I am currently testing some approaches for density estimation, and I think the basic approach of histograms may not be the best option to me and KDE is certainly a good alternative to go. While ago I found a very interesting tutorial by Jake VanderPlas which explains KDE in a nice way.
In his tutorial, Jake optimized KDE bandwidth selection using grid search maximizing the log-likelihood of the density estimation given some samples, but that is built-in in
sklearn and it's kind of hard to know how to compute the same metric for the histogram because I am not sure the formula they use (I search in the docs).
My question is, do you know a simple and usual way of comparing two density estimations from a set of points for example in 2D? My purpose is to evaluate how good is a particular KDE against a histogram.