ArticleProceedings of the National Academy of Sciences of the United States of America2024
On the surprising effectiveness of a simple matrix exponential derivative approximation, with application to global SARS-CoV-2.
Article in Proceedings of the National Academy of Sciences of the United States of America, 2024. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 7 papers.
What it found
Each row is one number read from the abstract, on the scale the paper reported it, with its interval. Left of the dashed line favours the treatment, right favours the comparator. Under each row is the sentence it came from. New to these charts? A ten-minute tutorial.
The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.
The trial behind it
Trials whose registry record cites this paper, or whose number appears in the abstract. A trial that started after this paper was published is citing it as background, not reporting it.
Neither the registry nor the abstract names a trial number. If this is a trial report, that itself is worth knowing.
Who cites it
7 citing papers in PubMed.
- Detecting Evolutionary Change-Points with Branch-Specific Substitution Models and Shrinkage Priors.ArXiv · 2025Article
- Detecting Evolutionary Change-Points with Branch-Specific Substitution Models and Shrinkage Priors.Research square · 2025Article
- International importance and spread of SARS-CoV-2 variants Alpha, Delta, and Omicron BA.1 into Spain.Communications medicine · 2025Article
- Random-Effects Substitution Models for Phylogenetics via Scalable Gradient Approximations.Systematic biology · 2024Article
- Dispersal history of SARS-CoV-2 in Galicia, Spain.Journal of medical virology · 2024Article
- Dispersal history of SARS-CoV-2 in Galicia, Spain.medRxiv : the preprint server for health sciences · 2024Article
- On the surprising effectiveness of a simple matrix exponential derivative approximation, with application to global SARS-CoV-2.Proceedings of the National Academy of Sciences of the United States of America · 2024Article
Corrections and comments
PubMed lists nothing against this paper. Absence here is not a guarantee, only a check that was made.
Authors and funding
5 authors.
Funding
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.
Indexed as
Identifiers
What OpenQuestion holds
Registered trials
Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.