no code implementations • 10 Oct 2018 • Romain Couillet, Malik Tiomoko, Steeve Zozor, Eric Moisan
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 $X$).
