# Kernel Density Estimation for Multiclass Quantification

arXiv: https://arxiv.org/abs/2401.00490 · HTML: https://mlsanity.com/paper/2401.00490/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 60 references that are in the map.
- First posted on arXiv 31 Dec 2023.

## Builds on (most cited first, 12 of 12)

- [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)
- [Should we really use post-hoc tests based on mean-ranks?](https://mlsanity.com/paper/1505.02288/) (2015)
- [A Tutorial on Kernel Density Estimation and Recent Advances](https://mlsanity.com/paper/1704.03924/) (2017)
- [Time for a change: a tutorial for comparing multiple classifiers through Bayesian analysis](https://mlsanity.com/paper/1606.04316/) (2016)
- [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)
- [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)
- [Label Shift Quantification with Robustness Guarantees via Distribution Feature Matching](https://mlsanity.com/paper/2306.04376/) (2023)

## Built on by (most cited first, 8 of 8)

- [On the Interconnections of Calibration, Quantification, and Classifier Accuracy Prediction under Dataset Shift](https://mlsanity.com/paper/2505.11380/) (2025)
- [Adjusted Count Quantification Learning on Graphs](https://mlsanity.com/paper/2503.09395/) (2025)
- [Estimating prevalence with precision and accuracy](https://mlsanity.com/paper/2507.06061/) (2025)
- [Distribution Matching for Graph Quantification Under Structural Covariate Shift](https://mlsanity.com/paper/2601.00864/) (2025)
- [Transductive Model Selection under Prior Probability Shift](https://mlsanity.com/paper/2507.22647/) (2025)
- [Quantifying Feature Importance for Online Content Moderation](https://mlsanity.com/paper/2510.19882/) (2025)
- [Geometry-Aware Bayesian Quantification via Compositional Data Analysis](https://mlsanity.com/paper/2607.04977/) (2026)
- [Generalized Distribution-Free Semi-Supervised Learning with Risk Rewrite](https://mlsanity.com/paper/2607.11947/) (2026)

## Abstract (arXiv)

Several disciplines, like the social sciences, epidemiology, sentiment analysis, or market research, are interested in knowing the distribution of the classes in a population rather than the individual labels of the members thereof. Quantification is the supervised machine learning task concerned with obtaining accurate predictors of class prevalence, and to do so particularly in the presence of label shift. The distribution-matching (DM) approaches represent one of the most important families among the quantification methods that have been proposed in the literature so far. Current DM approaches model the involved populations by means of histograms of posterior probabilities. In this paper, we argue that their application to the multiclass setting is suboptimal since the histograms become class-specific, thus missing the opportunity to model inter-class information that may exist in the data. We propose a new representation mechanism based on multivariate densities that we model via kernel density estimation (KDE). The experiments we have carried out show our method, dubbed KDEy, yields superior quantification performance with respect to previous DM approaches. We also investigate the KDE-based representation within the maximum likelihood framework and show KDEy often shows superior performance with respect to the expectation-maximization method for quantification, arguably the strongest contender in the quantification arena to date.