A Theoretical Analysis on Independence-driven Importance Weighting for Covariate-shift Generalization
This work provides theoretical foundations for a method used in out-of-distribution generalization, addressing a gap in stable learning literature, but it is incremental as it focuses on analysis rather than new algorithms.
The paper tackles the lack of theoretical analysis for independence-driven importance weighting algorithms in covariate-shift generalization by proving their effectiveness as feature selection processes, identifying a minimal stable variable set and validating the theories with synthetic experiments.
Covariate-shift generalization, a typical case in out-of-distribution (OOD) generalization, requires a good performance on the unknown test distribution, which varies from the accessible training distribution in the form of covariate shift. Recently, independence-driven importance weighting algorithms in stable learning literature have shown empirical effectiveness to deal with covariate-shift generalization on several learning models, including regression algorithms and deep neural networks, while their theoretical analyses are missing. In this paper, we theoretically prove the effectiveness of such algorithms by explaining them as feature selection processes. We first specify a set of variables, named minimal stable variable set, that is the minimal and optimal set of variables to deal with covariate-shift generalization for common loss functions, such as the mean squared loss and binary cross-entropy loss. Afterward, we prove that under ideal conditions, independence-driven importance weighting algorithms could identify the variables in this set. Analysis of asymptotic properties is also provided. These theories are further validated in several synthetic experiments.