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Factor Graphs [4 P]

Figure: Bayesian network for the lung cancer problem.
\includegraphics[width=10cm]{./fig_factorgraphs1.eps}\includegraphics[width=5cm]{./fig_factorgraphs2.eps}

Apply the sum-product algorithm to a Bayesian network for the lung cancer problem described in Figure 2. 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 $ P,S,C,D$ and $ X$ defined by the Bayesian network.

b)
All random variables in the graph are binary (or Boolean) variables $ x \in \{ 0,1\}$. The conditional distributions determined in a) can therefore be written in the form of the Bernoulli distribution

$\displaystyle Bern(x)=\mu^{x}(1-\mu)^{(1-x)}$

with parameter $ \mu$. Calculate the maximum likelihood value $ \mu_{ML}$ 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 graph obtained in c) to calculate the joined distributions of the query variables (black circles) given the indicated evidence (gray circles) for each of the four problem settings shown in Figure 2. Assume that the observed random variables always have the value 1 (or true in case of Boolean variables).


next up previous
Next: Parameter Learning in Bayesian Up: MLA_Exercises_2007 Previous: Naive Bayes Classifier [4
Haeusler Stefan 2007-12-03