KDE is a non-parametric method: it can be used without specifying any assumptions regarding the density your are trying to estimate. β¦ Maximum Likelihood Estimation (MLE, which I guess is what you are referring to with "Max LLE") refers to a family of methods for performing parametric density estimation. Let us assume that you know that your observations {π₯π}1β€πβ€π have been generated from a Gaussian distribution, but that you don't know the parameters π (e.g. the mean π and variance π2) of this distribution.