Scalable approximation of the transformation-free linear simplicial-simplicial regression via constrained iterative reweighted least squares
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908729487654912 |
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| author | Tsagris, Michail Alzeley, Omar |
| author_facet | Tsagris, Michail Alzeley, Omar |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_13296 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Scalable approximation of the transformation-free linear simplicial-simplicial regression via constrained iterative reweighted least squares Tsagris, Michail Alzeley, Omar Methodology Computation 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. |
| title | Scalable approximation of the transformation-free linear simplicial-simplicial regression via constrained iterative reweighted least squares |
| topic | Methodology Computation |
| url | https://arxiv.org/abs/2511.13296 |