Project 1.2: Battleship: Bayes' Nets, HMMs


Due Tuesday 2/19 in class

What to submit: Submit a hard copy of your assignment at the start of class.

Bayes' Nets

Question 1 (2 points)  Consider the following network, in which a mouse agent is reasoning about the behavior of a cat.  The mouse really wants to know whether the cat will attack (A), which depends on whether the cat is hungry (H) and whether the cat is sleepy (S).  The mouse can observe two things, whether the cat is sleepy (S) and whether the cat has a collar (C). The cat is more often sleepy (S) when it's either full (f) or starved (v) than when it is peckish (p) and the collar (C) tends to indicate that the cat is not starved.  Note that entries are omitted, such as P(C=~c), when their complements are given.

P(C) P(H|C) P(S|H) P(A|H,S)

C

P
c 0.30

H

C

P
f c 0.60
v c 0.10
p c 0.30
f ~c 0.20
v ~c 0.50
p ~c 0.30

S

H

P
s f 0.90
s v 0.70
s p 0.30

A

H

S

P
a f s 0.01
a f ~s 0.10
a v s 0.50
a v ~s 0.90
a p s 0.20
a p ~s 0.70

Assume you have the following samples relative to the evidence C=c, S=s:

 

  1. Draw the graphical model associated with this problem.
  2. Calculate P(A | C=c, S=s) using joint inference by enumeration

Question 2 (2 points). In the network below, consider which nodes are possibly dependent on the listed node with the listed evidence:

  1. B with no observations
  2. B given G
  3. G given F and C
  4. C given E, F, and B

HMMs

Exercises from HMM Tutorial (4 points). Complete the exercises in section 5 of the HMM Tutorial (the ACME Chocolate Factory problem).