On the boosting ability of top-down decision tree learning algorithms
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Learning functions represented as multiplicity automata
Journal of the ACM (JACM)
Decision tree approximations of Boolean functions
Theoretical Computer Science
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 2
Algorithms and theory of computation handbook
| Hi-index | 0.00 |
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.