Tropical medians by transportation

Comăneci, Andrei; Joswig, Michael

doi:10.1007/s10107-023-01996-8

Cited by 2 publications

(1 citation statement)

References 36 publications

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“…Recently, Comǎneci and Joswig studied tropical Fermat–Weber points obtained using the asymmetric tropical distance (Comǎneci and Joswig 2023 ). They found that if all are ultrametric, then the resulting tropical Fermat–Weber points are also ultrametric, all with the same tree topology.…”

Section: Optimizationmentioning

confidence: 99%

Tropical Logistic Regression Model on Space of Phylogenetic Trees

Aliatimis,

Yoshida,

Boyacı

et al. 2024

Bull Math Biol

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Classification of gene trees is an important task both in the analysis of multi-locus phylogenetic data, and assessment of the convergence of Markov Chain Monte Carlo (MCMC) analyses used in Bayesian phylogenetic tree reconstruction. The logistic regression model is one of the most popular classification models in statistical learning, thanks to its computational speed and interpretability. However, it is not appropriate to directly apply the standard logistic regression model to a set of phylogenetic trees, as the space of phylogenetic trees is non-Euclidean and thus contradicts the standard assumptions on covariates. It is well-known in tropical geometry and phylogenetics that the space of phylogenetic trees is a tropical linear space in terms of the max-plus algebra. Therefore, in this paper, we propose an analogue approach of the logistic regression model in the setting of tropical geometry. Our proposed method outperforms classical logistic regression in terms of Area under the ROC Curve in numerical examples, including with data generated by the multi-species coalescent model. Theoretical properties such as statistical consistency have been proved and generalization error rates have been derived. Finally, our classification algorithm is proposed as an MCMC convergence criterion for . Unlike the convergence metric used by which is only dependent on tree topologies, our method is sensitive to branch lengths and therefore provides a more robust metric for convergence. In a test case, it is illustrated that the tropical logistic regression can differentiate between two independently run MCMC chains, even when the standard metric cannot.

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Section: Optimizationmentioning

confidence: 99%

Tropical Logistic Regression Model on Space of Phylogenetic Trees

Aliatimis,

Yoshida,

Boyacı

et al. 2024

Bull Math Biol

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Tropical convexity in location problems

Comăneci

2024

Math Meth Oper Res

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We investigate location problems where the optimal solution is found within the tropical convex hull of the given input points. Our initial focus is on geodesically star-convex sets, using the asymmetric tropical distance. We introduce the concept of tropically quasiconvex functions, which have sub-level sets with this shape, and are closely related to monotonic functions. Our findings demonstrate that location problems using tropically quasiconvex functions as distance measures will result in an optimal solution within the tropical convex hull of the input points. We also extend this result to cases where the input points are replaced with tropically convex sets. Finally, we explore the applications of our research in phylogenetics, highlighting the properties of consensus methods that arise from our class of location problems.

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Tropical medians by transportation

Cited by 2 publications

References 36 publications

Tropical Logistic Regression Model on Space of Phylogenetic Trees

Tropical Logistic Regression Model on Space of Phylogenetic Trees

Tropical convexity in location problems

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