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a) Assume that the likelihood function of each category has certain parametric form. Specifically, we have P(xwi)N, 07) and p(x₂)~ N(₂, 2). 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 σ₁ = 2,

a) Assume that the likelihood function of each category has certain parametric form. Specifically, we have P(xwi)N, 07) and p(x₂)~ N(₂, 2). 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 σ₁ = 2,

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Given the test example \( x = 5 \), please answer the following questions: a) Assume that the likelihood function of each category has a certain parametric form. Specifically, we have \( p(x \mid \omega_1) \sim N(\mu_1, \sigma_1^2) \) and \( p(x \mid \omega_2) \sim N(\mu_2, \sigma_2^2) \). Which category should we decide on \( x \) when maximum-likelihood estimation is employed to make the prediction? b) Following the above assumption, suppose we further know that \( \sigma_1 = 2 \),
Transcribed Image Text:Given the test example \( x = 5 \), please answer the following questions: a) Assume that the likelihood function of each category has a certain parametric form. Specifically, we have \( p(x \mid \omega_1) \sim N(\mu_1, \sigma_1^2) \) and \( p(x \mid \omega_2) \sim N(\mu_2, \sigma_2^2) \). Which category should we decide on \( x \) when maximum-likelihood estimation is employed to make the prediction? b) Following the above assumption, suppose we further know that \( \sigma_1 = 2 \),
The text presents a problem involving Bayesian estimation and Parzen windows as follows: Given: - \(\sigma^2 = 1\), - \(\mu_1 \sim N(0,1)\), - \(\mu_2 \sim N(2,1)\). **Question:** Which category should we decide on \(x\) when Bayesian estimation is employed to make the prediction? **Part 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 \(\omega_1\) and \(\omega_2\) is 2 and 5 respectively. Which category should we decide on \(x\) when Parzen windows is employed to make the prediction? (Note: No graphs or diagrams were present in the image.)
Transcribed Image Text:The text presents a problem involving Bayesian estimation and Parzen windows as follows: Given: - \(\sigma^2 = 1\), - \(\mu_1 \sim N(0,1)\), - \(\mu_2 \sim N(2,1)\). **Question:** Which category should we decide on \(x\) when Bayesian estimation is employed to make the prediction? **Part 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 \(\omega_1\) and \(\omega_2\) is 2 and 5 respectively. Which category should we decide on \(x\) when Parzen windows is employed to make the prediction? (Note: No graphs or diagrams were present in the image.)
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