Gradients Do Grow on Trees: A Linear-Time O(N)-Dimensional Gradient for Statistical Phylogenetics

Calculation of the log-likelihood stands as the computational bottleneck for many statistical phylogenetic algorithms. Even worse is its gradient evaluation, often used to target regions of high probability. Order O(N)-dimensional gradient calculations based on the standard pruning algorithm require...

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Vydáno v:	Molecular biology and evolution Ročník 37; číslo 10; s. 3047 - 3060
Hlavní autoři:	Ji, Xiang, Zhang, Zhenyu, Holbrook, Andrew, Nishimura, Akihiko, Baele, Guy, Rambaut, Andrew, Lemey, Philippe, Suchard, Marc A
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	United States Oxford University Press 01.10.2020
Témata:	Algorithms Bayesian analysis Computer applications Dengue fever Evolution, Molecular Flavivirus - genetics Heterogeneity Inference Lassa virus - genetics Markov processes Methods Models, Genetic Next-generation sequencing Phylogenetics Phylogeny Process parameters Sequences Statistical analysis Statistics Vector-borne diseases Viruses West Nile virus linear-time gradient algorithm random-effects molecular clock model Bayesian inference maximum likelihood
ISSN:	0737-4038, 1537-1719, 1537-1719
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Abstract	Calculation of the log-likelihood stands as the computational bottleneck for many statistical phylogenetic algorithms. Even worse is its gradient evaluation, often used to target regions of high probability. Order O(N)-dimensional gradient calculations based on the standard pruning algorithm require O(N2) operations, where N is the number of sampled molecular sequences. With the advent of high-throughput sequencing, recent phylogenetic studies have analyzed hundreds to thousands of sequences, with an apparent trend toward even larger data sets as a result of advancing technology. Such large-scale analyses challenge phylogenetic reconstruction by requiring inference on larger sets of process parameters to model the increasing data heterogeneity. To make these analyses tractable, we present a linear-time algorithm for O(N)-dimensional gradient evaluation and apply it to general continuous-time Markov processes of sequence substitution on a phylogenetic tree without a need to assume either stationarity or reversibility. We apply this approach to learn the branch-specific evolutionary rates of three pathogenic viruses: West Nile virus, Dengue virus, and Lassa virus. Our proposed algorithm significantly improves inference efficiency with a 126- to 234-fold increase in maximum-likelihood optimization and a 16- to 33-fold computational performance increase in a Bayesian framework.
AbstractList	Calculation of the log-likelihood stands as the computational bottleneck for many statistical phylogenetic algorithms. Even worse is its gradient evaluation, often used to target regions of high probability. Order O(N)-dimensional gradient calculations based on the standard pruning algorithm require O(N2) operations, where N is the number of sampled molecular sequences. With the advent of high-throughput sequencing, recent phylogenetic studies have analyzed hundreds to thousands of sequences, with an apparent trend toward even larger data sets as a result of advancing technology. Such large-scale analyses challenge phylogenetic reconstruction by requiring inference on larger sets of process parameters to model the increasing data heterogeneity. To make these analyses tractable, we present a linear-time algorithm for O(N)-dimensional gradient evaluation and apply it to general continuous-time Markov processes of sequence substitution on a phylogenetic tree without a need to assume either stationarity or reversibility. We apply this approach to learn the branch-specific evolutionary rates of three pathogenic viruses: West Nile virus, Dengue virus, and Lassa virus. Our proposed algorithm significantly improves inference efficiency with a 126- to 234-fold increase in maximum-likelihood optimization and a 16- to 33-fold computational performance increase in a Bayesian framework. Calculation of the log-likelihood stands as the computational bottleneck for many statistical phylogenetic algorithms. Even worse is its gradient evaluation, often used to target regions of high probability. Order O(N)-dimensional gradient calculations based on the standard pruning algorithm require O(N2) operations, where N is the number of sampled molecular sequences. With the advent of high-throughput sequencing, recent phylogenetic studies have analyzed hundreds to thousands of sequences, with an apparent trend toward even larger data sets as a result of advancing technology. Such large-scale analyses challenge phylogenetic reconstruction by requiring inference on larger sets of process parameters to model