# Minimising quantifier variance under prior probability shift

arXiv: https://arxiv.org/abs/2107.08209 · HTML: https://mlsanity.com/paper/2107.08209/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 31 references that are in the map.
- First posted on arXiv 17 Jul 2021.

## Builds on (most cited first, 7 of 7)

- [Detecting and Correcting for Label Shift with Black Box Predictors](https://mlsanity.com/paper/1802.03916/) (2018)
- [A Unified View of Label Shift Estimation](https://mlsanity.com/paper/2003.07554/) (2020)
- [Fisher consistency for prior probability shift](https://mlsanity.com/paper/1701.05512/) (2017)
- [Quantification under prior probability shift: the ratio estimator and its extensions](https://mlsanity.com/paper/1807.03929/) (2018)
- [QuaPy: A Python-Based Framework for Quantification](https://mlsanity.com/paper/2106.11057/) (2021)
- [Calibrating sufficiently](https://mlsanity.com/paper/2105.07283/) (2021)
- [Confidence intervals for class prevalences under prior probability shift](https://mlsanity.com/paper/1906.04119/) (2019)

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

- [Class Prior Estimation under Covariate Shift: No Problem?](https://mlsanity.com/paper/2206.02449/) (2022)
- [Estimating prevalence with precision and accuracy](https://mlsanity.com/paper/2507.06061/) (2025)
- [Continuous Sweep for Binary Quantification Learning](https://mlsanity.com/paper/2308.08387/) (2023)
- [Comments on Friedman's Method for Class Distribution Estimation](https://mlsanity.com/paper/2405.16666/) (2024)

## Abstract (arXiv)

For the binary prevalence quantification problem under prior probability shift, we determine the asymptotic variance of the maximum likelihood estimator. We find that it is a function of the Brier score for the regression of the class label on the features under the test data set distribution. This observation suggests that optimising the accuracy of a base classifier, as measured by the Brier score, on the training data set helps to reduce the variance of the related quantifier on the test data set. Therefore, we also point out training criteria for the base classifier that imply optimisation of both of the Brier scores on the training and the test data sets.