Factorizable joint shift revisited

TL;DR

This paper revisits factorizable joint shift, extending analysis from categorical labels to general label spaces, and explores its relation to generalized label shift and EM algorithms.

Contribution

It introduces a framework for analyzing distribution shift with general label spaces, generalizes existing FJS results, and examines extensions to label distribution estimation.

Findings

Extended FJS analysis to regression and classification.

Generalized FJS results for broader label spaces.

Analyzed EM algorithm extensions for class prior estimation.

Abstract

Factorizable joint shift (FJS) represents a type of distribution shift (or dataset shift) that comprises both covariate and label shift. Recently, it has been observed that FJS actually arises from consecutive label and covariate (or vice versa) shifts. Research into FJS so far has been confined mostly to the case of categorical labels. We propose a framework for analysing distribution shift in the case of a general label space, thus covering both classification and regression models. Based on the framework, we generalise existing results on FJS to general label spaces and present and analyse a related extension to label distribution estimation of the expectation maximisation (EM) algorithm for class prior probabilities. We also take a fresh look at generalized label shift (GLS) in the case of a general label space.