{"paper":{"title":"State Evolution for Approximate Message Passing with Non-Separable Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Andrea Montanari, Phan-Minh Nguyen, Raphael Berthier","submitted_at":"2017-08-13T18:38:10Z","abstract_excerpt":"Given a high-dimensional data matrix ${\\boldsymbol A}\\in{\\mathbb R}^{m\\times n}$, Approximate Message Passing (AMP) algorithms construct sequences of vectors ${\\boldsymbol u}^t\\in{\\mathbb R}^n$, ${\\boldsymbol v}^t\\in{\\mathbb R}^m$, indexed by $t\\in\\{0,1,2\\dots\\}$ by iteratively applying ${\\boldsymbol A}$ or ${\\boldsymbol A}^{{\\sf T}}$, and suitable non-linear functions, which depend on the specific application. Special instances of this approach have been developed --among other applications-- for compressed sensing reconstruction, robust regression, Bayesian estimation, low-rank matrix recove"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.03950","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"}