title: 斯坦福-随机图模型-week4.2
tags: note
notebook: 6- 英文课程-9-Probabilistic Graphical Models 1: Representation
---

斯坦福-随机图模型-week4.2

练习

1. Question 1

Utility Curves. What does the point marked A on the Y axis correspond to? (Mark all that apply.)

500

Un-selected is correct

U(ℓ) where ℓ is a lottery that pays 0 with probability 0.5 and 1000 with probability 0.5.

Correct 
Yes, this is correct, since the value of the lottery is equivalent to 0.5U(<img src="https://yqfile.alicdn.com/img_4edbf5b1f9cae596f44bc735b3da386e.gif"/>1000).

U(500)
Un-selected is correct

0.5U(0)+0.5U(1000)

Correct 
This is correct, as you can observe from the geometry of the triangles in the figure.

Question 2

Utility Curves. What does the point marked B on the Y axis correspond to? (Mark all that apply.)

0.5U(1000)

Un-selected is correct 

$500

Un-selected is correct 

U(ℓ) where ℓ is a lottery that pays 0 with probability 0.5 and 1000 with probability 0.5.

Un-selected is correct 

U(500)

Correct 
Yes, this is correct, since point B is on the curve, it represents U(500).

Question 3

Expected Utility. In the simple influence diagram on the right, with the CPD for M and the utility function V, what is the expected utility of the action f1?

20

2

Correct 
This is correct. The expected utility is given by 0.5*(-7) + 0.3*5 + 0.2*20 = 2.

0

5

Question 4

*Uninformative Variables. In the influence diagram on the right, what is an appropriate way to have the model account for the fact that if the Test wasn’t performed (t0), then the survey is uninformative?

Set P(S|M,t0) so that S takes some new value “not performed” with probability 1.

Correct 
This is the appropriate action. Assigning S to any other value would not be desirable, as these other values may represent survey results, but we have not actually conducted the survey.

Set P(S|M,t0) so that S takes the value s0 with probability 1.

Set P(S|M,t0) to be uniform.

Set P(S|M,t0)=P(S|M,t1).