Proceedings of IEEE 36th Annual Foundations of Computer Science (1995)
Oct. 23, 1995 to Oct. 25, 1995
N.H. Bshouty , Dept. of Comput. Sci., Calgary Univ., Alta., Canada
Y. Mansour , Dept. of Comput. Sci., Calgary Univ., Alta., Canada
In this paper we develop a new approach for learning decision trees and multivariate polynomials via interpolation of multivariate polynomials. This new approach yields simple learning algorithms for multivariate polynomials and decision trees over finite fields under any constant bounded product distribution. The output hypothesis is a (single) multivariate polynomial that is an /spl epsiv/-approximation of the target under any constant bounded product distribution. The new approach demonstrates the learnability of many classes under any constant bounded product distribution and using membership queries, such as j-disjoint DNF and multivariate polynomial with bounded degree over any field. The technique shows how to interpolate multivariate polynomials with bounded term size from membership queries only. This in particular gives a learning algorithm for O(log n)-depth decision tree from membership queries only and a new learning algorithm of any multivariate polynomial over sufficiently large fields from membership queries only. We show that our results for learning from membership queries only are the best possible.
polynomials; interpolation; learning (artificial intelligence); decision theory; learning algorithms; decision trees; multivariate polynomials; interpolation; finite fields; constant bounded product distribution; /spl epsiv/-approximation; learnability; membership queries; j-disjoint DNF; bounded degree; bounded term size
N. Bshouty and Y. Mansour, "Simple learning algorithms for decision trees and multivariate polynomials," Proceedings of IEEE 36th Annual Foundations of Computer Science(FOCS), Milwaukee, Wisconsin, 1995, pp. 304.