# Structural Learning

## (Tutorial)

Structural learning in Hugin is supported through the PC-algorithm. Consider the data file asia_no_e.dat for the ASIA_NO_E network. Figure 1 shows the first few lines of the data file.

Figure 1: The data file

The structural learning functionality is available under the "File" menu and through the structural learning icon. The structural learning icon is shown in figure 2.

Figure 2: The structural learning icon.

When the icon is depressed the structural learning window appears. Note that the field "Significance level" which specifies the significance level of the statistical independence tests performed during structural learning. Depress the "Select File" button and choose a file from which the structure is to be estimated. When the file is selected the "OK" button appears as shown in figure 3.

Figure 3: The structural learning window.

Depressing the "OK" button starts the structural learning algorithm. Based on the database of cases given in the file, the structural learning algorithm learns the structure of the graph of the Bayesian network. Figure 4 shows the result of structural learning based on the asia_no_e.dat file.

Figure 4: The learned Bayesian network graph.

The network graph from which the data file has been sampled is shown in figure 5. When comparing the original network graph with the learned network graph, it can be seen that the only difference is that the link from the "Visit to Asia"-node to the "Tuberculosis"-node is missing in the learned network graph. This is due to the fact, that the strength of the dependency between these two nodes is rather weak. If the "Significance Level Of Dependency Test" factor were set to a higher value, this link would most likely be identified as well. However, other (uncorrect) links may be identified as well if the "Significance Level Of Dependency Test" factor is raised.

Figure 5: The Bayesian network graph used for sampling the data file.

Once the structure of the graph of the Bayesian network has been constructed. The conditional probability distributions of the Bayesian network can be estimated from the data using the EM-learning algorithm, see the EM tutorial

| HUGIN Expert A/S | , 2001

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