{"paper":{"title":"Matrix Inference in Growing Rank Regimes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Farzad Pourkamali, Jean Barbier, Nicolas Macris","submitted_at":"2023-06-02T10:04:15Z","abstract_excerpt":"The inference of a large symmetric signal-matrix $\\mathbf{S} \\in \\mathbb{R}^{N\\times N}$ corrupted by additive Gaussian noise, is considered for two regimes of growth of the rank $M$ as a function of $N$. For sub-linear ranks $M=\\Theta(N^\\alpha)$ with $\\alpha\\in(0,1)$ the mutual information and minimum mean-square error (MMSE) are derived for two classes of signal-matrices: (a) $\\mathbf{S}=\\mathbf{X}\\mathbf{X}^\\intercal$ with entries of $\\mathbf{X}\\in\\mathbb{R}^{N\\times M}$ independent identically distributed; (b) $\\mathbf{S}$ sampled from a rotationally invariant distribution. Surprisingly, t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.01412","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/2306.01412/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"}