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Stabilizing Neural Likelihood Ratio Estimation
High Energy Physics - Phenomenology · Submitted 26 Mar 2025
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim 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.
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The abstract, sentence by sentence
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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Likelihood ratios are used for a variety of applications in particle physics data analysis, including parameter estimation, unfolding, and anomaly detection. | background 1.00 | 0.04 | 0.01 | asserted 1.00 |
| s1 | When the data are high-dimensional, neural networks provide an effective tools for approximating these ratios. | background 1.00 | 0.07 | 0.02 | asserted 0.99 |
| s2 | However, neural network training has an inherent stochasticity that limits their precision. | background 0.89 | 0.08 | 0.02 | asserted 1.00 |
| s3 | A widely-used approach to reduce these fluctuations is to train many times and average the output (ensembling). | background 0.96 | 0.05 | 0.03 | asserted 1.00 |
| s4 | We explore different approaches to ensembling and pretraining neural networks for stabilizing likelihood ratio estimation. | contribution 1.00 | 0.69 | 0.05 | unclear 0.52 |
| s5 | For numerical studies focus on unbinned unfolding with OmniFold, as it requires many likelihood ratio estimations. | method 0.88 | 0.47 | 0.03 | asserted 0.86 |
| s6 | 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. | result 1.00 | 0.96 | 0.64 | asserted 1.00 |
| s7 | Variance can be further improved by pre-training, however at the cost increasing bias. | result 0.96 | 0.93 | 0.18 | asserted 0.99 |
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The paper
Original 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.
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Uses the method or tool of 2 papers
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The classification output is encoded using a trainable classification token [ref] , which summarizes the information from the entire point cloud and returns a binary output used for the classification task.
An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale · Neural Likelihood Ratio-based Unfolding · 0.87
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The training is done on the Perlmutter Supercomputer [ref] using 64 A100 GPUs simultaneously with Horovod [ref] package for data distributed training.
Horovod: fast and easy distributed deep learning in TensorFlow · Results · 1.00
Cites as background 1 paper
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Activation and loss functions have been well-studied [ref] and recent proposals for new optimizers have explored likelihood ratio stability [ref] .
Training Neural Networks for Likelihood/Density Ratio Estimation · Introduction · 0.98
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