Download AT HOME - Subbarao Kambhampati

CSE 471/598: Intro to Artificial Intelligence
(Instructor: Subbarao Kambhampati)
Spring 201
Name:________________________________
I certify that I did the “at-home” version of the test without consulting
anyone.
Signature:_____________________________
AT HOME VERSION IS OPEN BOOK/OPEN NOTES .
Total points: 75
****PLEASE WRITE LEGIBLY AND STAPLE ANSWERS IN THE CORRECT ORDER. (You
do not have to type the answers). You have to write your answers in the
space provided (use backsides if necessary).
Prop Logic (24pt)
Bayes Nets (29pt)
Planning Graph (10pt)
Short answer (12pt)
AT HOME
1
Propositional Logic
[3+2] Suppose we are trying to find a model satisfying all the following
clauses using Davis-Putnam procedure.
1. (~p, q)
2. (~q, r)
3. (r, j)
Part 1. If the procedure starts by setting p=True, show that it is able to
find a model without branching on any other variable.
Part 2. If we start with the complete assignment (p=True, q=False r=True,
j=False), what is its “score” (number of clauses satisfied) according to
min-conflicts algorithm?
[4pt]
Here is a piece of “Python logic”
Things made of wood float on water
Mary floats on water
--------We can infer that Mary is made of wood
Show, using truth tables, that this inference is “unsound” (you can use
just two propositional symbols “MW” (to stand for made of wood) and “FW”
(to stand for floats on water)
2
[15pt] Consider the following
If Rao is happy, he sets hard but interesting exams.
If Rao is not happy, he sets long and boring exams.
Prove: This exam is either hard but interesting or long and boring
(1)[3] Encode it into propositional logic (you need just 3 propositional
symbols—RH for rao’s happiness, HI for hard but interesting and LB for
long and boring).
(2)[4] Convert the sentences (including the appropriately converted goal
sentence) into clausal form.
(3)[6] Show a resolution refutation proof tree that proves the theorem.
(4)[1] Mark a resolution you did that has set of support.
(5)[1] Could this theorem have been proved with Modus Ponens?
3
Qn II [Swine flu in the South West][29pt] Suppose we are interested in
helping a hospital in Phoenix area in using bayes networks to help
diagnose flu.
The following is the knowledge about the domain:
Presence of H1N1 virus in the body typically (with probability 0.6) leads
to what is known as dispotensia (a weakening of T-cell resistance).
Dispotensia might often lead to a pathological condition called Flu (with
probability 0.8). Flu itself can lead to a variety of symptoms including:
Runny
nose
(probability
0.8),
body
aches(probability
0.6),
fever
(probability 0.5).
In phoenix area, during winter, H1N1 viruses are
typically present in humans (with probability 0.7). Finally, dispotensia
may be there even when there is no H1N1 virus (probability 0.3). Flu can
be caused even in the absence of dispotensia(probability 0.1). Runny nose
may be there in the absense of flu (prob 0.1), body aches may be there in
the absence of flu (0.3), and fever could be present in the absense of flu
(0.3).
Part A.[5+1+1] (1) Draw a bayes network for representing this knowledge.
Show the conditional probability tables at each node. (2) How many
probabilities did we avoid gathering because we used the bayes network
topology. (3) Is inference on this kind of network polynomial or
exponential in the size of the network?
Part B.[2] Dispotensia is not always caused by H1N1 virus. Sometimes
H1N1 virus may not cause dispotensia at all, if certain conditions
don't pre-exist in the patient. But the theory regarding this is not
yet complete. Some times, dispotensia may be caused by things other
than H1N1 virus. What, if any, changes do we need to make to the bayes net
above if we want to incorporate this knowledge?
4
Part C.[4] Use d-sep algorithm to show that H1N1 Virus is independent of
runny nose and body aches, given that the patient has flu. Use this and
any other obvious conditional independencies to compute the probability
that a random patient who has H1N1 virus and flu will have both runny nose
and body aches.
Now, suppose a patient walks into the hospital.
checked for anything.
She hasn’t yet been
Part D.[3] What is the probability that this patient is one sick puppy
(ie., has H1N1 virus, dyspotensia, flu, runny nose, body ache *and*
fever).
Part E.[8] Now you actually examine the patient and find out that she
has a runny nose, but no body aches and no fever. What is the
probability that she has Flu? (Use either the enumeration method or the
elimination method to compute the probability).
5
Part F [4] Suppose we decide to do inference by sampling techniques—
specifically likelihood weighting. Suppose we are trying to compute
probability that H1N1 Virus is true given that the patient has no fever
and no body aches. Suppose we generate a sample from the network using
likelihood weighting. Assume we sample the network in the order of H1N1
Virus, Dyspotensia, Flu, Runny Nose, Body Aches and Fever. Suppose our
samples return True, False, False, True, True, False (take only the
samples you need). What is the complete sample and what is its weight?
6
Qn III.[10][Planning Graph]
Consider a
simple planning domain with just two actions, A and B
A has precondition P. As effects, it deletes P and adds Q
B has precondition ~P (i.e., P must be false). As effects it adds P
Suppose the agent is at an intial state where P is true and Q is false.
(1)
(a) (For this part, you don’t need to mark/propagate mutexes)
Draw a planning graph upto two levels (i.e., two action levels and
two proposition levels, in addition to the initial state). (b) Do
you think the graph has leveled-off? Why? (c) What is the heuristic
value of getting P & Q using level heuristic? (d) Mark a “relaxed
plan” in the graph for supporting P and Q. What is its length?
(2)
In the graph above, mark the mutex status of P and Q at each
level. (You don’t need to mark other mutexes unless they are needed
to mark P and Q correctly)
7
Qn IV Short Answer Questions [12] 2 points per question. For T/F
questions You must justify your answers to get points.
1. [T/F]Given a database D and a fact f, if D does not entail f, then D
entails ~f.
2. [T/F] Min-conflict based SAT algorithms can be used as an efficient
basis for computing propositional entailment.
3. Consider an uncertain world where there are n state-variables, an
intelligent agent has the best chance of success if all the
variables are independent, as this is the case where the fewest
number of probabilities (n) are needed to specify the joint
distribution.
4.
[True/False--explain] The “phase-transition” behavior of CSP
problems is surprising because plotted against R, the ratio of
number of constraints to number of variables, the hardest problems
lie not at the highest or lowest values of R, but in the middle.
5 [4] Given a bayes network
ABC, show, using bayes rule and
definition of conditional probabilities, that A is conditionally
independent C given B.
8