CS262A: Reasoning with Partial Beliefs
Solutions to HW#2
Exercise 4.1
(a) The Markovian assumptions are:
I (cfw_A, , cfw_B, E );
I (cfw_B , , cfw_A, C );
I (cfw_C , cfw_A, cfw_B, D, E );
I (cfw_D, cfw_A, B , cfw_C, E );
I (cfw_E , cfw_B , cfw_A, C, D, F,
CS262A: Reasoning with Partial Beliefs
Solutions to HW#1
Exercise 2.1
The sentence (A = B ) (A = B ) is satised by any world that sets A to false. The
sentence (A B ) = (A B ) is satised by any world that sets A to false and B to false.
Exercise 2.3
(a)
CS 262A: Learning and Reasoning with Bayesian Networks
Winter 2016
Assignment 2 Due 11:55pm Wednesday, January 27
1. Consider the DAG in Figure 1:
(a) List the Markovian assumptions asserted by the DAG.
(b) Express Pr(a, b, c, d, e, f, g, h) in terms of n
CS 262A: Homework 5
No Author Given
1
A
B
D
C
The empirical distribution for the data set is:
A B C D P rD (.)
TFFF
1
TFFT
2
F FTF
2
TTFT
1
F FTT
1
F TTF
1
F TTT
1
TTTT
1
The parameter estimates:
ml
A H
T 0.5
F 0.5
ml
A B H
T T 0.4
T F 0.6
F T 0.4
F F 0.6
CS 262A: REASONING WITH PARTIAL BELIEFS
Winter 2015
Assignment 3 - Due 11:55pm Wednesday, February 11
1. Consider the Bayesian network in Figure 1. Use variable elimination with ordering D, C, A to compute
Pr(B, C = true), Pr(C = true) and Pr(B|C = true).
CS 262A: REASONING WITH PARTIAL BELIEFS
Winter 2015
Assignment 1 - Due 11:55pm Wednesday, January 21
1. Which of the following pairs of sentences are mutually exclusive? Which are exhaustive? If a pair of
sentences is not mutually exclusive, identify a wo
CS 262A: Homework 3
March 14, 2016
1. e: C = true
P
P
P
P
P r(B, C = true) = D,C,A (D|B C|B B|A A )e = A eD|B A C eC|B D eD|B
P
e
B
D D|B
True 1
False 1
P
P
e
e
B
D D|B
C C|B
True 1
False 0.5
P
P
A
B
eD|B A C eC|B D eD|B
True True 0.1
True False 0.05
Fals
CS 262A: Homework 1
March 14, 2016
1.
world
1
2
3
4
A
T
T
F
F
B
T
F
T
F
Mods(A B) = cfw_1 , 2 , 3
Mods(A B) = cfw_2 , 3 , 4
Mods(A B) = cfw_4
(a) A B and A B
A B and A B are not mutually exclusive. They both hold 2 , 3.
A B and A B are exhaustive
(b) A
CS 262A: Homework 4
March 14, 2016
1. The elimination tree is as follows, the separator for each edge is denote on the each edge:
fA
1
A
2
fB
AB
3
fC
BC
4
fE
BE
5
fD
DE
6
fF
EF
7
fG
FG
8
fH
Cluster:
C1 : A
C2 : AB
C3 : ABC
C4 : BCE
C5 : BDE
C6 : DEF
C7 :
CS 262A: REASONING WITH PARTIAL BELIEFS
Winter 2015
Assignment 5 - Due 11:55pm Sunday, March 15
1. Consider a Bayesian network structure with the following edges A B, A C, and A D. Compute
the maximum-likelihood parameter estimates for this structure give
CS 262A: REASONING WITH PARTIAL BELIEFS
Winter 2015
Assignment 4 - Due 11:55pm Monday, March 2
1. Consider the Bayesian network in Figure 1. Construct an elimination tree for the Bayesian network
CPTs that has the smallest width possible and assigns at mo
CS262A: Reasoning with Partial Beliefs
Solutions to HW#4
Exercise 7.2 Consider the elimination tree fA fB fC fE fD fF fG fH . The clusters () and
separators [] are as follows: (ABC )[BC](BCE )[BE](BDE )[DE](DEF )[EF](EF G)[FG]
(F GH ). The tree has width
CS262A: Reasoning with Partial Beliefs
Solutions to HW#6
Exercise 17.1
A
T
F
A
T
T
F
F
a
0.5
0.5
B
T
F
T
F
b|a
0.4
0.6
0.4
0.6
A
T
T
F
F
C
T
F
T
F
c |a
0.2
0.8
1.0
0.0
A
T
T
F
F
D
T
F
T
F
d|a
0.8
0.2
0.4
0.6
Exercise 17.9 Consider the EM estimates for it
CS262A: Reasoning with Partial Beliefs
Solutions to HW#5
Exercise 14.1
(a) See Figure 1.
(b) See Figure 1.
(c) Pr(A = true|e) = 0.6 and Pr(B = true|e) = 0.3.
(d) The single-node marginals computed in Part (c) are the same when computed by marginalizing
fa
CS262A: Reasoning with Partial Beliefs
Solutions to HW#3
Exercise 6.2 Let e = cfw_C = true. Eliminating D, we nd that
f1 =
B
true
true
false
false
D|B =
D
D
D
true
false
true
false
D|B
B
0.75
0.25 = true
false
0.3
0.7
f1
1.0
1.0
which is simply an identit
CS 262A: Homework 2
March 14, 2016
1.
For every root variable X, any other root variable Y is not descendants of X. According to the
decomposition property, we have
IP r (X, , W ) for everyW Non Descendants(X)
So for every other root variable Y , we have