基于正则化的系统发育推断的一致性和收敛速度
Consistency and convergence rate of phylogenetic inference via regularization
摘要：
在生物遗传学中，通常有一些关于一组生物体的整体进化树的信息，也许是部分信息，并希望为这些生物体找到一个特定基因的进化树。仅在基因序列中可能没有足够的信息来准确地重建正确的“基因树”。虽然基因树可能会由于各种遗传过程而偏离“物种树”，但在缺乏相反证据的情况下，假设它们是一致的是很吝啬的。在这些情况下，一个常见的统计方法是制定一个可能性惩罚，以纳入这些额外的信息。最近的研究使用模拟和经验数据表明，可能性惩罚量化与物种树的一致性可以显着提高基因树重建的准确性相比，单独使用序列数据。然而，这种方法的一致性尚未建立，也没有收敛速度的限制。由于遗传学是一个非标准推理问题，标准理论并不适用。在本文中，我们提出了一个惩罚的最大似然估计基因树重建，其中的惩罚是从基因树的物种树的Billera-Holmes-Vogtmann测地线距离的平方。我们证明了这种方法是一致的，并推导出其收敛速度估计的离散基因树结构和连续的边缘长度（代表的进化量，已发生在该分支）同时。我们发现，正则化估计是“自适应快速收敛”，这意味着它可以重建所有的边缘长度大于任何给定的阈值从基因序列的多项式长度。我们的方法不需要物种树是确切知道的，事实上，我们的渐近理论适用于任何这样的指导树。
英文摘要：
It is common in phylogenetics to have some, perhaps partial, information about the overall evolutionary tree of a group of organisms and wish to find an evolutionary tree of a specific gene for those organisms. There may not be enough information in the gene sequences alone to accurately reconstruct the correct "gene tree." Although the gene tree may deviate from the "species tree" due to a variety of genetic processes, in the absence of evidence to the contrary it is parsimonious to assume that they agree. A common statistical approach in these situations is to develop a likelihood penalty to incorporate such additional information. Recent studies using simulation and empirical data suggest that a likelihood penalty quantifying concordance with a species tree can significantly improve the accuracy of gene tree reconstruction compared to using sequence data alone. However, the consistency of such an approach has not yet been established, nor have convergence rates been bounded. Because phylogenetics is a non-standard inference problem, the standard theory does not apply. In this paper, we propose a penalized maximum likelihood estimator for gene tree reconstruction, where the penalty is the square of the Billera-Holmes-Vogtmann geodesic distance from the gene tree to the species tree. We prove that this method is consistent, and derive its convergence rate for estimating the discrete gene tree structure and continuous edge lengths (representing the amount of evolution that has occurred on that branch) simultaneously. We find that the regularized estimator is "adaptive fast converging," meaning that it can reconstruct all edges of length greater than any given threshold from gene sequences of polynomial length. Our method does not require the species tree to be known exactly; in fact, our asymptotic theory holds for any such guide tree.
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