K-Nearest Neighbors Estimator

The full entropy expression:

$$\hat{H}(\mathbf{X}) = \psi(N) - \psi(k) + \log{c_d} + \frac{d}{N}\sum_{i=1}^{N} \log{\epsilon(i)}$$

where: * $\psi$ - the digamma function. * $c_d=\frac{\pi^{\frac{d}{2}}}{\Gamma(1+\frac{d}{2})}$ * $\Gamma$ - is the gamma function * $\epsilon(i)$ is the distance to the $i^{th}$ sample to its $k^{th}$ neighbour.