title: 斯坦福-随机图模型-week3.1
tags: note
notebook: 6- 英文课程-9-Probabilistic Graphical Models 1: Representation
---

斯坦福-随机图模型-week3.1

习题题

1. Question 1

Factor Scope. Let ϕ(a,b) be a factor in a graphical model, where a is a value of A and b is a value of B. What is the scope of ϕ?

{A}

{A, B, C, D, E}

{A, B, C}

{A, B}

Correct 

Question 2

Independence in Markov Networks. Consider this graphical model from week 1's quizzes. This time, all of the edges are undirected (see modified graph below). Which pairs of variables are independent in this network? You may select 1 or more options.

No pair of variables are independent on each other.

Correct 
No pairs of variables are independent in a fully connected Markov network.

B, E

Un-selected is correct 

C, D

Un-selected is correct 

Question 3

Factorization. Which of the following is a valid Gibbs distribution over this graph?

ϕ(A,B,C,D,E,F)

ϕ(A)×ϕ(B)×ϕ(C)×ϕ(D)×ϕ(E)×ϕ(F)Z, where Z is the partition function

Correct 
A Gibbs distribution is a factor product divided by the partition function, and this expression complies with this definition.

ϕ(A)×ϕ(B)×ϕ(C)×ϕ(D)×ϕ(E)×ϕ(F)

ϕ(A,B,D)×ϕ(C,E,F)Z, where Z is the partition function

Question 4

Factors in Markov Network. Let ϕ(A,B,C) be a factor in a probability distribution that factorizes over a Markov network. Which of the following must be true? You may select 1 or more options.

ϕ(a,b,c)≥0, where a is a value of A, b is a value of B, and c is a value of C.

Correct 

ϕ(a,b,c)≤1, where a is a value of A, b is a value of B, and c is a value of C.

Un-selected is correct 

A, B, and C do not form a clique in the network.

Un-selected is correct 

There is a path connecting A, B, and C in the network.

Correct 

A, B, and C form a clique in the network.

Correct