# Class Prior Estimation under Covariate Shift: No Problem?

arXiv: https://arxiv.org/abs/2206.02449 · HTML: https://mlsanity.com/paper/2206.02449/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 31 references that are in the map.
- First posted on arXiv 6 Jun 2022.

## Builds on (most cited first, 8 of 8)

- [Detecting and Correcting for Label Shift with Black Box Predictors](https://mlsanity.com/paper/1802.03916/) (2018)
- [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)
- [Domain Adaptation with Factorizable Joint Shift](https://mlsanity.com/paper/2203.02902/) (2022)
- [Minimising quantifier variance under prior probability shift](https://mlsanity.com/paper/2107.08209/) (2021)
- [Exact fit of simple finite mixture models](https://mlsanity.com/paper/1406.6038/) (2014)

## Built on by (most cited first, 10 of 10)

- [Binary Quantification and Dataset Shift: An Experimental Investigation](https://mlsanity.com/paper/2310.04565/) (2023)
- [Sparse joint shift in multinomial classification](https://mlsanity.com/paper/2303.16971/) (2023)
- [Factorizable Joint Shift in Multinomial Classification](https://mlsanity.com/paper/2207.14514/) (2022)
- [Invariance assumptions for class distribution estimation](https://mlsanity.com/paper/2311.17225/) (2023)
- [Quantification using Permutation-Invariant Networks based on Histograms](https://mlsanity.com/paper/2403.15123/) (2024)
- [On the Interconnections of Calibration, Quantification, and Classifier Accuracy Prediction under Dataset Shift](https://mlsanity.com/paper/2505.11380/) (2025)
- [Distribution Matching for Graph Quantification Under Structural Covariate Shift](https://mlsanity.com/paper/2601.00864/) (2025)
- [Quantifying Feature Importance for Online Content Moderation](https://mlsanity.com/paper/2510.19882/) (2025)
- [Multicalibration for Unbiased Model-Based Prevalence Estimation](https://mlsanity.com/paper/2604.21549/) (2026)
- [Geometry-Aware Bayesian Quantification via Compositional Data Analysis](https://mlsanity.com/paper/2607.04977/) (2026)

## Abstract (arXiv)

We show that in the context of classification the property of source and target distributions to be related by covariate shift may be lost if the information content captured in the covariates is reduced, for instance by dropping components or mapping into a lower-dimensional or finite space. As a consequence, under covariate shift simple approaches to class prior estimation in the style of classify and count with or without adjustment are infeasible. We prove that transformations of the covariates that preserve the covariate shift property are necessarily sufficient in the statistical sense for the full set of covariates. A probing algorithm as alternative approach to class prior estimation under covariate shift is proposed.