Differential Entropy of Gaussian Process

I have $N$ datapoints that have $d$ features in a GP and their covariance matrix $K$ and I want to calculate the differential entropy of that GP.

Is this formula right?

$E(I)= \frac{1}{2} \log((2πe)^d \det(K))$

Moreover, given $L$ the cholesky decomposition of $K$ is there a faster way?

Thank you

Yes. You can see the formula here. At least, I am assuming that you have performed the "kernel trick" and are doing the analysis in feature space. K would have $d$ dimensions.
• Thank you! then the $2πe$ is powered in the number of datapoints and not the number of features? Finally do you take the absolute value of the determinant? – Yannis Assael Jun 22 '14 at 13:29
• If the determinant is negative then $K$ cannot be a covariance matrix, so no absolute value is needed or even recommended. – whuber Jun 22 '14 at 15:04