Optimal statistical inference in the presence of systematic uncertainties using neural network optimization based on binned Poisson likelihoods with nuisance parameters
| Autor: | Stefan Wunsch, Simon Jörger, Günter Quast, Roger Wolf |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
FOS: Computer and information sciences
Feature engineering Nuclear and High Energy Physics Computer science Other Fields of Physics FOS: Physical sciences Machine Learning (stat.ML) Poisson distribution 01 natural sciences physics.data-an symbols.namesake Statistics - Machine Learning Histogram 0103 physical sciences Computer Science (miscellaneous) Statistical inference 010306 general physics Mathematical Physics and Mathematics Engineering & allied operations Artificial neural network 010308 nuclear & particles physics Dimensionality reduction Variance (accounting) stat.ML Physics - Data Analysis Statistics and Probability symbols ddc:620 Algorithm Data Analysis Statistics and Probability (physics.data-an) Software Curse of dimensionality |
| Zdroj: | Computing and software for big science, 5 (1), Art. Nr.: 4 |
| ISSN: | 2510-2036 2510-2044 |
| Popis: | Data analysis in science, e.g., high-energy particle physics, is often subject to an intractable likelihood if the observables and observations span a high-dimensional input space. Typically the problem is solved by reducing the dimensionality using feature engineering and histograms, whereby the latter allows to build the likelihood using Poisson statistics. However, in the presence of systematic uncertainties represented by nuisance parameters in the likelihood, an optimal dimensionality reduction with a minimal loss of information about the parameters of interest is not known. This work presents a novel strategy to construct the dimensionality reduction with neural networks for feature engineering and a differential formulation of histograms so that the full workflow can be optimized with the result of the statistical inference, e.g., the variance of a parameter of interest, as objective. We discuss how this approach results in an estimate of the parameters of interest that is close to optimal and the applicability of the technique is demonstrated with a simple example based on pseudo-experiments and a more complex example from high-energy particle physics. Data analysis in science, e.g., high-energy particle physics, is often subject to an intractable likelihood if the observables and observations span a high-dimensional input space. Typically the problem is solved by reducing the dimensionality using feature engineering and histograms, whereby the latter technique allows to build the likelihood using Poisson statistics. However, in the presence of systematic uncertainties represented by nuisance parameters in the likelihood, the optimal dimensionality reduction with a minimal loss of information about the parameters of interest is not known. This work presents a novel strategy to construct the dimensionality reduction with neural networks for feature engineering and a differential formulation of histograms so that the full workflow can be optimized with the result of the statistical inference, e.g., the variance of a parameter of interest, as objective. We discuss how this approach results in an estimate of the parameters of interest that is close to optimal and the applicability of the technique is demonstrated with a simple example based on pseudo-experiments and a more complex example from high-energy particle physics. |
| Databáze: | OpenAIRE |
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