On the surprising effectiveness of a simple matrix exponential derivative approximation, with application to global SARS-CoV-2.
Proc Natl Acad Sci U S A
; 121(3): e2318989121, 2024 Jan 16.
Article
em En
| MEDLINE
| ID: mdl-38215186
ABSTRACT
The continuous-time Markov chain (CTMC) is the mathematical workhorse of evolutionary biology. Learning CTMC model parameters using modern, gradient-based methods requires the derivative of the matrix exponential evaluated at the CTMC's infinitesimal generator (rate) matrix. Motivated by the derivative's extreme computational complexity as a function of state space cardinality, recent work demonstrates the surprising effectiveness of a naive, first-order approximation for a host of problems in computational biology. In response to this empirical success, we obtain rigorous deterministic and probabilistic bounds for the error accrued by the naive approximation and establish a "blessing of dimensionality" result that is universal for a large class of rate matrices with random entries. Finally, we apply the first-order approximation within surrogate-trajectory Hamiltonian Monte Carlo for the analysis of the early spread of Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) across 44 geographic regions that comprise a state space of unprecedented dimensionality for unstructured (flexible) CTMC models within evolutionary biology.
Palavras-chave
Texto completo:
1
Coleções:
01-internacional
Base de dados:
MEDLINE
Assunto principal:
SARS-CoV-2
/
COVID-19
Tipo de estudo:
Health_economic_evaluation
Limite:
Humans
Idioma:
En
Ano de publicação:
2024
Tipo de documento:
Article