{"paper":{"title":"Random Matrix-Improved Estimation of the Wasserstein Distance between two Centered Gaussian Distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Malik Tiomoko, Romain Couillet","submitted_at":"2019-03-08T13:54:14Z","abstract_excerpt":"This article proposes a method to consistently estimate functionals $\\frac1p\\sum_{i=1}^pf(\\lambda_i(C_1C_2))$ of the eigenvalues of the product of two covariance matrices $C_1,C_2\\in\\mathbb{R}^{p\\times p}$ based on the empirical estimates $\\lambda_i(\\hat C_1\\hat C_2)$ ($\\hat C_a=\\frac1{n_a}\\sum_{i=1}^{n_a} x_i^{(a)}x_i^{(a){{\\sf T}}}$), when the size $p$ and number $n_a$ of the (zero mean) samples $x_i^{(a)}$ are similar. As a corollary, a consistent estimate of the Wasserstein distance (related to the case $f(t)=\\sqrt{t}$) between centered Gaussian distributions is derived.\n  The new estimate"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.03447","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"}