CS 1571: Homework 4 (written)
Planning, Uncertainty and Probabilistic Reasoning
(Chapters 10, 13-14)
Assigned: November 15, 2017
Due: December 1 , 2017
1. Planning (25 pts)
Consider the following simple domain:
Initial State: A, B, C
Goal: C, D, E
Operator O1 Preconditions: A; Add Effects: F; Delete Effects: C
Operator O2 Preconditions: A; Add Effects: D; Delete Effects: B
Operator O3 Preconditions: B; Add Effects: C
Operator O4 Preconditions: F; Add Effects: D, E, G
(a) State-Space Search: Draw the full search tree with a depth limit=2 in a forward progression state-space search (assume no
repeated states). For full credit, be sure to show the list of
predicates (or the equivalent graphical representation of the blocks)
for each state, and explicitly label the actions that get you from one
state to another (as in Figure 10.5). State whether your search finds a plan which achieves the goal, and why?
(b) Partially Ordered Planning:
Show the final plan that would be output by a partial-order regression planner for this problem (as in Figure 10.13c). Give an example of one linearization of the partial-order plan.
2. Probability (15 pts)
13.8 (Russell and Norvig, p. 507)
3. Probability (15 pts)
Of the entire population, 2% has a certain disease X. A test Y, which
indicates whether or not a person has the disease, is not 100%
accurate. If a person has the disease, there is a 6% chance that it
will go undetected by the test. However, there is also a 9% chance of
"false alarm" (meaning that the person does not have the disease but
the test indicates otherwise). A person Z takes a test which later
comes out positive (meaning that the test says he has the
disease). What is the probability of this person having the disease in
reality?
4. Bayesian Networks (25 pts)
14.8 a, b, c, d (Russell and Norvig, p. 561). Here is some relevant car
knowledge: Icy weather is not caused by any car-related variables,
but it directly affects the battery and the starter motor. The starter
motor in turn directly impacts whether the car starts.
In addition, answer the following questions using the original
network topology (that is in Figure 14.21) rather than the extension
used above.
Give the expression for the full joint probability
for: Battery=T, Radio=T, Ignition=T, Gas=F, Starts=T, Moves=F.
Assume we want to compute the probability of the car not moving, that
is P(Moves = False). Write down the expression for computing the
probability from conditionals.
5. Diagnosis using Bayesian Networks (20 pts)
Assume a Bayesian network with 5 boolean random variables, where the
topology represents that Pneumonia causes Fever, Paleness, Cough, and
HighWBCcount. The associated CPT are as follows:
P(Pneumonia = True) = 0.02
P(Fever = True|Pneumonia = True) = 0.9
P(Fever = True|Pneumonia = False) = 0.6
P(Paleness = True|Pneumonia = True) = 0.7
P(Paleness = True|Pneumonia = False) = 0.5
P(Cough = True|Pneumonia = True) = 0.9
P(Cough = True|Pneumonia = False) = 0.1
P(HighWBCcount = True|Pneumonia = True) = 0.8
P(HighWBCcount = True|Pneumonia = False) = 0.5
Assume that you have the following set of symptoms: Fever and Cough
are true; Paleness and HighWBCcount are false. What is the probability
P(Pneumonia = T|Fever = T, Paleness = F, Cough = T,HighWBCcount = F),
that is, the probability that you suffer from Pneumonia, given the
symptoms? Simplify the expression as much as possible before plugging
in the values.