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

Abstract

In the past few years, approximate Bayesian Neural Networks (BNNs) have demonstrated the ability to produce statistically consistent posteriors on a wide range of inference problems at unprecedented speed and scale. However, any disconnect between training sets and the distribution of real-world objects can introduce bias when BNNs are applied to data. This is a common challenge in astrophysics and cosmology, where the unknown distribution of objects in our Universe is often the science goal. In this work, we incorporate BNNs with flexible posterior parameterizations into a hierarchical inference framework that allows for the reconstruction of population hyperparameters and removes the bias introduced by the training distribution. We focus on the challenge of producing posterior PDFs for strong gravitational lens mass model parameters given Hubble Space Telescope (HST) quality single-filter, lens-subtracted, synthetic imaging data. We show that the posterior PDFs are sufficiently accurate (i.e., statistically consistent with the truth) across a wide variety of power-law elliptical lens mass distributions. We then apply our approach to test data sets whose lens parameters are drawn from distributions that are drastically different from the training set. We show that our hierarchical inference framework mitigates the bias introduced by an unrepresentative training set's interim prior. Simultaneously, given a sufficiently broad training set, we can precisely reconstruct the population hyperparameters governing our test distributions. Our full pipeline, from training to hierarchical inference on thousands of lenses, can be run in a day. The framework presented here will allow us to efficiently exploit the full constraining power of future ground- and space-based surveys.

arXiv commentAccepted by ApJ. Code available at https://github.com/swagnercarena/ovejero

References in corpus (32)

• emcee: The MCMC Hammer
• Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics Beyond LambdaCDM
• Tensions between the Early and the Late Universe
• H0LiCOW XIII. A 2.4% measurement of $H_0$ from lensed quasars: $5.3\sigma$ tension between early and late-Universe probes
• The Carnegie-Chicago Hubble Program. VIII. An Independent Determination of the Hubble Constant Based on the Tip of the Red Giant Branch
• The Sloan Lens ACS Survey. III - The Structure and Formation of Early-type Galaxies and their Evolution since z~1
• The Sloan Lens ACS Survey. I. A Large Spectroscopically Selected Sample of Massive Early-Type Lens Galaxies
• Strong Lensing by Galaxies
• Massive Dark-matter halos and Evolution of Early-type Galaxies to z=1
• Gravitationally lensed quasars and supernovae in future wide-field optical imaging surveys
• Calibration of the Tip of the Red Giant Branch (TRGB)
• TDCOSMO IV: Hierarchical time-delay cosmography -- joint inference of the Hubble constant and galaxy density profiles
• Two accurate time-delay distances from strong lensing: Implications for cosmology
• The population of galaxy-galaxy strong lenses in forthcoming optical imaging surveys
• Lenstronomy: multi-purpose gravitational lens modelling software package
• Exoplanet population inference and the abundance of Earth analogs from noisy, incomplete catalogs
• STRIDES: a 3.9 per cent measurement of the Hubble constant from the strong lens system DES J0408-5354
• The Sloan Lens ACS Survey. VII. Elliptical Galaxy Scaling Laws from Direct Observational Mass Measurements
• Inferring the eccentricity distribution
• The SL2S Galaxy-scale Lens Sample. V. Dark Matter Halos and Stellar IMF of Massive Early-type Galaxies out to Redshift 0.8
• Fast calculation of a family of elliptical mass gravitational lens models
• Uncertainties in Parameters Estimated with Neural Networks: Application to Strong Gravitational Lensing
• The SL2S Galaxy-scale Lens Sample. III. Lens Models, Surface Photometry and Stellar Masses for the final sample
• Is every strong lens model unhappy in its own way? Uniform modelling of a sample of 13 quadruply+ imaged quasars
• Mining for Dark Matter Substructure: Inferring subhalo population properties from strong lenses with machine learning
• Improving time-delay cosmography with spatially resolved kinematics
• Parameters Estimation for the Cosmic Microwave Background with Bayesian Neural Networks
• HOLISMOKES -- IV. Efficient mass modeling of strong lenses through deep learning
• Direct Detection of Dark Matter Substructure in Strong Lens Images with Convolutional Neural Networks
• Differentiable Strong Lensing: Uniting Gravity and Neural Nets through Differentiable Probabilistic Programming
• Constraining the Reionization History using Bayesian Normalizing Flows
• Cosmic Shear with Einstein Rings

