Conformal Prediction for Compositional Data

TL;DR

This paper develops conformal prediction methods tailored for compositional data modeled by Dirichlet regression, addressing the challenge of constructing valid prediction regions respecting the simplex geometry.

Contribution

It introduces three conformal prediction strategies for Dirichlet regression, including quantile residuals, HDR approximation, and grid-based HDR, with comprehensive evaluation and real data applications.

Findings

HDR approximation shows good coverage robustness

Grid discretization reduces overcoverage and prediction area

Quantile method yields larger prediction regions with adequate coverage

Abstract

Dirichlet regression models are suitable for compositional data, in which the response variable represents proportions that sum to one. However, there are still no well-established methods for constructing valid prediction sets in this context, especially considering the geometry of the compositional space. In this work, we investigate conformal prediction-based strategies for constructing valid predictive regions in Dirichlet regression models. We evaluate three distinct approaches: a method based on quantile residuals, an approximate construction of highest density regions (HDR), and an adaptation of the approximate HDR using grid-based discretization over the simplex. The performance of the methods was analyzed through simulation studies under different scenarios, varying the model complexity, response dimensionality, and covariate structure. The results indicated that the HDR approximation approach exhibits good robustness in terms of coverage, while the grid discretization proved effective in reducing overcoverage and the area of the prediction region compared to the original method. The quantile method provided larger prediction regions compared to the grid method, while maintaining adequate coverage. The methodologies were also applied to two real datasets: one concerning sleep stages and another on biomass allocation in plants. In both cases, the proposed methods demonstrated practical feasibility and produced coherent interpretations within the compositional space. Finally, we discuss possible extensions of this work