{"paper":{"title":"Near Optimal Sketching of Low-Rank Tensor Regression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","stat.ML"],"primary_cat":"cs.LG","authors_text":"David P. Woodruff, Jarvis Haupt, Xingguo Li","submitted_at":"2017-09-20T22:05:49Z","abstract_excerpt":"We study the least squares regression problem \\begin{align*} \\min_{\\Theta \\in \\mathcal{S}_{\\odot D,R}} \\|A\\Theta-b\\|_2, \\end{align*} where $\\mathcal{S}_{\\odot D,R}$ is the set of $\\Theta$ for which $\\Theta = \\sum_{r=1}^{R} \\theta_1^{(r)} \\circ \\cdots \\circ \\theta_D^{(r)}$ for vectors $\\theta_d^{(r)} \\in \\mathbb{R}^{p_d}$ for all $r \\in [R]$ and $d \\in [D]$, and $\\circ$ denotes the outer product of vectors. That is, $\\Theta$ is a low-dimensional, low-rank tensor. This is motivated by the fact that the number of parameters in $\\Theta$ is only $R \\cdot \\sum_{d=1}^D p_d$, which is significantly sm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.07093","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":""},"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"}