Sample Selection Bias Correction Theory

TL;DR

This paper provides a theoretical framework for understanding how errors in estimating weights for sample bias correction affect machine learning accuracy, introducing the concept of distributional stability.

Contribution

It introduces the novel concept of distributional stability to analyze the impact of estimation errors on bias correction techniques in machine learning.

Findings

Estimation errors can significantly affect hypothesis accuracy.

Distributional stability generalizes point-based stability.

Experimental results validate the theoretical analysis.

Abstract

This paper presents a theoretical analysis of sample selection bias correction. The sample bias correction technique commonly used in machine learning consists of reweighting the cost of an error on each training point of a biased sample to more closely reflect the unbiased distribution. This relies on weights derived by various estimation techniques based on finite samples. We analyze the effect of an error in that estimation on the accuracy of the hypothesis returned by the learning algorithm for two estimation techniques: a cluster-based estimation technique and kernel mean matching. We also report the results of sample bias correction experiments with several data sets using these techniques. Our analysis is based on the novel concept of distributional stability which generalizes the existing concept of point-based stability. Much of our work and proof techniques can be used to analyze other importance weighting techniques and their effect on accuracy when using a distributionally stable algorithm.