Algorithm 1.

A Taylor series approach to estimate the entropy.

1:	INPUT: $\mathbf{R}\in {\mathbb{R}}^{n\times n}$, accuracy parameter ε > 0, failure probability δ, and integer m > 0.
2:	Compute ${\tilde{p}}_1$, the estimate of the largest eigenvalue of R, p1, using Algorithm 8 (see Appendix) with $t=\mathcal{O}(\ln n)$ and $q=\mathcal{O}(\ln (1/\delta ))$.
3:	Set $u=\min \{1,6{\tilde{p}}_1\}$.
4:	Set s = ⌈20 ln(2/δ)/ε2⌉.
5:	Let ${\mathbf{g}}_1,{\mathbf{g}}_2,\dots ,{\mathbf{g}}_s\in {\mathbb{R}}^n$ be i.i.d. random Gaussian vectors.
6:	OUTPUT: return $\widehat{\mathcal{H}}\left(\mathbf{R}\right)=\text{ln}{u}^{-1}+\frac{1}{s}\sum _{i=1}^s\sum _{k=1}^m\frac{{\mathbf{g}}_i^T\mathbf{R}{\left({\mathbf{I}}_n-u^{-1}\mathbf{R}\right)}^k{\mathbf{g}}_i}{k}$.