 # CSE 5522 Homework 2

```CSE 5522 Homework 2
February 18, 2015
Problem 1 (1 point)
Figure 1: GM for problem 1
Consider the DAG G in Figure 1. Assume it is a minimal I-map for
P (A, B, C, D, E, F, X). Now consider marginalizing out X. Construct a new
DAG G0 which is a minimal I-map for P (A, B, C, D, E, F ). Specify and
justify which extra edges need to be added.
Problem 2 (1 point)
Here we compute global independence statements from some directed graphical models. You can use the “bayes ball” algorithm or the d-seperation
criteria.
• Consider the DAG in figure 2, list all the variables that are independent
of A given evidence on B.
• Consider the DAG in figure 3, list all the variables that are independent
of A given evidence on J.
1
G
H
D
I
E
F
B
C
A
Figure 2: GM for problem 2 part 1
B
A
D
G
C
E
H
F
I
J
Figure 3: GM for problem 2 part 2
Problem 3 (3 points)
Consider an HMM with three states, three outputs, and the following transition and emission probabilities. Assume a uniform distribution for the
initial state, 0.
πi
a
b
c
πi+1
a
0.5
0.1
0.4
2
b
0.4
0.5
0.1
c
0.1
0.4
0.5
π
a
b
c
xi
p
0.7
0.2
0.1
q
0.1
0.7
0.2
r
0.2
0.1
0.7
1. Compute the most likely sequence of hidden states for the observed
sequence (p, p, r, r, q, r) by stepping through the Viterbi algorithm
by hand.
2. Use the forward-backward algorithm to compute the probability distribution over states at position 3.
3. Is the most likely state the same as the state in the most likely sequence? Will this always be the case? Why?
3
``` # Math 3D03 Assignment #5 Due: Tuesday, March 31st, 2015 in class # NFOGM Temadag 19.3.2015 - Norwegian Society For Oil and Gas # This is a test given in the past - it... - it is not meant for practice and these particular... # Time and Motion Study Rebecca Johnston Operations Management Dr. Foster # UW CSE 473 Final Exam, Fall 2014 P1 P6 Instructions Please 