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Motivation: Navigating the high dimensional space of discrete trees for
phylogenetics presents a challenging problem for tree optimisation. To address
this, hyperbolic embeddings of trees offer a promising approach to encoding
trees efficiently in continuous spaces. However, they require a differentiable
tree decoder to optimise the phylogenetic likelihood. We present soft-NJ, a
differentiable version of neighbour-joining that enables gradient-based
optimisation over the space of trees.
Results: We illustrate the potential for differentiable optimisation over
tree space for maximum likelihood inference. We then perform variational
Bayesian phylogenetics by optimising embedding distributions in hyperbolic
space. We compare the performance of this approximation technique on eight
benchmark datasets to state-of-art methods. However, geometric frustrations of
the embedding locations produce local optima that pose a challenge for
optimisation.
Availability: Dodonaphy is freely available on the web at
www.https://github.com/mattapow/dodonaphy. It includes an implementation of
soft-NJ.
No creative common's license