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 homepage

- 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
- 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).