Bayes Networks Consider the Bayes network given below, where the only (conditional) independence assumptions between the random variables A to E are those enforced by the shape of the network: A В C D E (a) Write down the full joint probability of all random variables A,..., E in terms of the distributions implied by the Bayes network. (b) For this question only assume that all random variables A,...,E are binary. What is the minimum total number of elements required in probability tables to store the joint probability of variables in this Bayes network? Assume the tables need only to store the positive results for cach binary variable. Show your working. (c) Based on the Bayes network, what can you say about dependencies between each of the following pairs of variables? Choose the type of dependency from {none, conditionally independent given ., independent} (1) C and D (2) B and C (3) A and E (4) D and E (d) Consider the Bayes network as above where the arrow between D and E is reversed, i.c. is now pointing from E to D. What is the new dependency type for each of the pairs of variables from the previous subquestion (c)? (1) C and D (2) B and C (3) A and E (4) D and E

Bayes Networks Consider the Bayes network given below, where the only (conditional) independence assumptions between the random variables A to E are those enforced by the shape of the network: A В C D E (a) Write down the full joint probability of all random variables A,..., E in terms of the distributions implied by the Bayes network. (b) For this question only assume that all random variables A,...,E are binary. What is the minimum total number of elements required in probability tables to store the joint probability of variables in this Bayes network? Assume the tables need only to store the positive results for cach binary variable. Show your working. (c) Based on the Bayes network, what can you say about dependencies between each of the following pairs of variables? Choose the type of dependency from {none, conditionally independent given ., independent} (1) C and D (2) B and C (3) A and E (4) D and E (d) Consider the Bayes network as above where the arrow between D and E is reversed, i.c. is now pointing from E to D. What is the new dependency type for each of the pairs of variables from the previous subquestion (c)? (1) C and D (2) B and C (3) A and E (4) D and E

Computer Networking: A Top-Down Approach (7th Edition)

7th Edition

ISBN:9780133594140

Author:James Kurose, Keith Ross

Publisher:James Kurose, Keith Ross

Chapter1: Computer Networks And The Internet

Section: Chapter Questions

Problem R1RQ: What is the difference between a host and an end system? List several different types of end...

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Question

Bayes Networks
Consider the Bayes network given below, where the only (conditional) independence
assumptions between the random variables A to E are those enforced by the shape
of the network:
A
В
C
D
E
(a) Write down the full joint probability of all random variables A,..., E in terms
of the distributions implied by the Bayes network.
(b) For this question only assume that all random variables A,...,E are binary.
What is the minimum total number of elements required in probability tables
to store the joint probability of variables in this Bayes network? Assume the
tables need only to store the positive results for each binary variable. Show your
working.
(c) Based on the Bayes network, what can you say about dependencies between each
of the following pairs of variables? Choose the type of dependency from {none,
conditionally independent given ., independent}
(1) C and D
(2) B and C
(3) A and E
(4) D and E
(d) Consider the Bayes network as above where the arrow between D and E is
reversed, i.e. is now pointing from E to D. What is the new dependency type
for each of the pairs of variables from the previous subquestion (c)?
(1) C and D
(2) B and C
(3) А and E
(4) D and E

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