 
Summary: Improved NoiseTolerant Learning and
Generalized Statistical Queries
Javed A. Aslam # Scott E. Decatur +
Aiken Computation Laboratory
Harvard University
Cambridge, MA 02138
July 1994
Abstract
The statistical query learning model can be viewed as a tool for creating (or demon
strating the existence of) noisetolerant learning algorithms in the PAC model. The
complexity of a statistical query algorithm, in conjunction with the complexity of sim
ulating SQ algorithms in the PAC model with noise, determine the complexity of the
noisetolerant PAC algorithms produced. Although roughly optimal upper bounds have
been shown for the complexity of statistical query learning, the corresponding noise
tolerant PAC algorithms are not optimal due to ine#cient simulations. In this paper
we provide both improved simulations and a new variant of the statistical query model
in order to overcome these ine#ciencies.
We improve the time complexity of the classification noise simulation of statistical
query algorithms. Our new simulation has a roughly optimal dependence on the noise
rate. We also derive a simpler proof that statistical queries can be simulated in the
