Stabilizing Neural Likelihood Ratio Estimation

Abstract: Likelihood ratios are used for a variety of applications in particle physics data analysis, including parameter estimation, unfolding, and anomaly detection. When the data are high-dimensional, neural networks provide an effective tools for approximating these ratios. However, neural network training has an inherent stochasticity that limits their precision. A widely-used approach to reduce these fluctuations is to train many times and average the output (ensembling). We explore different approaches to ensembling and pretraining neural networks for stabilizing likelihood ratio estimation. For numerical studies focus on unbinned unfolding with OmniFold, as it requires many likelihood ratio estimations. We find that ensembling approaches that aggregate the models at step 1, before pushing the weights to step 2 improve both bias and variance of final results. Variance can be further improved by pre-training, however at the cost increasing bias.