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Improved NoiseTolerant Learning and Generalized Statistical Queries

Summary: Improved Noise­Tolerant Learning and
Generalized Statistical Queries
Javed A. Aslam # Scott E. Decatur +
Aiken Computation Laboratory
Harvard University
Cambridge, MA 02138
July 1994
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


Source: Aslam, Javed - College of Computer Science, Northeastern University


Collections: Computer Technologies and Information Sciences