{"paper":{"title":"Fast and Reliable Parameter Estimation from Nonlinear Observations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","math.OC"],"primary_cat":"stat.ML","authors_text":"Mahdi Soltanolkotabi, Samet Oymak","submitted_at":"2016-10-23T00:36:12Z","abstract_excerpt":"In this paper we study the problem of recovering a structured but unknown parameter ${\\bf{\\theta}}^*$ from $n$ nonlinear observations of the form $y_i=f(\\langle {\\bf{x}}_i,{\\bf{\\theta}}^*\\rangle)$ for $i=1,2,\\ldots,n$. We develop a framework for characterizing time-data tradeoffs for a variety of parameter estimation algorithms when the nonlinear function $f$ is unknown. This framework includes many popular heuristics such as projected/proximal gradient descent and stochastic schemes. For example, we show that a projected gradient descent scheme converges at a linear rate to a reliable solutio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.07108","kind":"arxiv","version":1},"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"}