{"paper":{"title":"A Maximal Large Deviation Inequality for Sub-Gaussian Variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Claudio Gentile, Dotan Di Castro, Shie Mannor","submitted_at":"2011-05-12T19:29:21Z","abstract_excerpt":"In this short note we prove a maximal concentration lemma for sub-Gaussian random variables stating that for independent sub-Gaussian random variables we have \\[P<(\\max_{1\\le i\\le N}S_{i}>\\epsilon>) \\le\\exp<(-\\frac{1}{N^2}\\sum_{i=1}^{N}\\frac{\\epsilon^{2}}{2\\sigma_{i}^{2}}>), \\] where $S_i$ is the sum of $i$ zero mean independent sub-Gaussian random variables and $\\sigma_i$ is the variance of the $i$th random variable."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.2550","kind":"arxiv","version":3},"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"}