# Factorizable joint shift revisited

arXiv: https://arxiv.org/abs/2601.15036 · HTML: https://mlsanity.com/paper/2601.15036/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 54 references that are in the map.
- First posted on arXiv 21 Jan 2026.

## Builds on (most cited first, 16 of 16)

- [Detecting and Correcting for Label Shift with Black Box Predictors](https://mlsanity.com/paper/1802.03916/) (2018)
- [A review of domain adaptation without target labels](https://mlsanity.com/paper/1901.05335/) (2019)
- [Domain Adaptation with Conditional Distribution Matching and Generalized Label Shift](https://mlsanity.com/paper/2003.04475/) (2020)
- [Support and Invertibility in Domain-Invariant Representations](https://mlsanity.com/paper/1903.03448/) (2019)
- [A Generalized Neyman-Pearson Criterion for Optimal Domain Adaptation](https://mlsanity.com/paper/1810.01545/) (2018)
- [Fisher consistency for prior probability shift](https://mlsanity.com/paper/1701.05512/) (2017)
- [Estimating and Explaining Model Performance When Both Covariates and Labels Shift](https://mlsanity.com/paper/2209.08436/) (2022)
- [Importance Weight Estimation and Generalization in Domain Adaptation under Label Shift](https://mlsanity.com/paper/2011.14251/) (2020)
- [Calibrating sufficiently](https://mlsanity.com/paper/2105.07283/) (2021)
- [Domain Adaptation with Factorizable Joint Shift](https://mlsanity.com/paper/2203.02902/) (2022)
- [Sparse joint shift in multinomial classification](https://mlsanity.com/paper/2303.16971/) (2023)
- [Prominent Roles of Conditionally Invariant Components in Domain Adaptation: Theory and Algorithms](https://mlsanity.com/paper/2309.10301/) (2023)
- [Factorizable Joint Shift in Multinomial Classification](https://mlsanity.com/paper/2207.14514/) (2022)
- [Exact fit of simple finite mixture models](https://mlsanity.com/paper/1406.6038/) (2014)
- [Kernel Density Machines](https://mlsanity.com/paper/2504.21419/) (2025)
- [Recalibrating binary probabilistic classifiers](https://mlsanity.com/paper/2505.19068/) (2025)

## Abstract (arXiv)

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.