Dynamic programming approach to optimization of approximate decision rules

  • Authors:

  • Talha Amin;Igor Chikalov;Mikhail Moshkov;Beata Zielosko

  • Affiliations:

  • Mathematical and Computer Sciences & Engineering Division, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia;Mathematical and Computer Sciences & Engineering Division, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia;Mathematical and Computer Sciences & Engineering Division, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia;Mathematical and Computer Sciences & Engineering Division, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia and Institute of Computer Science, University of Sile ...

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2013

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Abstract

This paper is devoted to the study of an extension of dynamic programming approach which allows sequential optimization of approximate decision rules relative to the length and coverage. We introduce an uncertainty measure R(T) which is the number of unordered pairs of rows with different decisions in the decision table T. For a nonnegative real number @b, we consider @b-decision rules that localize rows in subtables of T with uncertainty at most @b. Our algorithm constructs a directed acyclic graph @D"@b(T) which nodes are subtables of the decision table T given by systems of equations of the kind ''attribute=value''. This algorithm finishes the partitioning of a subtable when its uncertainty is at most @b. The graph @D"@b(T) allows us to describe the whole set of so-called irredundant @b-decision rules. We can describe all irredundant @b-decision rules with minimum length, and after that among these rules describe all rules with maximum coverage. We can also change the order of optimization. The consideration of irredundant rules only does not change the results of optimization. This paper contains also results of experiments with decision tables from UCI Machine Learning Repository.