{"paper":{"title":"Optimal Sketching for Kronecker Product Regression and Low Rank Approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ML"],"primary_cat":"cs.DS","authors_text":"David P. Woodruff, Huaian Diao, Rajesh Jayaram, Wen Sun, Zhao Song","submitted_at":"2019-09-29T22:24:28Z","abstract_excerpt":"We study the Kronecker product regression problem, in which the design matrix is a Kronecker product of two or more matrices. Given $A_i \\in \\mathbb{R}^{n_i \\times d_i}$ for $i=1,2,\\dots,q$ where $n_i \\gg d_i$ for each $i$, and $b \\in \\mathbb{R}^{n_1 n_2 \\cdots n_q}$, let $\\mathcal{A} = A_1 \\otimes A_2 \\otimes \\cdots \\otimes A_q$. Then for $p \\in [1,2]$, the goal is to find $x \\in \\mathbb{R}^{d_1 \\cdots d_q}$ that approximately minimizes $\\|\\mathcal{A}x - b\\|_p$. Recently, Diao, Song, Sun, and Woodruff (AISTATS, 2018) gave an algorithm which is faster than forming the Kronecker product $\\mathc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.13384","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/1909.13384/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"}