Uncertainties in Parameters Estimated with Neural Networks: Application to Strong Gravitational Lensing

2017/08/29 by Laurence Perreault-Levasseur, Laurence Perreault Levasseur, Yashar Hezaveh +2 · 8 citations
Mathematics · Physics and Astronomy · #Adaptive optics and wavefront sensing #Algorithm #Artificial intelligence #Artificial neural network #Bayesian probability #Computer science #Convolutional neural network #Estimation theory #Gamma-ray bursts and supernovae #Hyperparameter #Markov chain Monte Carlo #Mathematics #Monte Carlo method #Pulsars and Gravitational Waves Research #Statistics #astro-ph.CO #astro-ph.IM

paper · pdf · doi:10.3847/2041-8213/aa9704

submitted to ApJL

arxiv created 2017/08/29 · openalex publication_date 2017/11/15 · arxiv updated 2017/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Abstract In Hezaveh et al. we showed that deep learning can be used for model parameter estimation and trained convolutional neural networks to determine the parameters of strong gravitational-lensing systems. Here we demonstrate a method for obtaining the uncertainties of these parameters. We review the framework of variational inference to obtain approximate posteriors of Bayesian neural networks and apply it to a network trained to estimate the parameters of the Singular Isothermal Ellipsoid plus external shear and total flux magnification. We show that the method can capture the uncertainties due to different levels of noise in the input data, as well as training and architecture-related errors made by the network. To evaluate the accuracy of the resulting uncertainties, we calculate the coverage probabilities of marginalized distributions for each lensing parameter. By tuning a single variational parameter, the dropout rate, we obtain coverage probabilities approximately equal to the confidence levels for which they were calculated, resulting in accurate and precise uncertainty estimates. Our results suggest that the application of approximate Bayesian neural networks to astrophysical modeling problems can be a fast alternative to Monte Carlo Markov Chains, allowing orders of magnitude improvement in speed.

Citations

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