Fidelity of hyperbolic space for Bayesian phylogenetic inference

Area of Science:

• Computational Biology
• Phylogenetics
• Machine Learning

Background:

• Bayesian inference is crucial for phylogenetic analysis, but computationally intensive due to high-dimensional tree spaces.
• Hyperbolic space offers a lower-dimensional representation suitable for tree-like data, potentially simplifying computations.

Purpose of the Study:

• To develop and evaluate a novel method for Bayesian phylogenetic inference using hyperbolic space.
• To assess the performance and fidelity of hyperbolic Markov Chain Monte Carlo for phylogenetic tree reconstruction.

Main Methods:

• Genomic sequences were embedded as points in hyperbolic space.
• Hyperbolic Markov Chain Monte Carlo was employed for Bayesian inference within this space.
• Posterior probabilities were computed by decoding neighbour-joining trees from sequence embeddings.

Main Results:

• The method demonstrated high fidelity in reconstructing phylogenetic trees across eight diverse datasets.
• Systematic investigation showed that embedding dimension and hyperbolic curvature impact Markov Chain performance.
• The sampled posterior distributions accurately recovered tree splits and branch lengths.

Conclusions:

• Hyperbolic space provides a suitable and effective low-dimensional representation for Bayesian phylogenetic inference.
• The proposed hyperbolic Markov Chain Monte Carlo method offers a computationally efficient alternative for analyzing complex genomic data.
• This approach enhances the accuracy and feasibility of phylogenetic analyses, particularly for large datasets.