Learning Random Monotone DNF

Authors:
Jeffrey C. Jackson;Homin K. Lee;Rocco A. Servedio;Andrew Wan
Affiliations:
Duquesne University, Pittsburgh, PA 15282;Columbia University, New York, NY 10027;Columbia University, New York, NY 10027;Columbia University, New York, NY 10027
Venue:
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Year:
2008

Citing 19
Cited 2

A theory of the learnable

Communications of the ACM
Learning DNF under the uniform distribution in quasi-polynomial time

COLT '90 Proceedings of the third annual workshop on Computational learning theory
Learning monotone ku DNF formulas on product distributions

COLT '91 Proceedings of the fourth annual workshop on Computational learning theory
On learning monotone DNF formulae under uniform distributions

Information and Computation
Weakly learning DNF and characterizing statistical query learning using Fourier analysis

STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Learning Boolean formulas

Journal of the ACM (JACM)
An introduction to computational learning theory

An introduction to computational learning theory
On the Learnability of Disjunctive Normal Form Formulas

Machine Learning
An O(nlog log n) learning algorithm for DNF under the uniform distribution

Journal of Computer and System Sciences
On the Fourier spectrum of monotone functions

Journal of the ACM (JACM)
An efficient membership-query algorithm for learning DNF with respect to the uniform distribution

Journal of Computer and System Sciences
Learning Sub-classes of Monotone DNF on the Uniform Distribution

ALT '98 Proceedings of the 9th International Conference on Algorithmic Learning Theory
On Learning Monotone Boolean Functions under the Uniform Distribution

ALT '02 Proceedings of the 13th International Conference on Algorithmic Learning Theory
On Learning Monotone Boolean Functions

FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Machine Learning: My Favorite Results, Directions, and Open Problems

FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
On the noise sensitivity of monotone functions

Random Structures & Algorithms
On learning monotone DNF under product distributions

Information and Computation
Learning Random Log-Depth Decision Trees under Uniform Distribution

SIAM Journal on Computing
Learning Monotone Decision Trees in Polynomial Time

CCC '06 Proceedings of the 21st Annual IEEE Conference on Computational Complexity

Lower bounds on learning random structures with statistical queries

ALT'10 Proceedings of the 21st international conference on Algorithmic learning theory
On noise-tolerant learning of sparse parities and related problems

ALT'11 Proceedings of the 22nd international conference on Algorithmic learning theory

Quantified Score

Hi-index	0.00

Visualization

Abstract

We give an algorithm that with high probability properly learns random monotone DNF with t(n) terms of length ≈ logt(n) under the uniform distribution on the Boolean cube {0,1}n. For any function t(n) ≤ poly(n) the algorithm runs in time poly(n,1/茂戮驴) and with high probability outputs an 茂戮驴-accurate monotone DNF hypothesis. This is the first algorithm that can learn monotone DNF of arbitrary polynomial size in a reasonable average-case model of learning from random examples only.