{"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/variational-cross-validation-of-slow","title":"Variational cross-validation of slow dynamical modes in molecular kinetics","arxiv_id":"1407.8083","date":"2015-03-27","proceeding":null,"authors":[],"abstract":"Markov state models (MSMs) are a widely used method for approximating the\neigenspectrum of the molecular dynamics propagator, yielding insight into the\nlong-timescale statistical kinetics and slow dynamical modes of biomolecular\nsystems. However, the lack of a unified theoretical framework for choosing\nbetween alternative models has hampered progress, especially for non-experts\napplying these methods to novel biological systems. Here, we consider\ncross-validation with a new objective function for estimators of these slow\ndynamical modes, a generalized matrix Rayleigh quotient (GMRQ), which measures\nthe ability of a rank-$m$ projection operator to capture the slow subspace of\nthe system. It is shown that a variational theorem bounds the GMRQ from above\nby the sum of the first $m$ eigenvalues of the system's propagator, but that\nthis bound can be violated when the requisite matrix elements are estimated\nsubject to statistical uncertainty. This overfitting can be detected and\navoided through cross-validation. These result make it possible to construct\nMarkov state models for protein dynamics in a way that appropriately captures\nthe tradeoff between systematic and statistical errors.","url_abs":"http://arxiv.org/abs/1407.8083v3","url_pdf":"http://arxiv.org/pdf/1407.8083v3.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":"variational-cross-validation-of-slow","repo_url":"https://github.com/msmbuilder/msmbuilder","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}