{"paper":{"title":"Equivalence of Approximate Message Passing and Low-Degree Polynomials in Rank-One Matrix Estimation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"Alexander S. Wein, Andrea Montanari","submitted_at":"2022-12-14T03:05:09Z","abstract_excerpt":"We consider the problem of estimating an unknown parameter vector ${\\boldsymbol \\theta}\\in{\\mathbb R}^n$, given noisy observations ${\\boldsymbol Y} = {\\boldsymbol \\theta}{\\boldsymbol \\theta}^{\\top}/\\sqrt{n}+{\\boldsymbol Z}$ of the rank-one matrix ${\\boldsymbol \\theta}{\\boldsymbol \\theta}^{\\top}$, where ${\\boldsymbol Z}$ has independent Gaussian entries. When information is available about the distribution of the entries of ${\\boldsymbol \\theta}$, spectral methods are known to be strictly sub-optimal. Past work characterized the asymptotics of the accuracy achieved by the optimal estimator. How"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.06996","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2212.06996/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"}