Given a two-category classification problem under the univariate case, where there are two training sets (one for each category) as follows: D₁ = {-3,-1,0,4} D₂ = {2,1,2,3,6,8} Given the test example x = 5, please answer the following questions: =) Assume that the likelihood function of each category has certain parametric form. Specifically, we and p(x|w₂) have p(x|w₁) N(₁7) N(2, 2). Which category should we decide on when maximum-likelihood estimation is employed to make the prediction? ) Following the abou

Operations Research : Applications and Algorithms
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ISBN:9780534380588
Author:Wayne L. Winston
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Chapter13: Decision Making Under Uncertainty
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2. Given a two-category classification problem under the univariate case, where
there are two training sets (one for each category) as follows:
D₁ = (-3,-1,0,4}
D₂ = {-2,1,2,3,6,8}
Given the test example x = 5, please answer the following questions:
have
and
a) Assume that the likelihood function of each category has certain paramétric
form. Specifically, we
p(x | w₁) N, 07)
p(x₂)~ N(μ₂, 02). Which category should we decide on when
maximum-likelihood estimation is employed to make the prediction?
b) Following the above assumption, suppose we further know that o = 2,
Transcribed Image Text:2. Given a two-category classification problem under the univariate case, where there are two training sets (one for each category) as follows: D₁ = (-3,-1,0,4} D₂ = {-2,1,2,3,6,8} Given the test example x = 5, please answer the following questions: have and a) Assume that the likelihood function of each category has certain paramétric form. Specifically, we p(x | w₁) N, 07) p(x₂)~ N(μ₂, 02). Which category should we decide on when maximum-likelihood estimation is employed to make the prediction? b) Following the above assumption, suppose we further know that o = 2,
02= 1, ₁ ~ N(0, 1) and 2~ N(2, 1). Which category should we decide
on t when Bayesian estimation is employed to make the prediction?
c) Assume that the likelihood function of each category doesn't have any
parametric form. Furthermore, the window function for either category takes
the form of N(0, 1), while the window width for ₁ and is 2 and 5
respectively. Which category should we decide on x when Parzen windows
is employed to make the prediction?
Transcribed Image Text:02= 1, ₁ ~ N(0, 1) and 2~ N(2, 1). Which category should we decide on t when Bayesian estimation is employed to make the prediction? c) Assume that the likelihood function of each category doesn't have any parametric form. Furthermore, the window function for either category takes the form of N(0, 1), while the window width for ₁ and is 2 and 5 respectively. Which category should we decide on x when Parzen windows is employed to make the prediction?
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Given a two-category classification problem under the univariate case, where there are two training sets (one for each category) as follows: D₁ = (-3,-1,0,4} D₂ = {-2,1,2,3,6,8} Given the test example x = 5, please answer the following questions: have and a) Assume that the likelihood function of each category has certain paramétric form. Specifically, we p(x | w₁) N, 07) p(x₂)~ N(μ₂, 02). Which category should we decide on when maximum-likelihood estimation is employed to make the prediction? 

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