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

TL;DR

This paper introduces a neural network-based method using variational inference to efficiently estimate uncertainties in parameters of strong gravitational lensing systems, offering a fast alternative to traditional techniques.

Contribution

It demonstrates the application of Bayesian neural networks with variational inference to quantify uncertainties in gravitational lensing parameters, improving speed and accuracy over existing methods.

Findings

The method captures uncertainties due to noise and model errors.

Coverage probabilities align with confidence levels after tuning dropout.

Neural networks outperform Monte Carlo methods in speed by over seven orders of magnitude.

Abstract

In Hezaveh et al. 2017 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 hyperparameter, 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 neural networks can be a fast alternative to Monte Carlo Markov Chains for parameter uncertainty estimation in many practical applications, allowing more than seven orders of magnitude improvement in speed.