# Sparse joint shift in multinomial classification

arXiv: https://arxiv.org/abs/2303.16971 · HTML: https://mlsanity.com/paper/2303.16971/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 30 references that are in the map.
- First posted on arXiv 29 Mar 2023.

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

- [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)
- [Estimating and Explaining Model Performance When Both Covariates and Labels Shift](https://mlsanity.com/paper/2209.08436/) (2022)
- [Mapping conditional distributions for domain adaptation under generalized target shift](https://mlsanity.com/paper/2110.15057/) (2021)
- [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)
- [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)
- [Factorizable Joint Shift in Multinomial Classification](https://mlsanity.com/paper/2207.14514/) (2022)

## Built on by (most cited first, 5 of 5)

- [Invariance assumptions for class distribution estimation](https://mlsanity.com/paper/2311.17225/) (2023)
- [Mining Invariance from Nonlinear Multi-Environment Data: Binary Classification](https://mlsanity.com/paper/2404.15245/) (2024)
- [A generalized approach to label shift: the Conditional Probability Shift Model](https://mlsanity.com/paper/2503.02583/) (2025)
- [Factorizable joint shift revisited](https://mlsanity.com/paper/2601.15036/) (2026)
- [Entropic Projection Alignment: Estimating, Explaining, and Improving Model Performance Under Distribution Shift](https://mlsanity.com/paper/2605.31250/) (2026)

## Abstract (arXiv)

Sparse joint shift (SJS) was recently proposed as a tractable model for general dataset shift which may cause changes to the marginal distributions of features and labels as well as the posterior probabilities and the class-conditional feature distributions. Fitting SJS for a target dataset without label observations may produce valid predictions of labels and estimates of class prior probabilities. We present new results on the transmission of SJS from sets of features to larger sets of features, a conditional correction formula for the class posterior probabilities under the target distribution, identifiability of SJS, and the relationship between SJS and covariate shift. In addition, we point out inconsistencies in the algorithms which were proposed for estimating the characteristics of SJS, as they could hamper the search for optimal solutions, and suggest potential improvements.