{"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/latent-variable-time-varying-network","title":"Latent Variable Time-varying Network Inference","arxiv_id":"1802.03987","date":"2018-02-12","proceeding":null,"authors":["Federico Tomasi","Veronica Tozzo","Saverio Salzo","Alessandro Verri"],"abstract":"In many applications of finance, biology and sociology, complex systems\ninvolve entities interacting with each other. These processes have the\npeculiarity of evolving over time and of comprising latent factors, which\ninfluence the system without being explicitly measured. In this work we present\nlatent variable time-varying graphical lasso (LTGL), a method for multivariate\ntime-series graphical modelling that considers the influence of hidden or\nunmeasurable factors. The estimation of the contribution of the latent factors\nis embedded in the model which produces both sparse and low-rank components for\neach time point. In particular, the first component represents the connectivity\nstructure of observable variables of the system, while the second represents\nthe influence of hidden factors, assumed to be few with respect to the observed\nvariables. Our model includes temporal consistency on both components,\nproviding an accurate evolutionary pattern of the system. We derive a tractable\noptimisation algorithm based on alternating direction method of multipliers,\nand develop a scalable and efficient implementation which exploits proximity\noperators in closed form. LTGL is extensively validated on synthetic data,\nachieving optimal performance in terms of accuracy, structure learning and\nscalability with respect to ground truth and state-of-the-art methods for\ngraphical inference. We conclude with the application of LTGL to real case\nstudies, from biology and finance, to illustrate how our method can be\nsuccessfully employed to gain insights on multivariate time-series data.","url_abs":"http://arxiv.org/abs/1802.03987v2","url_pdf":"http://arxiv.org/pdf/1802.03987v2.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":"latent-variable-time-varying-network","repo_url":"https://github.com/fdtomasi/regain","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"sociology","task_name":"Sociology"},{"task_slug":"time-series-1","task_name":"Time Series"},{"task_slug":"time-series","task_name":"Time Series Analysis"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}