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We provide a very sparse data structure, the ADtree, to minimize memory use. We provide analytical worst-case bounds for this structure for several models of data distribution. We empirically demonstrate that tractably-sized data structures can be produced for large real-world datasets by (a) using a sparse tree structure that never allocates memory for counts of zero, (b) never allocating memory for counts that can be deduced from other counts, and (c) not bothering to expand the tree fully near its leaves.
We show how the ADtree can be used to accelerate Bayes net structure finding algorithms, rule learning algorithms, and feature selection algorithms, and we provide a number of empirical results comparing ADtree methods against traditional direct counting approaches. We also discuss the possible uses of ADtrees in other machine learning methods, and discuss the merits of ADtrees in comparison with alternative representations such as kd-trees, R-trees and Frequent Sets.