{"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/learning-linear-dynamical-systems-with-semi","title":"Learning Linear Dynamical Systems with Semi-Parametric Least Squares","arxiv_id":"1902.00768","date":"2019-02-02","proceeding":null,"authors":["Max Simchowitz","Ross Boczar","Benjamin Recht"],"abstract":"We analyze a simple prefiltered variation of the least squares estimator for\nthe problem of estimation with biased, semi-parametric noise, an error model\nstudied more broadly in causal statistics and active learning. We prove an\noracle inequality which demonstrates that this procedure provably mitigates the\nvariance introduced by long-term dependencies. We then demonstrate that\nprefiltered least squares yields, to our knowledge, the first algorithm that\nprovably estimates the parameters of partially-observed linear systems that\nattains rates which do not not incur a worst-case dependence on the rate at\nwhich these dependencies decay. The algorithm is provably consistent even for\nsystems which satisfy the weaker marginal stability condition obeyed by many\nclassical models based on Newtonian mechanics. In this context, our\nsemi-parametric framework yields guarantees for both stochastic and worst-case\nnoise.","url_abs":"http://arxiv.org/abs/1902.00768v1","url_pdf":"http://arxiv.org/pdf/1902.00768v1.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":"learning-linear-dynamical-systems-with-semi","repo_url":"https://github.com/zhengy09/SysId","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"active-learning","task_name":"Active Learning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1902.00768","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}