{"paper":{"title":"Separating Oblivious and Adaptive Models of Variable Selection","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DS","cs.LG","math.OC","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Jerry Li, Kevin Tian, Yusong Zhu, Ziyun Chen","submitted_at":"2026-02-18T16:10:35Z","abstract_excerpt":"Sparse recovery is among the most well-studied problems in learning theory and high-dimensional statistics. In this work, we investigate the statistical and computational landscapes of sparse recovery with $\\ell_\\infty$ error guarantees. This variant of the problem is motivated by \\emph{variable selection} tasks, where the goal is to estimate the support of a $k$-sparse signal in $\\mathbb{R}^d$. Our main contribution is a provable separation between the \\emph{oblivious} (``for each'') and \\emph{adaptive} (``for all'') models of $\\ell_\\infty$ sparse recovery. We show that under an oblivious mod"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.16568","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2602.16568/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}