Machine-Learned Exclusion Limits without Binning

TL;DR

This paper introduces an improved machine-learning likelihood method using Kernel Density Estimators to accurately estimate significance in high-dimensional data without binning, demonstrated on toy models and LHC data.

Contribution

The authors extend the Machine-Learned Likelihoods method by integrating KDE to avoid binning, enabling more precise density estimation for high-dimensional data analysis.

Findings

KDE effectively smooths non-smooth ML output distributions.

The method provides reliable significance estimates in LHC analyses.

Significance results are robust against non-smoothness in ML outputs.

Abstract

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.