{"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-via","title":"Learning Linear Dynamical Systems via Spectral Filtering","arxiv_id":"1711.00946","date":"2017-11-02","proceeding":"NeurIPS 2017 12","authors":["Elad Hazan","Karan Singh","Cyril Zhang"],"abstract":"We present an efficient and practical algorithm for the online prediction of\ndiscrete-time linear dynamical systems with a symmetric transition matrix. We\ncircumvent the non-convex optimization problem using improper learning:\ncarefully overparameterize the class of LDSs by a polylogarithmic factor, in\nexchange for convexity of the loss functions. From this arises a\npolynomial-time algorithm with a near-optimal regret guarantee, with an\nanalogous sample complexity bound for agnostic learning. Our algorithm is based\non a novel filtering technique, which may be of independent interest: we\nconvolve the time series with the eigenvectors of a certain Hankel matrix.","url_abs":"http://arxiv.org/abs/1711.00946v1","url_pdf":"http://arxiv.org/pdf/1711.00946v1.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-via","repo_url":"https://github.com/catid/spectral_ssm","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[{"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":"https://app.syntology.ai/?focus=1711.00946","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}