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

Perreault Levasseur, Laurence; Hezaveh, Yashar D.; Wechsler, Risa H.

doi:10.3847/2041-8213/aa9704

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

Journal Article · Wed Nov 15 00:00:00 EST 2017 · The Astrophysical Journal. Letters (Online)

DOI:https://doi.org/10.3847/2041-8213/aa9704· OSTI ID:1419653

^[1];

^[1]

Stanford Univ. (United States). Kavli Inst. for Particle Astrophysics and Cosmology; SLAC National Accelerator Lab., Menlo Park, CA (United States)

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.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC02-76SF00515

OSTI ID:: 1419653

Journal Information:: The Astrophysical Journal. Letters (Online), Vol. 850, Issue 1; ISSN 2041-8213

Publisher:: Institute of Physics (IOP)Copyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 63 works

Citation information provided by
Web of Science

References (7)

Dermatologist-level classification of skin cancer with deep neural networks Esteva, Andre; Kuprel, Brett; Novoa, Roberto A. Nature, Vol. 542, Issue 7639 https://doi.org/10.1038/nature21056	journal	January 2017
Fast automated analysis of strong gravitational lenses with convolutional neural networks Hezaveh, Yashar D.; Levasseur, Laurence Perreault; Marshall, Philip J. Nature, Vol. 548, Issue 7669 https://doi.org/10.1038/nature23463	journal	August 2017
Finding strong lenses in CFHTLS using convolutional neural networks Jacobs, C.; Glazebrook, K.; Collett, T. Monthly Notices of the Royal Astronomical Society, Vol. 471, Issue 1 https://doi.org/10.1093/mnras/stx1492	journal	June 2017
Human-level control through deep reinforcement learning Mnih, Volodymyr; Kavukcuoglu, Koray; Silver, David Nature, Vol. 518, Issue 7540 https://doi.org/10.1038/nature14236	journal	February 2015
Finding strong gravitational lenses in the Kilo Degree Survey with Convolutional Neural Networks Petrillo, C. E.; Tortora, C.; Chatterjee, S. Monthly Notices of the Royal Astronomical Society, Vol. 472, Issue 1 https://doi.org/10.1093/mnras/stx2052	journal	August 2017
Mastering the game of Go with deep neural networks and tree search Silver, David; Huang, Aja; Maddison, Chris J. Nature, Vol. 529, Issue 7587 https://doi.org/10.1038/nature16961	journal	January 2016
The sl2s Galaxy-Scale lens Sample. v. dark Matter Halos and Stellar imf of Massive Early-Type Galaxies out to Redshift 0.8 Sonnenfeld, Alessandro; Treu, Tommaso; Marshall, Philip J. The Astrophysical Journal, Vol. 800, Issue 2 https://doi.org/10.1088/0004-637X/800/2/94	journal	February 2015

Cited By (23)

