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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Bibliographic Details
Published in:Molecular biology and evolution Vol. 37; no. 10; pp. 3047 - 3060
Main Authors: Ji, Xiang, Zhang, Zhenyu, Holbrook, Andrew, Nishimura, Akihiko, Baele, Guy, Rambaut, Andrew, Lemey, Philippe, Suchard, Marc A
Format: Journal Article
Language:English
Published: United States Oxford University Press 01.10.2020
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:0737-4038
1537-1719
1537-1719
DOI:10.1093/molbev/msaa130