Stable Learning via Sample Reweighting

TL;DR

This paper introduces a sample reweighting technique to reduce collinearity in linear models, enhancing stability and robustness when training and test data distributions differ.

Contribution

The paper proposes a novel data pretreatment method that improves the condition of the design matrix, applicable with any standard learning algorithm.

Findings

Improved stability of predictions across different data distributions.

Effective reduction of collinearity among input variables.

Demonstrated success on both simulated and real datasets.

Abstract

We consider the problem of learning linear prediction models with model misspecification bias. In such case, the collinearity among input variables may inflate the error of parameter estimation, resulting in instability of prediction results when training and test distributions do not match. In this paper we theoretically analyze this fundamental problem and propose a sample reweighting method that reduces collinearity among input variables. Our method can be seen as a pretreatment of data to improve the condition of design matrix, and it can then be combined with any standard learning method for parameter estimation and variable selection. Empirical studies on both simulation and real datasets demonstrate the effectiveness of our method in terms of more stable performance across different distributed data.