{"doi":"10.1073/pnas.2318989121","title":"On the surprising effectiveness of a simple matrix exponential derivative approximation, with application to global SARS-CoV-2","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.","journal":"Proceedings of the National Academy of Sciences","year":2024,"id":455160,"datarank":0.0,"base_score":0.0,"endowment":0.0,"self_citation_contribution":0.0,"citation_network_contribution":0.0,"self_endowment_contribution":0.0,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":6,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":0.9485,"is_data_producer":false,"deposit_databanks":null,"is_oa":true,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":"2024-01-01","fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":1278990,"name":"Nathan Glatt-Holtz","orcid":"0000-0002-4031-8924","position":1,"is_corresponding":false},{"id":336580,"name":"Andrew J. Holbrook","orcid":"0000-0002-3558-200X","position":2,"is_corresponding":false},{"id":329443,"name":"Andrew F. Magee","orcid":"0000-0002-7403-5455","position":3,"is_corresponding":false},{"id":32104,"name":"Marc A. Suchard","orcid":"0000-0001-9818-479X","position":4,"is_corresponding":false},{"id":1278989,"name":"Gustavo Didier","orcid":"0000-0003-1363-5868","position":0,"is_corresponding":true}],"reference_count":42,"raw_metadata":null,"created_at":"2026-07-19T02:03:17.458329Z","pmid":"38215186","pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}