An Optimal Approach to Mining Boolean Functions from Noisy Data

Abstract

Data Mining of binary sequences has been an area of profound research and is often used as a proof of concept in various aspects of computational learning theory. The inference task in this paper, a specialized version of the segmentation problem, is the estimation of a predefined Boolean function on the real interval [0,1] from a noisy random sample. The framework for this problem was introduced by Kearns et al. (1997) in an earlier empirical evaluation of model selection methods. This paper presents an optimal approach to mining for Boolean functions from noisy data samples based on the Minimum Message Length (MML) principle. The MML method is shown to be optimal in comparison to well-known model selection methods based on Guaranteed Risk Minimization, Minimum Description Length (MDL) Principle and Cross Validation after a thorough empirical evaluation with varying levels of noisy data.