{"paper":{"title":"A Mathematical Framework for Feature Selection from Real-World Data with Non-Linear Observations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.ST","stat.TH"],"primary_cat":"stat.ML","authors_text":"Gitta Kutyniok, Martin Genzel","submitted_at":"2016-08-31T13:53:09Z","abstract_excerpt":"In this paper, we study the challenge of feature selection based on a relatively small collection of sample pairs $\\{(x_i, y_i)\\}_{1 \\leq i \\leq m}$. The observations $y_i \\in \\mathbb{R}$ are thereby supposed to follow a noisy single-index model, depending on a certain set of signal variables. A major difficulty is that these variables usually cannot be observed directly, but rather arise as hidden factors in the actual data vectors $x_i \\in \\mathbb{R}^d$ (feature variables). We will prove that a successful variable selection is still possible in this setup, even when the applied estimator doe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.08852","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"}