Scalable approximation of the transformation-free linear simplicial-simplicial regression via constrained iterative reweighted least squares

TL;DR

This paper presents a scalable, efficient method for simplex-constrained regression by reformulating the problem as constrained logistic regression and using iterative reweighted least squares, significantly improving computational speed.

Contribution

It introduces a new reformulation of simplex regression as constrained logistic regression and develops an iterative reweighted least squares algorithm for faster estimation.

Findings

Speed gains of 6 to 326 times over previous EM-based methods

Estimates closely match those from EM algorithm

Enhanced computational efficiency for large-scale problems

Abstract

Simplicia-simplicial regression concerns statistical modeling scenarios in which both the predictors and the responses are vectors constrained to lie on the simplex. \cite{fiksel2022} introduced a transformation-free linear regression framework for this setting, wherein the regression coefficients are estimated by minimizing the Kullback-Leibler divergence between the observed and fitted compositions, using an expectation-maximization (EM) algorithm for optimization. In this work, we reformulate the problem as a constrained logistic regression model, in line with the methodological perspective of \cite{tsagris2025}, and we obtain parameter estimates via constrained iteratively reweighted least squares. Simulation results indicate that the proposed procedure substantially improves computational efficiency-yielding speed gains ranging from $6\times--326\times$-while providing estimates that closely approximate those obtained from the EM-based approach.