Tropical Foundations for Probability & Statistics on Phylogenetic Tree Space
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We introduce a novel framework for the statistical analysis of phylogenetic trees: Palm tree space is con- structed on principles of tropical algebraic geometry, and represents phylogenetic trees as a point in a space endowed with the tropical metric. We show that palm tree space possesses a variety of properties that allow for the definition of probability measures, and thus expectations, variances, and other fundamental statistical quantities. This provides a new, tropical basis for a statistical treatment of evolutionary biological processes represented by phylogenetic trees. In particular, we show that a geometric approach to phylogenetic tree space — first introduced by Billera, Holmes, and Vogtmann, which we reinterpret in this paper via tropical geometry — results in analytic, geometric, and topological characteristics that are desirable for probability, statistics, and increased computational efficiency.
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Tang, Xiaoxian; Wang, Houjie; Yoshid, Ruriko (ArXiv, 2020);Most data in genome-wide phylogenetic analysis (phylogenomics) is essentially multidimensional, posing a major challenge to human comprehension and computational analysis. Also, we can not directly apply statistical learning ...
Monod, Anthea; Lin, Bo; Yoshida, Ruriko; Kang, Qiwen (ArXiv, 2018);Phylogenetic trees are the fundamental mathematical representation of evolutionary processes in biology. As data objects, they are characterized by the challenges associated with “big data,” as well as the complication ...
Page, Robert L. (Monterey, CA; Naval Postgraduate School, 2019-06);A known challenge in the rapidly growing area of phylogenomics is the lack of tools to analyze the large volume of genome data. Genomic data includes information on the evolution, structure and mapping of genomes. Phylogenetic ...