Cited by in corpus (35)

• lenstronomy II: A gravitational lensing software ecosystem
• Strong lensing time-delay cosmography in the 2020s
• Simulation-Based Inference of Reionization Parameters From 3D Tomographic 21 cm Lightcone Images
• Automated galaxy-galaxy strong lens modelling: no lens left behind
• The Hubble constant from strongly lensed supernovae with standardizable magnifications
• TDCOSMO. VII. Boxyness/discyness in lensing galaxies : Detectability and impact on $H_0$
• From Images to Dark Matter: End-To-End Inference of Substructure From Hundreds of Strong Gravitational Lenses
• Statistical strong lensing. I. Constraints on the inner structure of galaxies from samples of a thousand lenses
• Strong lens modelling: comparing and combining Bayesian neural networks and parametric profile fitting
• Strong Lensing by Galaxies
• GAlaxy Light profile convolutional neural NETworks (GaLNets). I. fast and accurate structural parameters for billion galaxy samples
• Consequences of the lack of azimuthal freedom in the modeling of lensing galaxies
• HOLISMOKES -- IX. Neural network inference of strong-lens parameters and uncertainties from ground-based images
• LeMoN: Lens Modelling with Neural networks -- I. Automated modelling of strong gravitational lenses with Bayesian Neural Networks
• Machine Learning and Cosmology
• Scalable inference with Autoregressive Neural Ratio Estimation
• TDCOSMO XV: Population Analysis of Lines of Sight of 25 Strong Galaxy-Galaxy Lenses with Extreme Value Statistics
• A Framework for Obtaining Accurate Posteriors of Strong Gravitational Lensing Parameters with Flexible Priors and Implicit Likelihoods using Density Estimation
• GaMPEN: A Machine Learning Framework for Estimating Bayesian Posteriors of Galaxy Morphological Parameters
• Pixelated Reconstruction of Foreground Density and Background Surface Brightness in Gravitational Lensing Systems using Recurrent Inference Machines
• AI-driven spatio-temporal engine for finding gravitationally lensed type Ia supernovae
• A Bayesian Approach to Strong Lens Finding in the Era of Wide-area Surveys
• Modeling lens potentials with continuous neural fields in galaxy-scale strong lenses
• Constraining cosmological parameters from N-body simulations with Variational Bayesian Neural Networks
• Machine Learning the 6th Dimension: Stellar Radial Velocities from 5D Phase-Space Correlations
• Inferring subhalo effective density slopes from strong lensing observations with neural likelihood-ratio estimation
• Peculiar Velocity Estimation from Kinetic SZ Effect using Deep Neural Networks
• Lens Modeling of STRIDES Strongly Lensed Quasars using Neural Posterior Estimation
• Joint Modeling of Quasar Variability and Accretion Disk Reprocessing using Latent Stochastic Differential Equations
• Measuring the Substructure Mass Power Spectrum of 23 SLACS Strong Galaxy-Galaxy Lenses with Convolutional Neural Networks
• Understanding the predication mechanism of deep learning through error propagation among parameters in strong lensing case
• Robustness of Neural Ratio and Posterior Estimators to Distributional Shifts for Population-Level Dark Matter Analysis in Strong Gravitational Lensing
• Deep inference of simulated strong lenses in ground-based surveys
• Quantifying Weighted Morphological Content of Large-Scale Structures via Simulation-Based Inference
• Correlated Read Noise Reduction in Infrared Arrays Using Deep Learning