Simple learning algorithms for decision trees and multivariate polynomials

Nader H. Bshouty, Yishay Mansour

Research output: Contribution to journalConference articlepeer-review

Abstract

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 ε-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.

Original languageEnglish
Pages (from-to)304-311
Number of pages8
JournalAnnual Symposium on Foundations of Computer Science - Proceedings
StatePublished - 1995
Externally publishedYes
EventProceedings of the 1995 IEEE 36th Annual Symposium on Foundations of Computer Science - Milwaukee, WI, USA
Duration: 23 Oct 199525 Oct 1995

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