# Unified Framework for Quantification

arXiv: https://arxiv.org/abs/1606.00868 · HTML: https://mlsanity.com/paper/1606.00868/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jun 2016.

## Built on by (most cited first, 7 of 7)

- [A Comparative Evaluation of Quantification Methods](https://mlsanity.com/paper/2103.03223/) (2021)
- [Kernel Density Estimation for Multiclass Quantification](https://mlsanity.com/paper/2401.00490/) (2023)
- [On the Interconnections of Calibration, Quantification, and Classifier Accuracy Prediction under Dataset Shift](https://mlsanity.com/paper/2505.11380/) (2025)
- [Probabilistic Consistency in Machine Learning and Its Connection to Uncertainty Quantification](https://mlsanity.com/paper/2507.21670/) (2025)
- [Distribution Matching for Graph Quantification Under Structural Covariate Shift](https://mlsanity.com/paper/2601.00864/) (2025)
- [Multi-Label Quantification](https://mlsanity.com/paper/2211.08063/) (2022)
- [Comments on Friedman's Method for Class Distribution Estimation](https://mlsanity.com/paper/2405.16666/) (2024)

## Abstract (arXiv)

Quantification is the machine learning task of estimating test-data class proportions that are not necessarily similar to those in training. Apart from its intrinsic value as an aggregate statistic, quantification output can also be used to optimize classifier probabilities, thereby increasing classification accuracy. We unify major quantification approaches under a constrained multi-variate regression framework, and use mathematical programming to estimate class proportions for different loss functions. With this modeling approach, we extend existing binary-only quantification approaches to multi-class settings as well. We empirically verify our unified framework by experimenting with several multi-class datasets including the Stanford Sentiment Treebank and CIFAR-10.