{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/relaxed-random-walks-at-scale","title":"Relaxed random walks at scale","arxiv_id":"1906.04834","date":"2019-11-14","proceeding":null,"authors":[],"abstract":"Relaxed random walk (RRW) models of trait evolution introduce branch-specific\nrate multipliers to modulate the variance of a standard Brownian diffusion\nprocess along a phylogeny and more accurately model overdispersed biological\ndata. Increased taxonomic sampling challenges inference under RRWs as the\nnumber of unknown parameters grows with the number of taxa. To solve this\nproblem, we present a scalable method to efficiently fit RRWs and infer this\nbranch-specific variation in a Bayesian framework. We develop a Hamiltonian\nMonte Carlo (HMC) sampler to approximate the high-dimensional, correlated\nposterior that exploits a closed-form evaluation of the gradient of the trait\ndata log-likelihood with respect to all branch-rate multipliers simultaneously.\nOur gradient calculation achieves computational complexity that scales only\nlinearly with the number of taxa under study. We compare the efficiency of our\nHMC sampler to the previously standard univariable Metropolis-Hastings approach\nwhile studying the spatial emergence of the West Nile virus in North America in\nthe early 2000s. Our method achieves an over 300-fold speed-increase over the\nunivariable approach. Additionally, we demonstrate the scalability of our\nmethod by applying the RRW to study the correlation between five mammalian life\nhistory traits in a phylogenetic tree with 3650 tips.","url_abs":"http://arxiv.org/abs/1906.04834v2","url_pdf":"http://arxiv.org/pdf/1906.04834v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"relaxed-random-walks-at-scale","repo_url":"https://github.com/suchard-group/RRW_at_scale","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}