The Set Covering Machine

Mario Marchand, John Shawe-Taylor; 3(Dec):723-746, 2002.


We extend the classical algorithms of Valiant and Haussler for learning compact conjunctions and disjunctions of Boolean attributes to allow features that are constructed from the data and to allow a trade-off between accuracy and complexity. The result is a general-purpose learning machine, suitable for practical learning tasks, that we call the set covering machine. We present a version of the set covering machine that uses data-dependent balls for its set of features and compare its performance with the support vector machine. By extending a technique pioneered by Littlestone and Warmuth, we bound its generalization error as a function of the amount of data compression it achieves during training. In experiments with real-world learning tasks, the bound is shown to be extremely tight and to provide an effective guide for model selection.

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