{"paper":{"title":"$\\lambda$-Regularized A-Optimal Design and its Approximation by $\\lambda$-Regularized Proportional Volume Sampling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.OC","stat.CO","stat.ML"],"primary_cat":"cs.DS","authors_text":"Uthaipon Tantipongpipat","submitted_at":"2020-06-19T15:17:57Z","abstract_excerpt":"In this work, we study the $\\lambda$-regularized $A$-optimal design problem and introduce the $\\lambda$-regularized proportional volume sampling algorithm, generalized from [Nikolov, Singh, and Tantipongpipat, 2019], for this problem with the approximation guarantee that extends upon the previous work. In this problem, we are given vectors $v_1,\\ldots,v_n\\in\\mathbb{R}^d$ in $d$ dimensions, a budget $k\\leq n$, and the regularizer parameter $\\lambda\\geq0$, and the goal is to find a subset $S\\subseteq [n]$ of size $k$ that minimizes the trace of $\\left(\\sum_{i\\in S}v_iv_i^\\top + \\lambda I_d\\right"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.11182","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/2006.11182/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"}