斯坦福-随机图模型-week3.3_
title: 斯坦福-随机图模型-week3.3
tags: note
notebook: 6- 英文课程-9-Probabilistic Graphical Models 1: Representation
斯坦福-随机图模型-week3.3
习题
1. Question 1
I-Maps. Graph G (shown below) is a perfect I-map for distribution P, i.e. I(G)=I(P). Which of the other graphs is an I-map (not necessarily a perfect map) for P?
III
Correct
I isn't because it has the extra independence (A⊥C).
II has the extra independence relation (B⊥C∣D) (among others).
III has no extra independencies. In fact, it has fewer independencies, but the definition of I-map allows for this.
II and III
I
I and II
Question 2
I-Equivalence. In the figure below, graph G is I-equivalent to which other graph(s)?
I
Correct
II, III, and IV all have extra independencies.
III
None of the above
I and III
Question 3
*I-Equivalence. Let Bayesian network G be a simple directed chain X1→X2→...→Xn for some number n. How many Bayesian networks are I-equivalent to G including G itself?
n
Correct
The chain X1←...←Xi→...→Xn is I-equivalent, where i can be 2 through n (when i=n, all arrows point left). Thus, there are n−1 I-equivalent networks like this. Including the original network makes n.
2n
n−1
n!