In this problem you will analyze a very simple artificially created data set from the book Web site http://www.csse.monash.edu.au/bai.html which was created by a v-structure process X ! Y Z — i.e., one with three variables of which one is the child of the other two which are themselves not directly related. However, it will be instructive if you also locate a real data set generated by a similar v-structure process and answer the questions for both data sets.

Parameterize the Bayesian network X ! Y Z from the data set in at least two of the following ways:

 using the algorithm for the full CPT, that is, Algorithm 6.1

 using a noisy-or parameterization

 using a classification tree algorithm, such as J48 (available from the WEKA Web site: http://www.cs.waikato.ac.nz/˜ ml/weka/)

 using an order 1 logit model Compare the results. Which parameterization fits the data better? For example, which one gives better classification accuracy?

Since in answering this last question you have (presumably) used the very same data both to parameterize the network and to test it, a close fit to the data may be more an indication of overfitting than of predictive accuracy. In order to test a model’s generalization accuracy you can divide the data set into a training set and a test set, using only the former to parameterize it and the latter to test predictive (classification)

accuracy (see Part II introduction).

Programming Problems