Next: Bonus example: Moral graph Up: MLA_Exercises_2009 Previous: Inference in Factor Graphs

# Inference in Factor Graphs II [2+2* P]

Apply the sum-product algorithm to a Bayesian network for the lung cancer problem described in Figure 3. The lung cancer dataset is available for download on the course homepage2. See lungcancer.txt for a description of the data set. You are required to use MATLAB for this assignment.

a)
Write down the joint distribution over the five random variables and defined by the Bayesian network.

b)
All random variables in the graph are binary (or Boolean) variables . The conditional distributions determined in a) can therefore be written in the form of the Bernoulli distribution

with parameter . Calculate the maximum likelihood value for each of the conditional distributions from the data.

c)
Construct a factor graph from the Bayesian network.

d)
Apply the sum-product algorithm to the factor graphs obtained in c) for the two problem settings shown in the bottom panels of Figure 3 to calculate the marginal distributions of the query variables (black circles) given the indicated evidence (gray circles). Assume that the observed random variables always have the value 1 (or true in case of Boolean variables).

e)
[2* P] Apply the sum-product algorithm to the factor graphs obtained in c) for the two problem settings shown in the top panels of Figure 3 to calculate the joined distributions of the query variables (black circles) given the indicated evidence (gray circles). Assume that the observed random variables always have the value 1 (or true in case of Boolean variables).

Next: Bonus example: Moral graph Up: MLA_Exercises_2009 Previous: Inference in Factor Graphs
Haeusler Stefan 2010-01-26