{"paper":{"title":"Empirical risk minimization and complexity of dynamical models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","stat.TH"],"primary_cat":"math.ST","authors_text":"Andrew B. Nobel, Kevin McGoff","submitted_at":"2016-11-18T17:48:10Z","abstract_excerpt":"A dynamical model consists of a continuous self-map $T: \\mathcal{X} \\to \\mathcal{X}$ of a compact state space $\\mathcal{X}$ and a continuous observation function $f: \\mathcal{X} \\to \\mathbb{R}$. This paper considers the fitting of a parametrized family of dynamical models to an observed real-valued stochastic process using empirical risk minimization. The limiting behavior of the minimum risk parameters is studied in a general setting. We establish a general convergence theorem for minimum risk estimators and ergodic observations. We then study conditions under which empirical risk minimizatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.06173","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}