Title: Imputing phylogenetic trees using tropical polytopes over the space of phylogenetic trees Show Chinese title

Title: 使用热带多面体在系统发育树空间中进行系统发育树填补

Abstract: When we apply comparative phylogenetic analyses to genome data, it is a well-known problem and challenge that some of given species (or taxa) often have missing genes. In such a case, we have to impute a missing part of a gene tree from a sample of gene trees. In this short paper we propose a novel method to infer a missing part of a phylogenetic tree using an analogue of a classical linear regression in the setting of tropical geometry. In our approach, we consider a tropical polytope, a convex hull with respect to the tropical metric closest to the data points. We show a condition that we can guarantee that an estimated tree from our method has at most four Robinson-Foulds (RF) distance from the ground truth and computational experiments with simulated data show our method works well. Show Chinese abstract

Abstract: 当我们将比较系统发育分析应用于基因组数据时，一个众所周知的问题和挑战是某些给定的物种（或分类单元）常常有缺失的基因。 在这种情况下的时候，我们必须从基因树的样本中推断出基因树缺失的部分。 在这篇简短的论文中，我们提出了一种新方法，使用经典线性回归的类比，在热带几何的设置下推断系统发育树的缺失部分。 在我们的方法中，我们考虑一个热带多面体，即相对于热带度量最接近数据点的凸包。 我们展示了一个条件，可以保证我们方法估计的树与真实树之间的 Robinson-Foulds（RF）距离最多为四，并且用模拟数据进行的计算实验表明我们的方法效果良好。