Surveying the reach and maturity of machine learning and artificial intelligence in astronomy Fluke, Christopher J.; Jacobs, Colin WIREs Data Mining and Knowledge Discovery, Vol. 10, Issue 2 https://doi.org/10.1002/widm.1349	journal	September 2019
Gaia GraL: Gaia DR2 gravitational lens systems : II. The known multiply imaged quasars⋆ Ducourant, C.; Wertz, O.; Krone-Martins, A. Astronomy & Astrophysics, Vol. 618 https://doi.org/10.1051/0004-6361/201833480	journal	October 2018
Is every strong lens model unhappy in its own way? Uniform modelling of a sample of 13 quadruply+ imaged quasars Shajib, A. J.; Birrer, S.; Treu, T. Monthly Notices of the Royal Astronomical Society, Vol. 483, Issue 4 https://doi.org/10.1093/mnras/sty3397	journal	December 2018
Direct detection of dark matter substructure in strong lens images with convolutional neural networks Diaz Rivero, Ana; Dvorkin, Cora Physical Review D, Vol. 101, Issue 2 https://doi.org/10.1103/physrevd.101.023515	journal	January 2020
Deep neural networks to enable real-time multimessenger astrophysics George, Daniel; Huerta, E. A. Physical Review D, Vol. 97, Issue 4 https://doi.org/10.1103/physrevd.97.044039	journal	February 2018
Cosmological constraints from noisy convergence maps through deep learning Fluri, Janis; Kacprzak, Tomasz; Refregier, Alexandre Physical Review D, Vol. 98, Issue 12 https://doi.org/10.1103/physrevd.98.123518	journal	December 2018
An Ensemble of Bayesian Neural Networks for Exoplanetary Atmospheric Retrieval Cobb, Adam D.; Himes, Michael D.; Soboczenski, Frank The Astronomical Journal, Vol. 158, Issue 1 https://doi.org/10.3847/1538-3881/ab2390	journal	June 2019
Nonparametric Star Formation History Reconstruction with Gaussian Processes. I. Counting Major Episodes of Star Formation Iyer, Kartheik G.; Gawiser, Eric; Faber, Sandra M. The Astrophysical Journal, Vol. 879, Issue 2 https://doi.org/10.3847/1538-4357/ab2052	journal	July 2019
Data-driven Reconstruction of Gravitationally Lensed Galaxies Using Recurrent Inference Machines Morningstar, Warren R.; Levasseur, Laurence Perreault; Hezaveh, Yashar D. The Astrophysical Journal, Vol. 883, Issue 1 https://doi.org/10.3847/1538-4357/ab35d7	journal	September 2019
Mining for Dark Matter Substructure: Inferring Subhalo Population Properties from Strong Lenses with Machine Learning Brehmer, Johann; Mishra-Sharma, Siddharth; Hermans, Joeri The Astrophysical Journal, Vol. 886, Issue 1 https://doi.org/10.3847/1538-4357/ab4c41	journal	November 2019
A Machine Learning Based Morphological Classification of 14,245 Radio AGNs Selected from the Best–Heckman Sample Ma, Zhixian; Xu, Haiguang; Zhu, Jie The Astrophysical Journal Supplement Series, Vol. 240, Issue 2 https://doi.org/10.3847/1538-4365/aaf9a2	journal	February 2019
Gaia GraL: Gaia DR2 gravitational lens systems : I. New quadruply imaged quasar candidates around known quasars Krone-Martins, A.; Delchambre, L.; Wertz, O. Astronomy & Astrophysics, Vol. 616 https://doi.org/10.1051/0004-6361/201833337	journal	August 2018
Cosmological constraints from noisy convergence maps through deep learning Fluri, Janis; Kacprzak, Tomasz; Lucchi, Aurelien arXiv https://doi.org/10.48550/arxiv.1807.08732	text	January 2018
Is every strong lens model unhappy in its own way? Uniform modelling of a sample of 13 quadruply+ imaged quasars Shajib, A. J.; Birrer, S.; Treu, T. arXiv https://doi.org/10.48550/arxiv.1807.09278	text	January 2018
A Machine Learning Based Morphological Classification of 14,245 Radio AGNs Selected From The Best-Heckman Sample Ma, Zhixian; Xu, Haiguang; Zhu, Jie arXiv https://doi.org/10.48550/arxiv.1812.07190	text	January 2018
An Ensemble of Bayesian Neural Networks for Exoplanetary Atmospheric Retrieval Cobb, Adam D.; Himes, Michael D.; Soboczenski, Frank arXiv https://doi.org/10.48550/arxiv.1905.10659	text	January 2019
Direct Detection of Dark Matter Substructure in Strong Lens Images with Convolutional Neural Networks Rivero, Ana Diaz; Dvorkin, Cora arXiv https://doi.org/10.48550/arxiv.1910.00015	text	January 2019
Parameter estimation for the cosmic microwave background with Bayesian neural networks Hortúa, Héctor J.; Volpi, Riccardo; Marinelli, Dimitri Physical Review D, Vol. 102, Issue 10 https://doi.org/10.1103/physrevd.102.103509	journal	November 2020
Building Calibrated Deep Models via Uncertainty Matching with Auxiliary Interval Predictors Thiagarajan, Jayaraman J.; Venkatesh, Bindya; Sattigeri, Prasanna Proceedings of the AAAI Conference on Artificial Intelligence, Vol. 34, Issue 04 https://doi.org/10.1609/aaai.v34i04.6062	journal	April 2020
Variational Inference as an alternative to MCMC for parameter estimation and model selection Gunapati, Geetakrishnasai; Jain, Anirudh; Srijith, P. K. arXiv https://doi.org/10.48550/arxiv.1803.06473	text	January 2018
Deep Learning in Wide-field Surveys: Fast Analysis of Strong Lenses in Ground-based Cosmic Experiments Bom, Clecio; Poh, Jason; Nord, Brian arXiv https://doi.org/10.48550/arxiv.1911.06341	preprint	January 2019
Dark Matter Subhalos, Strong Lensing and Machine Learning Varma, Sreedevi; Fairbairn, Malcolm; Figueroa, Julio arXiv https://doi.org/10.48550/arxiv.2005.05353	preprint	January 2020
Gravitational-Wave Detector Networks: Standard Sirens on Cosmology and Modified Gravity Theory Yang, Tao arXiv https://doi.org/10.48550/arxiv.2103.01923	text	January 2021

Similar Records

Hierarchical Inference with Bayesian Neural Networks: An Application to Strong Gravitational Lensing

Journal Article · Wed Mar 17 00:00:00 EDT 2021 · The Astrophysical Journal · OSTI ID:1419653

Wagner-Carena, Sebastian; Park, Ji Won; Birrer, Simon; +3 more

Multi-fidelity Bayesian neural networks: Algorithms and applications

Journal Article · Fri Apr 16 00:00:00 EDT 2021 · Journal of Computational Physics · OSTI ID:1419653

Meng, Xuhui; Babaee, Hessam; Karniadakis, George Em

Fast automated analysis of strong gravitational lenses with convolutional neural networks

Journal Article · Wed Aug 30 00:00:00 EDT 2017 · Nature (London) · OSTI ID:1419653

Hezaveh, Yashar D.; Levasseur, Laurence Perreault; Marshall, Philip J.

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

Citation Formats

References (7)

Cited By (23)

Similar Records

Related Subjects