{"paper":{"title":"PCA from noisy, linearly reduced data: the diagonal case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"Amit Singer, Edgar Dobriban, William Leeb","submitted_at":"2016-11-30T20:01:21Z","abstract_excerpt":"Suppose we observe data of the form $Y_i = D_i (S_i + \\varepsilon_i) \\in \\mathbb{R}^p$ or $Y_i = D_i S_i + \\varepsilon_i \\in \\mathbb{R}^p$, $i=1,\\ldots,n$, where $D_i \\in \\mathbb{R}^{p\\times p}$ are known diagonal matrices, $\\varepsilon_i$ are noise, and we wish to perform principal component analysis (PCA) on the unobserved signals $S_i \\in \\mathbb{R}^p$. The first model arises in missing data problems, where the $D_i$ are binary. The second model captures noisy deconvolution problems, where the $D_i$ are the Fourier transforms of the convolution kernels. It is often reasonable to assume the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.10333","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"}