The function score_samples from sklearn.neighbors.kde.KernelDensity returns the log of the density. What is the advantage of that over returning the density it self?
I know that the logarithm makes sense for probabilities, which are between 0 and 1 (See this quenstion: Why use log-probability estimates in GaussianNB [scikit-learn]?) But why do you do the same for densities which are between 0 and infinity?
Is there a way to estimate log-density directly, or is it just the logarithm taken from the estimated density?
Much of what applies to probabilities also applies to densities, so the answers in Why use log-probability estimates in GaussianNB [scikit-learn]? apply:
As long as the density is everywhere positive, the logarithm is well defined. It has much better numerical resolution and stability as density tends toward 0. Imagine a gaussian kernel of a certain width to model your points and imagine them in a cluster somewhere. As you move away from this dense area, the log density amounts to the negative squared distance to the cluster. The exponential of that will quickly yield very small quantities in which you may rightfully not trust anymore.