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Abstract: In Hezaveh et al. 2017 we showed that deep learning can be used for modelparameter estimation and trained convolutional neural networks to determine theparameters of strong gravitational lensing systems. Here we demonstrate amethod for obtaining the uncertainties of these parameters. We review theframework of variational inference to obtain approximate posteriors of Bayesianneural networks and apply it to a network trained to estimate the parameters ofthe Singular Isothermal Ellipsoid plus external shear and total fluxmagnification. We show that the method can capture the uncertainties due todifferent levels of noise in the input data, as well as training andarchitecture-related errors made by the network. To evaluate the accuracy ofthe resulting uncertainties, we calculate the coverage probabilities ofmarginalized distributions for each lensing parameter. By tuning a singlehyperparameter, the dropout rate, we obtain coverage probabilitiesapproximately equal to the confidence levels for which they were calculated,resulting in accurate and precise uncertainty estimates. Our results suggestthat neural networks can be a fast alternative to Monte Carlo Markov Chains forparameter uncertainty estimation in many practical applications, allowing morethan seven orders of magnitude improvement in speed.
Submission history
From: Yashar Hezaveh [view email][v1]Tue, 29 Aug 2017 15:56:31 UTC (501 KB)
Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?) Browse v0.2.1 released 2019-04-18