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##

Discrete variables of arbitrary arity

We briefly describe the extension of the ACCL algorithm
to the case of discrete domains in which the variables can take more
than two values.
First we extend the definition of data sparseness: we assume that
for each variable there exists a special value that appears with
higher frequency than all the other values. This value will be denoted
by 0, without loss of generality. For example, in a medical domain,
the value 0 for a variable would represent the ``normal'' value,
whereas the abnormal values of each variable would be designated by
non-zero values. An ``occurrence'' for variable will be the event
and a ``co-occurrence'' of and means that and are
both non-zero for the same data point. We define as the number of
non-zero values in observation . The sparseness is, as
before, the maximum of over the data set.
To exploit the high frequency of the zero values we represent
only the occurrences explicitly, creating thereby a compact and
efficient data structure. We obtain performance gains by
presorting mutual information values for non-co-occurring variables.

**Subsections**

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Journal of Machine Learning Research
2000-10-19