Given the test example = 5, please answer the following questions: and a) Assume that the likelihood function of each category has certain paramétric form. Specifically, we have p(x/a₁)~ N(₁07) p(x₂)~ N(1₂,02). 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 o₁ = 2, 2

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
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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 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 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 \( \sigma_1 = 2 \),
### Bayesian Estimation and Parzen Windows

Given:
- \( \sigma_2 = 1 \)
- \( \mu_1 \sim N(0, 1) \)
- \( \mu_2 \sim N(2, 1) \)

#### Question 1:
Which category should we decide on \( x \) when **Bayesian estimation** is employed to make the prediction?

#### Question 2:
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?
Transcribed Image Text:### Bayesian Estimation and Parzen Windows Given: - \( \sigma_2 = 1 \) - \( \mu_1 \sim N(0, 1) \) - \( \mu_2 \sim N(2, 1) \) #### Question 1: Which category should we decide on \( x \) when **Bayesian estimation** is employed to make the prediction? #### Question 2: 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?
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