{"paper":{"title":"Bidirectional Random Projections","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","stat.TH"],"primary_cat":"math.ST","authors_text":"Chao Lan, Luyuan Yang","submitted_at":"2026-06-09T03:40:09Z","abstract_excerpt":"This paper analyzes bidirectional random projections for ordinary least squares (OLS) regression under the fixed design setting. Let $(X,Y) \\in \\mathbb{R}^{n \\times p} \\times \\mathbb{R}^n$ be a sample and $R \\in \\mathbb{R}^{n_1 \\times n}, W \\in \\mathbb{R}^{p \\times p_1}$ be two properly distributed random projections. We develop an expected excess loss bound for the OLS estimator built on $(WXR, WY)$. Compared to an established bound for OLS estimator built on $(XR, Y)$, the gap is approximately $O\\left( p_1 + C \\frac{1}{p_1} \\right)$, where $C$ scales with $n_1/n$ and can be negative for smal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.10377","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.10377/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"}