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Figure 17 presents a summary of the
tree structures learned from the dataset in
the form of a cumulated adjacency matrix. The adjacency matrices of
the 20 graph structures obtained in the experiment have been summed.
The size of the black square at coordinates in the figure
is proportional to the value of the -th element of the
cumulated adjacency matrix. No square means that the
respective element is 0. Since the adjacency matrix is
symmetric, only half of the matrix is shown. From
Figure 17 we see that the tree structure is
very stable over the 20 trials. Variable 0 represents the class
variable; the hypothetical splice junction is situated between variables
30 and 31. The figure shows that the splice junction (variable 0)
depends only on DNA sites that are in its vicinity. The sites that
are remote from the splice junction are dependent on their immediate
neighbors. Moreover, examining the tree parameters, for the edges
adjacent to the class variable, we observe that these variables build
certain patterns when the splice junction is present, but are random
and almost uniformly distributed in the absence of a splice
junction. The patterns extracted from the learned trees are shown in
Figure 18. The same figure displays the ``true''
encodings of the IE and EI junctions as given by watson:87. The
match between the two encodings is almost perfect. Thus, we can
conclude that for this domain, the tree model not only provides a good
classifier but also discovers a model of the physical reality
underlying the data. Note that the algorithm arrives at this
result in the absence of prior knowledge: (1) it does not know
which variable is the class variable, and (2) it does not know that
the variables are in a sequence (i.e., the same result would be obtained if
the indices of the variables were scrambled).

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Journal of Machine Learning Research
2000-10-19