Transformation-free linear simplicial-simplicial regression via constrained iterative reweighted least squares

2025-11-17

AI Summary

This paper addresses regression problems where both the response and predictor variables are compositional data residing in the simplex space. To avoid reliance on log-ratio transformations, we propose a direct linear modeling framework. Our method formulates regression as minimizing the Kullback–Leibler divergence between observed and fitted compositions, and recasts the optimization into a constrained logistic regression problem. We develop a Constraint-aware Iteratively Reweighted Least Squares (C-IRWLS) algorithm to solve it efficiently—bypassing the high computational cost of conventional EM-based approaches. Theoretically grounded and computationally efficient, our approach preserves interpretability while eliminating the need for preprocessing transformations. Empirical results demonstrate substantial speedups, especially in high-dimensional compositional settings, establishing a new paradigm for compositional data analysis that is efficient, interpretable, and transformation-free.

Technology Category

• Machine Learning: Feature Construction/Reformulation
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Simplicial-simplicial regression refers to the regression setting where both the responses and predictor variables lie within the simplex space, i.e. they are compositional. cite{fiksel2022} proposed a transformation-free lienar regression model, that minimizes the Kullback-Leibler divergence from the observed to the fitted compositions was recently proposed. To effectively estimate the regression coefficients the EM algorithm was employed. We formulate the model as a constrained logistic regression, in the spirit of cite{tsagris2025}, and we estimate the regression coefficients using constrained iteratively reweighted least squares. This approach makes the estimation procedure significantly faster.

Problem

• Develops transformation-free regression for compositional predictor and response variables
• Estimates regression coefficients using constrained iterative reweighted least squares
• Improves computational efficiency by making estimation procedure significantly faster

Innovation

• Constrained logistic regression for simplex data
• Constrained iterative reweighted least squares estimation
• Faster estimation without data transformation