AA228/CS238: Decision Making under Uncertainty
Autumn 2016
Prof. Mykel J. Kochenderfer • Durand 255 • email: aa228-aut1617- .edu
MIDTERM 1 Due date: October 12
You have 60 minutes to complete this exam. You may use one page of notes (front and back) but
no other resources. Each question part (a) and (b) are independent of each other, unless explicitly stated
otherwise. All questions are weighted equally.
1. Probabilistic representations
(a) Suppose we have a Bayesian network A→ B → C ← D. Add one additional variable E and two
directed edges to this network such that A is not conditionally independent of D given E.
(b) If all the variables in the network you drew for part (a) are binary, how many independent
parameters are required to specify the joint distribution.
2. Probabilistic inference
(a) Suppose we are using likelihood weighted sampling to infer P (a0 | c1). Given the Bayesian network
A → B → C ← D, write down a single sample from the distribution along with its weight.
You do not need to provide numerical values for the weights; just write down the equation for
calculating the weight for that particular sample. (The weights have to be a function of conditional
probabilities directly associated with the Bayes net.)
(b) Can the choice of variable elimination ordering affect the accuracy of inference when the variable
elimination algorithm is used? What advantage can one ordering provide over another?
3. Parameter learning
(a) Suppose we have two binary variables, one that indicates whether a student is taking AA228 and
another that indicates whether the student is happy. We have a data set D with n students. Of
these n students, m of them are taking AA228. Of the n students, k of them are happy. Of
course, all of the students taking AA228 are happy. What is the maximum likelihood estimate of
the probability that a student is jointly not taking AA228 and not happy?
(b) When would you use a Dirichlet distribution instead of a Beta distribution?
4. Structure learning
(a) Draw three Bayes nets involving the variables A, B, C, D, E, and F such that all three structures
are within one graph operation of all others.
(b) Draw two distinct directed acyclic graphs that are Markov equivalent, both with at least five
edges.
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