{"paper":{"title":"The landscape of the spiked tensor model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Andrea Montanari, Gerard Ben Arous, Mihai Nica, Song Mei","submitted_at":"2017-11-15T06:23:43Z","abstract_excerpt":"We consider the problem of estimating a large rank-one tensor ${\\boldsymbol u}^{\\otimes k}\\in({\\mathbb R}^{n})^{\\otimes k}$, $k\\ge 3$ in Gaussian noise. Earlier work characterized a critical signal-to-noise ratio $\\lambda_{Bayes}= O(1)$ above which an ideal estimator achieves strictly positive correlation with the unknown vector of interest. Remarkably no polynomial-time algorithm is known that achieved this goal unless $\\lambda\\ge C n^{(k-2)/4}$ and even powerful semidefinite programming relaxations appear to fail for $1\\ll \\lambda\\ll n^{(k-2)/4}$.\n  In order to elucidate this behavior, we co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.05424","kind":"arxiv","version":2},"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"}