Machine-Learned Exclusion Limits without Binning
This work addresses a methodological challenge for particle physicists in improving sensitivity analysis, but it is incremental as it builds on existing MLL methods.
The paper tackles the problem of estimating experimental sensitivity in high-dimensional datasets by extending Machine-Learned Likelihoods with Kernel Density Estimators to avoid binning, and finds that significance estimation is not sensitive to non-smoothness in probability distributions, as validated on toy models and LHC cases like exotic Higgs bosons and Z' boson decays.
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.