# Multi-Label Quantification

arXiv: https://arxiv.org/abs/2211.08063 · HTML: https://mlsanity.com/paper/2211.08063/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 80 references that are in the map.
- First posted on arXiv 15 Nov 2022.

## Builds on (most cited first, 16 of 16)

- [DiSMEC - Distributed Sparse Machines for Extreme Multi-label Classification](https://mlsanity.com/paper/1609.02521/) (2016)
- [A Network Perspective on Stratification of Multi-Label Data](https://mlsanity.com/paper/1704.08756/) (2017)
- [A scikit-based Python environment for performing multi-label classification](https://mlsanity.com/paper/1702.01460/) (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)
- [Evaluation Measures for Quantification: An Axiomatic Approach](https://mlsanity.com/paper/1809.01991/) (2018)
- [A Comparative Evaluation of Quantification Methods](https://mlsanity.com/paper/2103.03223/) (2021)
- [A Recurrent Neural Network for Sentiment Quantification](https://mlsanity.com/paper/1809.00836/) (2018)
- [Cost-Sensitive Label Embedding for Multi-Label Classification](https://mlsanity.com/paper/1603.09048/) (2016)
- [Unified Framework for Quantification](https://mlsanity.com/paper/1606.00868/) (2016)
- [Re-Assessing the "Classify and Count" Quantification Method](https://mlsanity.com/paper/2011.02552/) (2020)
- [Tweet Sentiment Quantification: An Experimental Re-Evaluation](https://mlsanity.com/paper/2011.08091/) (2020)
- [Optimizing Text Quantifiers for Multivariate Loss Functions](https://mlsanity.com/paper/1502.05491/) (2015)
- [How is a data-driven approach better than random choice in label space division for multi-label classification?](https://mlsanity.com/paper/1606.02346/) (2016)
- [Funnelling: A New Ensemble Method for Heterogeneous Transfer Learning and its Application to Cross-Lingual Text Classification](https://mlsanity.com/paper/1901.11459/) (2019)
- [LeQua@CLEF2022: Learning to Quantify](https://mlsanity.com/paper/2111.11249/) (2021)

## Abstract (arXiv)

Quantification, variously called "supervised prevalence estimation" or "learning to quantify", is the supervised learning task of generating predictors of the relative frequencies (a.k.a. "prevalence values") of the classes of interest in unlabelled data samples. While many quantification methods have been proposed in the past for binary problems and, to a lesser extent, single-label multiclass problems, the multi-label setting (i.e., the scenario in which the classes of interest are not mutually exclusive) remains by and large unexplored. A straightforward solution to the multi-label quantification problem could simply consist of recasting the problem as a set of independent binary quantification problems. Such a solution is simple but na"ive, since the independence assumption upon which it rests is, in most cases, not satisfied. In these cases, knowing the relative frequency of one class could be of help in determining the prevalence of other related classes. We propose the first truly multi-label quantification methods, i.e., methods for inferring estimators of class prevalence values that strive to leverage the stochastic dependencies among the classes of interest in order to predict their relative frequencies more accurately. We show empirical evidence that natively multi-label solutions outperform the na"ive approaches by a large margin. The code to reproduce all our experiments is available online.