{"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/generalized-system-identification-with-stable","title":"Generalized system identification with stable spline kernels","arxiv_id":"1309.7857","date":"2013-09-30","proceeding":null,"authors":["Aleksandr Y. Aravkin","James V. Burke","Gianluigi Pillonetto"],"abstract":"Regularized least-squares approaches have been successfully applied to linear\nsystem identification. Recent approaches use quadratic penalty terms on the\nunknown impulse response defined by stable spline kernels, which control model\nspace complexity by leveraging regularity and bounded-input bounded-output\nstability. This paper extends linear system identification to a wide class of\nnonsmooth stable spline estimators, where regularization functionals and data\nmisfits can be selected from a rich set of piecewise linear-quadratic (PLQ)\npenalties. This class includes the 1-norm, Huber, and Vapnik, in addition to\nthe least-squares penalty.\n  By representing penalties through their conjugates, the modeler can specify\nany piecewise linear-quadratic penalty for misfit and regularizer, as well as\ninequality constraints on the response. The interior-point solver we implement\n(IPsolve) is locally quadratically convergent, with $O(\\min(m,n)^2(m+n))$\narithmetic operations per iteration, where $n$ the number of unknown impulse\nresponse coefficients and $m$ the number of observed output measurements.\nIPsolve is competitive with available alternatives for system identification.\nThis is shown by a comparison with TFOCS, libSVM, and the FISTA algorithm. The\ncode is open source (https://github.com/saravkin/IPsolve).\n  The impact of the approach for system identification is illustrated with\nnumerical experiments featuring robust formulations for contaminated data,\nrelaxation systems, nonnegativity and unimodality constraints on the impulse\nresponse, and sparsity promoting regularization. Incorporating constraints\nyields particularly significant improvements.","url_abs":"http://arxiv.org/abs/1309.7857v4","url_pdf":"http://arxiv.org/pdf/1309.7857v4.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":"generalized-system-identification-with-stable","repo_url":"https://github.com/saravkin/IPsolve","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}