Geometry-Aware Bayesian Quantification via Compositional Data Analysis

• URL: http://arxiv.org/abs/2607.04977v1
• Date: Mon, 06 Jul 2026 12:12:16 GMT
• Title: Geometry-Aware Bayesian Quantification via Compositional Data Analysis
• Abstract summary: We introduce a geometry-aware model for multiclass quantification based on log-ratio representations and Aitchison geometry.<n>We derive both point-estimation and Bayesian inference procedures for class prevalences.
• Score: 46.938595111911845
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

Related papers

• Simplex-to-Euclidean Bijection for Conjugate and Calibrated Multiclass Gaussian Process [7.729713754661845]
  We propose a conjugate and Gaussian process (GP) model for multi-class classification by exploiting the geometry of the probability simplex.<n>Our approach uses Aitchison geometry to map simplex-valued class probabilities to an unconstrained Euclidean representation.<n>This yields conjugate inference and reliable predictive probabilities without relying on distributional approximations in the model construction.
  arXiv  Detail & Related papers  (2026-03-17T14:58:11Z)
• The Kernel Manifold: A Geometric Approach to Gaussian Process Model Selection [0.8536502059643899]
  We present a Bayesian optimization framework built on kernel-of- Kernels geometry.<n>A multidimensional scaling (MDS) embedding maps a discrete kernel library into a continuous Euclidean manifold, enabling smooth BO.<n>We demonstrate the approach on synthetic benchmarks, real-world time-series datasets, and an additive manufacturing case study.
  arXiv  Detail & Related papers  (2026-01-08T20:52:53Z)
• From Kernels to Attention: A Transformer Framework for Density and Score Estimation [0.47745223151611654]
  We introduce a unified attention-based framework for joint score and density estimation.<n>We develop a permutation- and affine-equivariant transformer that estimates both the probability density $f(x)$ and its score $nabla_x log f(x)$ directly from i.i.d. samples.
  arXiv  Detail & Related papers  (2025-11-08T08:38:37Z)
• Kernel Density Estimation for Multiclass Quantification [52.419589623702336]
  Quantification is the supervised machine learning task concerned with obtaining accurate predictors of class prevalence. 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. We propose a new representation mechanism based on multivariate densities that we model via kernel density estimation (KDE)
  arXiv  Detail & Related papers  (2023-12-31T13:19:27Z)
• Spatially relaxed inference on high-dimensional linear models [48.989769153211995]
  We study the properties of ensembled clustered inference algorithms which combine spatially constrained clustering, statistical inference, and ensembling to aggregate several clustered inference solutions. We show that ensembled clustered inference algorithms control the $delta$-FWER under standard assumptions for $delta$ equal to the largest cluster diameter.
  arXiv  Detail & Related papers  (2021-06-04T16:37:19Z)
• Spectral clustering under degree heterogeneity: a case for the random walk Laplacian [83.79286663107845]
  This paper shows that graph spectral embedding using the random walk Laplacian produces vector representations which are completely corrected for node degree. In the special case of a degree-corrected block model, the embedding concentrates about K distinct points, representing communities.
  arXiv  Detail & Related papers  (2021-05-03T16:36:27Z)
• Bayesian data-driven discovery of partial differential equations with variable coefficients [9.331440154110117]
  We propose an advanced Bayesian sparse learning algorithm for PDE discovery with variable coefficients. In the experiments, we show that the tBGL-SS method is more robust than the baseline methods under noisy environments.
  arXiv  Detail & Related papers  (2021-02-02T11:05:34Z)
• Probabilistic Circuits for Variational Inference in Discrete Graphical Models [101.28528515775842]
  Inference in discrete graphical models with variational methods is difficult. Many sampling-based methods have been proposed for estimating Evidence Lower Bound (ELBO) We propose a new approach that leverages the tractability of probabilistic circuit models, such as Sum Product Networks (SPN) We show that selective-SPNs are suitable as an expressive variational distribution, and prove that when the log-density of the target model is aweighted the corresponding ELBO can be computed analytically.
  arXiv  Detail & Related papers  (2020-10-22T05:04:38Z)
• Nonparametric Density Estimation from Markov Chains [68.8204255655161]
  We introduce a new nonparametric density estimator inspired by Markov Chains, and generalizing the well-known Kernel Density Estor. Our estimator presents several benefits with respect to the usual ones and can be used straightforwardly as a foundation in all density-based algorithms.
  arXiv  Detail & Related papers  (2020-09-08T18:33:42Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.