# Geometry-Aware Bayesian Quantification via Compositional Data Analysis

arXiv: https://arxiv.org/abs/2607.04977 · HTML: https://mlsanity.com/paper/2607.04977/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 48 references that are in the map.
- First posted on arXiv 6 Jul 2026.

## Builds on (most cited first, 20 of 20)

- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Detecting and Correcting for Label Shift with Black Box Predictors](https://mlsanity.com/paper/1802.03916/) (2018)
- [Regularized Learning for Domain Adaptation under Label Shifts](https://mlsanity.com/paper/1903.09734/) (2019)
- [A Unified View of Label Shift Estimation](https://mlsanity.com/paper/2003.07554/) (2020)
- [Estimating and Explaining Model Performance When Both Covariates and Labels Shift](https://mlsanity.com/paper/2209.08436/) (2022)
- [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)
- [Class Prior Estimation under Covariate Shift: No Problem?](https://mlsanity.com/paper/2206.02449/) (2022)
- [Kernel Density Estimation for Multiclass Quantification](https://mlsanity.com/paper/2401.00490/) (2023)
- [Confidence intervals for class prevalences under prior probability shift](https://mlsanity.com/paper/1906.04119/) (2019)
- [Label Shift Quantification with Robustness Guarantees via Distribution Feature Matching](https://mlsanity.com/paper/2306.04376/) (2023)
- [Bayesian Quantification with Black-Box Estimators](https://mlsanity.com/paper/2302.09159/) (2023)
- [Quantifying Query Fairness Under Unawareness](https://mlsanity.com/paper/2506.04140/) (2025)
- [Efficient quantification on large-scale networks](https://mlsanity.com/paper/2503.15267/) (2025)
- [Estimating prevalence with precision and accuracy](https://mlsanity.com/paper/2507.06061/) (2025)
- [Bayesian-based Online Label Shift Estimation with Dynamic Dirichlet Priors](https://mlsanity.com/paper/2511.18615/) (2025)
- [Distribution Matching for Graph Quantification Under Structural Covariate Shift](https://mlsanity.com/paper/2601.00864/) (2025)

## Abstract (arXiv)

Accurately estimating the unknown target label distribution is the critical first step for adapting to label shift. This task, widely known as quantification or class prevalence estimation, has recently seen significant advances through continuous KDE-based methods which model the density of multiclass classifier posteriors. Posterior vectors might be regarded as compositional data, since they lie on the probability simplex. However, existing KDE-based quantifiers typically rely on Euclidean Gaussian kernels, which ignore simplex geometry and incorrectly assign probability mass outside its boundaries. We introduce a geometry-aware KDE model for multiclass quantification based on log-ratio representations and Aitchison geometry, together with a shrinkage regularization that improves robustness near the simplex boundary. Combined with a maximum-likelihood interpretation of KDE-based quantification, we derive both point-estimation and Bayesian inference procedures for class prevalences. Experiments on 42 datasets across tabular, text, and image domains show that the proposed method is competitive with state-of-the-art quantifiers, often improving over standard KDE-based baselines, while also yielding strong results among Bayesian quantification methods.