# Factorizable Joint Shift in Multinomial Classification

arXiv: https://arxiv.org/abs/2207.14514 · HTML: https://mlsanity.com/paper/2207.14514/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 25 references that are in the map.
- First posted on arXiv 29 Jul 2022.

## Builds on (most cited first, 9 of 9)

- [Detecting and Correcting for Label Shift with Black Box Predictors](https://mlsanity.com/paper/1802.03916/) (2018)
- [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)
- [Calibrating sufficiently](https://mlsanity.com/paper/2105.07283/) (2021)
- [Class Prior Estimation under Covariate Shift: No Problem?](https://mlsanity.com/paper/2206.02449/) (2022)
- [Domain Adaptation with Factorizable Joint Shift](https://mlsanity.com/paper/2203.02902/) (2022)
- [The Law of Total Odds](https://mlsanity.com/paper/1312.0365/) (2013)

## Built on by (most cited first, 4 of 4)

- [Sparse joint shift in multinomial classification](https://mlsanity.com/paper/2303.16971/) (2023)
- [Invariance assumptions for class distribution estimation](https://mlsanity.com/paper/2311.17225/) (2023)
- [Recalibrating binary probabilistic classifiers](https://mlsanity.com/paper/2505.19068/) (2025)
- [Factorizable joint shift revisited](https://mlsanity.com/paper/2601.15036/) (2026)

## Abstract (arXiv)

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.