Machine Learning

, Volume 2, Issue 4, pp 285–318

Learning quickly when irrelevant attributes abound: A new linear-threshold algorithm

  • Nick Littlestone

DOI: 10.1007/BF00116827

Cite this article as:
Littlestone, N. Mach Learn (1988) 2: 285. doi:10.1007/BF00116827


Valiant (1984) and others have studied the problem of learning various classes of Boolean functions from examples. Here we discuss incremental learning of these functions. We consider a setting in which the learner responds to each example according to a current hypothesis. Then the learner updates the hypothesis, if necessary, based on the correct classification of the example. One natural measure of the quality of learning in this setting is the number of mistakes the learner makes. For suitable classes of functions, learning algorithms are available that make a bounded number of mistakes, with the bound independent of the number of examples seen by the learner. We present one such algorithm that learns disjunctive Boolean functions, along with variants for learning other classes of Boolean functions. The basic method can be expressed as a linear-threshold algorithm. A primary advantage of this algorithm is that the number of mistakes grows only logarithmically with the number of irrelevant attributes in the examples. At the same time, the algorithm is computationally efficient in both time and space.


Learning from examplespredictionincremental learningmistake boundslearning Boolean functionslinear-threshold algorithms
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Copyright information

© Kluwer Academic Publishers 1988

Authors and Affiliations

  • Nick Littlestone
    • 1
  1. 1.Department of Computer and Information SciencesUniversity of CaliforniaSanta CruzU.S.A.