双曲空间用于贝叶斯系统发育推断的保真度
Fidelity of Hyperbolic Space for Bayesian Phylogenetic Inference
AI总结：
本文提出将基因组序列嵌入双曲空间并用双曲 MCMC 做贝叶斯系统发育推断，在八个数据集上验证其可高保真恢复分支划分与长度。
摘要：
系统发育学中的贝叶斯推断是计算系统发育树分布的黄金标准。它面临着在高维树空间中移动这一富有挑战性的问题。然而，双曲空间为树状数据提供了一种低维表示。在本文中，我们将基因组序列嵌入到双曲空间中，并执行双曲 Markov Chain Monte Carlo（MCMC，马尔可夫链蒙特卡洛）以进行贝叶斯推断。后验概率通过从所提议的嵌入位置解码出一棵邻接树来计算。我们在八个数据集上通过实验证明了该方法的保真度。采样得到的后验分布在很高程度上恢复了分支划分和分支长度。我们研究了曲率和嵌入维度对 Markov 链性能的影响。最后，我们讨论了调整该方法以利用梯度在树空间中导航的前景。
英文摘要：
Bayesian inference for phylogenetics is a gold standard for computing distributions of phylogenies. It faces the challenging problem of. moving throughout the high-dimensional space of trees. However, hyperbolic space offers a low dimensional representation of tree-like data. In this paper, we embed genomic sequences into hyperbolic space and perform hyperbolic Markov Chain Monte Carlo for Bayesian inference. The posterior probability is computed by decoding a neighbour joining tree from proposed embedding locations. We empirically demonstrate the fidelity of this method on eight data sets. The sampled posterior distribution recovers the splits and branch lengths to a high degree. We investigated the effects of curvature and embedding dimension on the Markov Chain's performance. Finally, we discuss the prospects for adapting this method to navigate tree space with gradients.
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