Geometry-Aware Bayesian Quantification via Compositional Data Analysis
2026-07-06 • Machine Learning
Machine Learning
AI summaryⓘ
The authors address the problem of estimating the distribution of labels when it changes, called quantification. They note that previous methods use a kind of density estimation that doesn't respect the special shape of probability data, which lies on a simplex. To fix this, they propose a new method that considers this geometry using log-ratio transformations and special math called Aitchison geometry, improving accuracy especially near the boundaries of the simplex. Their approach also includes regularization to handle tricky cases and offers both point estimates and Bayesian inference. Tests on many datasets across different types of data show their method works well compared to existing techniques.
quantificationlabel shiftclass prevalence estimationkernel density estimation (KDE)probability simplexcompositional dataAitchison geometrylog-ratio transformationsshrinkage regularizationBayesian inference
Authors
Alejandro Moreo, Pablo González, Juan José del Coz
Abstract
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.