  Machine-Learned Likelihoods (MLL) combines machine-learning classification
techniques with likelihood-based inference tests to estimate the experimental
sensitivity of high-dimensional data sets. We extend the MLL method by
including Kernel Density Estimators (KDE) to avoid binning the classifier
output to extract the resulting one-dimensional signal and background
probability density functions. We first test our method on toy models generated
with multivariate Gaussian distributions, where the true probability
distribution functions are known. Later, we apply the method to two cases of
interest at the LHC: a search for exotic Higgs bosons, and a $Z'$ boson
decaying into lepton pairs. In contrast to physical-based quantities, the
typical fluctuations of the ML outputs give non-smooth probability
distributions for pure-signal and pure-background samples. The non-smoothness
is propagated into the density estimation due to the good performance and
flexibility of the KDE method. We study its impact on the final significance
computation, and we compare the results using the average of several
independent ML output realizations, which allows us to obtain smoother
distributions. We conclude that the significance estimation turns out to be not
sensible to this issue.
