CS 188
Spring 2020
Introduction to
Artificial Intelligence Written HW 3 SolQ1. [30 pts] Quadcopter: Spectator
Flying a quadcopter can be modeled using a Bayes Net with the following variables:
• W (weather) 2 fclear
...
CS 188
Spring 2020
Introduction to
Artificial Intelligence Written HW 3 SolQ1. [30 pts] Quadcopter: Spectator
Flying a quadcopter can be modeled using a Bayes Net with the following variables:
• W (weather) 2 fclear, cloudy, rainyg
• S (signal strength) 2 fstrong, medium, weakg
• P (true position) = (x; y; z; θ) where x; y; z each can take on values 2 f0; 1; 2; 3; 4g and θ can take on values
2 f0°; 90°; 180°; 270°g
• R (reading of the position) = (x; y; z; θ) where x; y; z each can take on values 2 f0; 1; 2; 3; 4g and θ can take
on values 2 f0°; 90°; 180°; 270°g
• C (control from the pilot) 2 fforward, backward, rotate left, rotate right, ascend, descendg (6 controls in total)
• A (smart alarm to warn pilot if that control could cause a collision) 2 fbad, goodg
(a) Representation
(i) [2 pts] What is Np, where Np is the domain size of the variable P? Please explain your answer.
Answer: N
p = 500
Explanation: 5 * 5 * 5 * 4 = 500
(ii) [2 pts] Please list all of the Conditional Probability Tables that are needed in order to represent the Bayes
Net above.
P(W); P(SjW); P(P); P(RjS; P); P(CjR); P(AjC; P)
(iii) [1 pt] What is the size of the Conditional Probability Table for R? You may use Np in your answer.
P(RjS; P) has size 750000 or 3 ∗ (Np)2
Now, assume that we look at this setup from the perspective of Spencer { a spectator who can observe A and W.
Spencer observes A=bad and W=clear, and he now wants to infer the signal strength. In BN terminology, he wants
to calculate P(SjA = bad; W = clear).
(b) [5 pts] Inference by Enumeration
If Spencer chooses to solve for this quantity using inference by enumeration, what is the biggest factor that
must be calculated along the way, and what is its size? You may use Np in your answer. Please show your
work.
[Show More]