Factorizable Joint Shift in Multinomial Classification

TL;DR

This paper characterizes factorizable joint shift in multinomial classification, derives related correction formulas, and discusses identifiability issues when test labels are unavailable, advancing understanding of dataset shift adaptation.

Contribution

It provides a new representation of factorizable joint shift, proposes alternative methods to joint importance aligning, and analyzes the impact of assumptions on bias correction.

Findings

Representation of factorizable joint shift in terms of source and target distributions

Correction formulas for posterior class probabilities under shift

Identifiability issues without test labels or additional assumptions

Abstract

Factorizable joint shift (FJS) was recently proposed as a type of dataset shift for which the complete characteristics can be estimated from feature data observations on the test dataset by a method called Joint Importance Aligning. For the multinomial (multiclass) classification setting, we derive a representation of factorizable joint shift in terms of the source (training) distribution, the target (test) prior class probabilities and the target marginal distribution of the features. On the basis of this result, we propose alternatives to joint importance aligning and, at the same time, point out that factorizable joint shift is not fully identifiable if no class label information on the test dataset is available and no additional assumptions are made. Other results of the paper include correction formulae for the posterior class probabilities both under general dataset shift and factorizable joint shift. In addition, we investigate the consequences of assuming factorizable joint shift for the bias caused by sample selection.