the increasing data heterogeneity. To make these analyses tractable, we present a linear-time algorithm for O(N)-dimensional gradient evaluation and apply it to general continuous-time Markov processes of sequence substitution on a phylogenetic tree without a need to assume either stationarity or reversibility. We apply this approach to learn the branch-specific evolutionary rates of three pathogenic viruses: West Nile virus, Dengue virus, and Lassa virus. Our proposed algorithm significantly improves inference efficiency with a 126- to 234-fold increase in maximum-likelihood optimization and a 16- to 33-fold computational performance increase in a Bayesian framework.Calculation of the log-likelihood stands as the computational bottleneck for many statistical phylogenetic algorithms. Even worse is its gradient evaluation, often used to target regions of high probability. Order O(N)-dimensional gradient calculations based on the standard pruning algorithm require O(N2) operations, where N is the number of sampled molecular sequences. With the advent of high-throughput sequencing, recent phylogenetic studies have analyzed hundreds to thousands of sequences, with an apparent trend toward even larger data sets as a result of advancing technology. Such large-scale analyses challenge phylogenetic reconstruction by requiring inference on larger sets of process parameters to model the increasing data heterogeneity. To make these analyses tractable, we present a linear-time algorithm for O(N)-dimensional gradient evaluation and apply it to general continuous-time Markov processes of sequence substitution on a phylogenetic tree without a need to assume either stationarity or reversibility. We apply this approach to learn the branch-specific evolutionary rates of three pathogenic viruses: West Nile virus, Dengue virus, and Lassa virus. Our proposed algorithm significantly improves inference efficiency with a 126- to 234-fold increase in maximum-likelihood optimization and a 16- to 33-fold computational performance increase in a Bayesian framework.
Author	Zhang, Zhenyu Baele, Guy Nishimura, Akihiko Lemey, Philippe Rambaut, Andrew Holbrook, Andrew Ji, Xiang Suchard, Marc A
AuthorAffiliation	2 Department of Biostatistics, Fielding School of Public Health, University of California Los Angeles , Los Angeles, CA 7 Department of Mathematics, School of Science & Engineering, Tulane University , New Orleans, LA 4 Department of Microbiology, Immunology and Transplantation, Rega Institute , KU Leuven, Leuven, Belgium 5 Institute of Evolutionary Biology, Centre for Immunology, Infection and Evolution, University of Edinburgh , Edinburgh, United Kingdom 3 Department of Biostatistics, Bloomberg School of Public Health, Johns Hopkins University , Baltimore, MD 6 Department of Human Genetics, David Geffen School of Medicine, University of California Los Angeles , Los Angeles, CA 1 Department of Biomathematics, David Geffen School of Medicine, University of California Los Angeles , Los Angeles, CA
AuthorAffiliation_xml	– name: 7 Department of Mathematics, School of Science & Engineering, Tulane University , New Orleans, LA – name: 1 Department of Biomathematics, David Geffen School of Medicine, University of California Los Angeles , Los Angeles, CA – name: 6 Department of Human Genetics, David Geffen School of Medicine, University of California Los Angeles , Los Angeles, CA – name: 5 Institute of Evolutionary Biology, Centre for Immunology, Infection and Evolution, University of Edinburgh , Edinburgh, United Kingdom – name: 3 Department of Biostatistics, Bloomberg School of Public Health, Johns Hopkins University , Baltimore, MD – name: 4 Department of Microbiology, Immunology and Transplantation, Rega Institute , KU Leuven, Leuven, Belgium – name: 2 Department of Biostatistics, Fielding School of Public Health, University of California Los Angeles , Los Angeles, CA
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Keywords	linear-time gradient algorithm random-effects molecular clock model Bayesian inference maximum likelihood
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Snippet	Calculation of the log-likelihood stands as the computational bottleneck for many statistical phylogenetic algorithms. Even worse is its gradient evaluation,...
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SubjectTerms	Algorithms Bayesian analysis Computer applications Dengue fever Evolution, Molecular Flavivirus - genetics Heterogeneity Inference Lassa virus - genetics Markov processes Methods Models, Genetic Next-generation sequencing Phylogenetics Phylogeny Process parameters Sequences Statistical analysis Statistics Vector-borne diseases Viruses West Nile virus
Title	Gradients Do Grow on Trees: A Linear-Time O(N)-Dimensional Gradient for Statistical Phylogenetics
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