describe the classifier obtained by LDA, when the number of samples/observations goes to infinity. Justify your answer.

Consider input X being 1-D, and Y belongs to two classes, which have equal priors and the class- conditional densities of X are shifted versions of each other, as shown in the plot below. Each within-class density of X is a mixture of two normal distributions: Class 1 (red): 0.6N(-2, %4) + 0.4N(0, 1). Class 2 (blue): 0.6N(0, %) + 0.4N(2, 1). (a) Describe the classifier obtained by LDA when the number of samples/observations goes to infinity. Justify your answer. (b) Assume instead that the prior of class 1 is twice of that the prior of class 2. Describe the classifier obtained by LDA, when the number of samples/observations goes to infinity. Justify your answer.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 40CR
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Consider input X being 1-D, and Y belongs to two classes, which have equal priors and the class- conditional densities of X are shifted versions of each other, as shown in the plot below. 0.0 05 04 03 02 01 Each within-class density of X is a mixture of two normal distributions: Class 1 (red): 0.6N(-2, ¼ ) + 0.4N(0, 1). Class 2 (blue): 0.6N(0, 4 ) + 0.4N(2, 1). (a) Describe the classifier obtained by LDA when the number of samples/observations goes to infinity. Justify your answer. (b) Assume instead that the prior of class 1 is twice of that the prior of class 2. Describe the classifier obtained by LDA, when the number of samples/observations goes to infinity. Justify your answer.
Transcribed Image Text:Consider input X being 1-D, and Y belongs to two classes, which have equal priors and the class- conditional densities of X are shifted versions of each other, as shown in the plot below. 0.0 05 04 03 02 01 Each within-class density of X is a mixture of two normal distributions: Class 1 (red): 0.6N(-2, ¼ ) + 0.4N(0, 1). Class 2 (blue): 0.6N(0, 4 ) + 0.4N(2, 1). (a) Describe the classifier obtained by LDA when the number of samples/observations goes to infinity. Justify your answer. (b) Assume instead that the prior of class 1 is twice of that the prior of class 2. Describe the classifier obtained by LDA, when the number of samples/observations goes to infinity. Justify your answer.
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