{"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/sample-complexity-bounds-for-linear-system","title":"Sample Complexity Bounds for Linear System Identification from a Finite Set","arxiv_id":"2409.11141","date":"2024-09-17","proceeding":null,"authors":["Nicolas Chatzikiriakos","Andrea Iannelli"],"abstract":"This paper considers a finite sample perspective on the problem of identifying an LTI system from a finite set of possible systems using trajectory data. To this end, we use the maximum likelihood estimator to identify the true system and provide an upper bound for its sample complexity. Crucially, the derived bound does not rely on a potentially restrictive stability assumption. Additionally, we leverage tools from information theory to provide a lower bound to the sample complexity that holds independently of the used estimator. The derived sample complexity bounds are analyzed analytically and numerically.","url_abs":"https://arxiv.org/abs/2409.11141v2","url_pdf":"https://arxiv.org/pdf/2409.11141v2.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":"sample-complexity-bounds-for-linear-system","repo_url":"https://github.com/col-tasas/2024-bounds-finite-set-id","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[{"method_slug":"set","method_name":"SET"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2409.11141","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2409.11141"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/col-tasas/2024-bounds-finite-set-id","reach":{"status":"ok","spdx":"MIT"}}],"summary":{"ran":2},"by_repo_kind":{"official":{"samples":2,"ran":2,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":0,"samples":[{"code_sha256_prefix":"88c321434b4fac33","entry":"checkTheoCondLower","repo":"col-tasas/2024-bounds-finite-set-id","repo_kind":"official","path":"src/fcn/theoreticalCond.py","file_url":"https://github.com/col-tasas/2024-bounds-finite-set-id/blob/HEAD/src/fcn/theoreticalCond.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"88c321434b4fac33"}},{"code_sha256_prefix":"0784f28db9e814b0","entry":"checkTheoCondUpper","repo":"col-tasas/2024-bounds-finite-set-id","repo_kind":"official","path":"src/fcn/theoreticalCond.py","file_url":"https://github.com/col-tasas/2024-bounds-finite-set-id/blob/HEAD/src/fcn/theoreticalCond.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"0784f28db9e814b0"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}