Learning Hyperbolic Embedding for Phylogenetic Tree Placement and Updates.
Learning Hyperbolic Embedding for Phylogenetic Tree Placement and Updates.
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作者：
我们展示了为系统发育学开发的传统（欧几里得）深度学习方法如何从使用双曲几何中获益。结果表明，在更新树时距离失真降低且准确性提高，但对于系统发育定位而言未必如此。
系统发育定位在生态分析中广泛使用，旨在将一个新物种添加到现有树中。先前有人提出一种深度学习方法，通过构建从基因序列到一个保留物种树距离的高维空间的映射来估计查询物种和骨干物种之间的距离。然后他们使用一种基于距离的定位方法将查询物种放置在该物种树上。在本文中，我们研究了在嵌入基因序列时能忠实表示树距离的合适几何形状。理论预测，与传统的欧几里得空间相比，双曲空间应能大幅减少距离失真。然而，双曲嵌入带来了其自身与算术运算、指数增长函数和有限的位精度相关的独特挑战，我们解决了这些挑战。我们的结果证实，双曲嵌入的距离误差比欧几里得空间低得多。然而，这些估计得更好的距离并不总是能带来更好的系统发育定位。然后我们表明，深度学习框架不仅可用于在骨干树上进行定位，还可用于更新它以获得一棵完全解析的树。利用我们的双曲嵌入框架，仅用少数几个基因就可以非常准确地更新物种树。
We show how the conventional (Euclidean) deep learning methods developed for phylogenetics can benefit from using hyperbolic geometry. The results point to lowered distance distortion and better accuracy in updating trees but not necessarily for phylogenetic placement. Phylogenetic placement, used widely in ecological analyses, seeks to add a new species to an existing tree. A deep learning approach was previously proposed to estimate the distance between query and backbone species by building a map from gene sequences to a high-dimensional space that preserves species tree distances. They then use a distance-based placement method to place the queries on that species tree. In this paper, we examine the appropriate geometry for faithfully representing tree distances while embedding gene sequences. Theory predicts that hyperbolic spaces should provide a drastic reduction in distance distortion compared to the conventional Euclidean space. Nevertheless, hyperbolic embedding imposes its own unique challenges related to arithmetic operations, exponentially-growing functions, and limited bit precision, and we address these challenges. Our results confirm that hyperbolic embeddings have substantially lower distance errors than Euclidean space. However, these better-estimated distances do not always lead to better phylogenetic placement. We then show that the deep learning framework can be used not just to place on a backbone tree but to update it to obtain a fully resolved tree. With our hyperbolic embedding framework, species trees can be updated remarkably accurately with only a handful of genes.
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