Learning DNFs under product distributions via {\mu}-biased quantum Fourier sampling
Quantum Physics
2019-11-27 v3 Discrete Mathematics
Machine Learning
Abstract
We show that DNF formulae can be quantum PAC-learned in polynomial time under product distributions using a quantum example oracle. The best classical algorithm (without access to membership queries) runs in superpolynomial time. Our result extends the work by Bshouty and Jackson (1998) that proved that DNF formulae are efficiently learnable under the uniform distribution using a quantum example oracle. Our proof is based on a new quantum algorithm that efficiently samples the coefficients of a {\mu}-biased Fourier transform.
Keywords
Cite
@article{arxiv.1802.05690,
title = {Learning DNFs under product distributions via {\mu}-biased quantum Fourier sampling},
author = {Varun Kanade and Andrea Rocchetto and Simone Severini},
journal= {arXiv preprint arXiv:1802.05690},
year = {2019}
}
Comments
17 pages; v3 based on journal version; minor corrections and clarifications