# Fisher consistency for prior probability shift

arXiv: https://arxiv.org/abs/1701.05512 · HTML: https://mlsanity.com/paper/1701.05512/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jan 2017.

## Built on by (most cited first, 20 of 20)

- [A Comparative Evaluation of Quantification Methods](https://mlsanity.com/paper/2103.03223/) (2021)
- [Class Prior Estimation under Covariate Shift: No Problem?](https://mlsanity.com/paper/2206.02449/) (2022)
- [Measuring Fairness Under Unawareness of Sensitive Attributes: A Quantification-Based Approach](https://mlsanity.com/paper/2109.08549/) (2021)
- [Monitoring Model Deterioration with Explainable Uncertainty Estimation via Non-parametric Bootstrap](https://mlsanity.com/paper/2201.11676/) (2022)
- [Binary Quantification and Dataset Shift: An Experimental Investigation](https://mlsanity.com/paper/2310.04565/) (2023)
- [Efficient and Multiply Robust Risk Estimation under General Forms of Dataset Shift](https://mlsanity.com/paper/2306.16406/) (2023)
- [Minimising quantifier variance under prior probability shift](https://mlsanity.com/paper/2107.08209/) (2021)
- [Factorizable Joint Shift in Multinomial Classification](https://mlsanity.com/paper/2207.14514/) (2022)
- [Bayesian Quantification with Black-Box Estimators](https://mlsanity.com/paper/2302.09159/) (2023)
- [ReTaSA: A Nonparametric Functional Estimation Approach for Addressing Continuous Target Shift](https://mlsanity.com/paper/2401.16410/) (2024)
- [Adjusted Count Quantification Learning on Graphs](https://mlsanity.com/paper/2503.09395/) (2025)
- [Efficient quantification on large-scale networks](https://mlsanity.com/paper/2503.15267/) (2025)
- [Recalibrating binary probabilistic classifiers](https://mlsanity.com/paper/2505.19068/) (2025)
- [Distribution Matching for Graph Quantification Under Structural Covariate Shift](https://mlsanity.com/paper/2601.00864/) (2025)
- [A Symmetric Loss Perspective of Reliable Machine Learning](https://mlsanity.com/paper/2101.01366/) (2021)
- [A Domain-Region Based Evaluation of ML Performance Robustness to Covariate Shift](https://mlsanity.com/paper/2304.08855/) (2023)
- [Continuous Sweep for Binary Quantification Learning](https://mlsanity.com/paper/2308.08387/) (2023)
- [Theory-inspired Label Shift Adaptation via Aligned Distribution Mixture](https://mlsanity.com/paper/2411.02047/) (2024)
- [Unsupervised Domain Adaptation for Binary Classification with an Unobservable Source Subpopulation](https://mlsanity.com/paper/2509.20587/) (2025)
- [Factorizable joint shift revisited](https://mlsanity.com/paper/2601.15036/) (2026)

## Abstract (arXiv)

We introduce Fisher consistency in the sense of unbiasedness as a desirable property for estimators of class prior probabilities. Lack of Fisher consistency could be used as a criterion to dismiss estimators that are unlikely to deliver precise estimates in test datasets under prior probability and more general dataset shift. The usefulness of this unbiasedness concept is demonstrated with three examples of classifiers used for quantification: Adjusted Classify & Count, EM-algorithm and CDE-Iterate. We find that Adjusted Classify & Count and EM-algorithm are Fisher consistent. A counter-example shows that CDE-Iterate is not Fisher consistent and, therefore, cannot be trusted to deliver reliable estimates of class probabilities.