Skip to Main content Skip to Navigation
Conference papers

Random Matrix-Improved Estimation of the Wasserstein Distance between two Centered Gaussian Distributions

Abstract : This article proposes a method to consistently estimate functionals 1 p p i=1 f (λi(C1C2)) of the eigenvalues of the product of two covariance matrices C1, C2 ∈ R p×p based on the empirical estimates λi(Ĉ1Ĉ2) (Ĉa = 1 na na i=1 x (a) i x (a)T i), when the size p and number na of the (zero mean) samples x (a) i are similar. As a corollary, a consistent estimate of the Wasserstein distance (related to the case f (t) = √ t) between centered Gaussian distributions is derived. The new estimate is shown to largely outperform the classical sample covariance-based "plug-in" estimator. Based on this finding, a practical application to covariance estimation is then devised which demonstrates potentially significant performance gains with respect to state-of-the-art alternatives.
Document type :
Conference papers
Complete list of metadata

Cited literature [21 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-02965778
Contributor : Malik Tiomoko <>
Submitted on : Monday, October 19, 2020 - 11:53:25 AM
Last modification on : Monday, August 30, 2021 - 9:40:02 AM
Long-term archiving on: : Wednesday, January 20, 2021 - 6:03:16 PM

File

1903.03447.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

Malik Tiomoko, Romain Couillet. Random Matrix-Improved Estimation of the Wasserstein Distance between two Centered Gaussian Distributions. EUSIPCO 2019 - 27th European Signal Processing Conference, Sep 2019, A Coruna, Spain. pp.1-5, ⟨10.23919/EUSIPCO.2019.8902795⟩. ⟨hal-02965778⟩

Share

Metrics

Record views

65

Files downloads

96