{"paper":{"title":"Sparse Phase Retrieval via Sparse PCA Despite Model Misspecification: A Simplified and Extended Analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.IT","math.ST","stat.TH"],"primary_cat":"cs.IT","authors_text":"Yan Shuo Tan","submitted_at":"2017-12-12T02:59:05Z","abstract_excerpt":"We consider the problem of high-dimensional misspecified phase retrieval. This is where we have an $s$-sparse signal vector $\\mathbf{x}_*$ in $\\mathbb{R}^n$, which we wish to recover using sampling vectors $\\textbf{a}_1,\\ldots,\\textbf{a}_m$, and measurements $y_1,\\ldots,y_m$, which are related by the equation $f(\\left<\\textbf{a}_i,\\textbf{x}_*\\right>) = y_i$. Here, $f$ is an unknown link function satisfying a positive correlation with the quadratic function. This problem was analyzed in a recent paper by Neykov, Wang and Liu, who provided recovery guarantees for a two-stage algorithm with samp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.04106","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"}