{"paper":{"title":"Random matrix-improved estimation of covariance matrix distances","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Eric Moisan, Malik Tiomoko, Romain Couillet, Steeve Zozor","submitted_at":"2018-10-10T13:59:43Z","abstract_excerpt":"Given two sets $x_1^{(1)},\\ldots,x_{n_1}^{(1)}$ and $x_1^{(2)},\\ldots,x_{n_2}^{(2)}\\in\\mathbb{R}^p$ (or $\\mathbb{C}^p$) of random vectors with zero mean and positive definite covariance matrices $C_1$ and $C_2\\in\\mathbb{R}^{p\\times p}$ (or $\\mathbb{C}^{p\\times p}$), respectively, this article provides novel estimators for a wide range of distances between $C_1$ and $C_2$ (along with divergences between some zero mean and covariance $C_1$ or $C_2$ probability measures) of the form $\\frac1p\\sum_{i=1}^n f(\\lambda_i(C_1^{-1}C_2))$ (with $\\lambda_i(X)$ the eigenvalues of matrix $X$). These estimato"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.04534","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"}