Tropical Logistic Regression Model on Space of Phylogenetic Trees

Area of Science:

• Phylogenetics
• Statistical Learning
• Tropical Geometry

Background:

• Gene tree classification is crucial for phylogenetic analysis and Bayesian inference convergence.
• Standard logistic regression is unsuitable for non-Euclidean phylogenetic tree spaces.
• Phylogenetic tree spaces are recognized as tropical linear spaces in tropical geometry.

Purpose of the Study:

• To develop a logistic regression analogue within tropical geometry for gene tree classification.
• To assess the performance of the proposed tropical logistic regression against classical methods.
• To establish a novel Markov Chain Monte Carlo (MCMC) convergence criterion for phylogenetic tree reconstruction.

Main Methods:

• Proposed an adaptation of the logistic regression model using principles of tropical geometry.
• Evaluated the method using numerical examples and data from the multi-species coalescent model.
• Proved theoretical properties including statistical consistency and derived generalization error rates.
• Developed a classification algorithm as an MCMC convergence diagnostic tool.

Main Results:

• The tropical logistic regression demonstrated superior performance compared to classical logistic regression, evidenced by higher Area Under the ROC Curve values.
• The method proved statistically consistent with derived generalization error rates.
• The proposed algorithm functions as a sensitive MCMC convergence criterion, considering branch lengths unlike topology-only metrics.

Conclusions:

• Tropical logistic regression provides an effective and theoretically sound approach for gene tree classification.
• This method offers a more robust convergence assessment for Bayesian phylogenetic analyses than existing metrics.
• The algorithm can distinguish between independently run MCMC chains, even when standard metrics fail.