Posterior samples of source galaxies in strong gravitational lenses with score-based priors

Abstract

Inferring accurate posteriors for high-dimensional representations of the brightness of gravitationally-lensed sources is a major challenge, in part due to the difficulties of accurately quantifying the priors. Here, we report the use of a score-based model to encode the prior for the inference of undistorted images of background galaxies. This model is trained on a set of high-resolution images of undistorted galaxies. By adding the likelihood score to the prior score and using a reverse-time stochastic differential equation solver, we obtain samples from the posterior. Our method produces independent posterior samples and models the data almost down to the noise level. We show how the balance between the likelihood and the prior meet our expectations in an experiment with out-of-distribution data.

A Framework for Obtaining Accurate Posteriors of Strong Gravitational Lensing Parameters with Flexible Priors and Implicit Likelihoods Using Density Estimation

“…One possibility for circumventing this issue is to have a separate approximate inference of the nuisance parameters and draw the simulations for the density estimation stage from these posteriors. This may be possible in a scenario where a separate network is trained to infer a posterior distribution for the nuisance parameters (e.g., a generative model for the background source conditioned on the data; see Adam et al 2022aAdam et al , 2022b. As mentioned earlier, alternative implicit likelihood inference frameworks that allow implicit marginalization over nuisance parameters (e.g., likelihood ratio methods) are generally only practical in low-dimensional spaces.…”

Pixelated Reconstruction of Foreground Density and Background Surface Brightness in Gravitational Lensing Systems Using Recurrent Inference Machines

“…Perhaps the most important limitation of the method is the fact that, in its current form, the model only provides point estimates of the parameters of interest. Quantifying the posteriors of such high-dimensional data will require an efficient and accurate generative process (e.g., see Adam et al 2022), which we plan to explore and develop in future works.…”

Strong Lensing by Galaxies: Past Highlights, Current Status, and Future Prospects

“…However, analyzing such unprecedentedly large samples will also pose a computational challenge. One way to tackle this challenge is to use machine learning for lensing parameter extraction from the data, which is currently an active area of research (e.g., Hezaveh et al 2017;Morningstar et al 2019;Schuldt et al 2021;Adam et al 2022;Poh et al 2022;Mishra-Sharma and Yang 2022;Biggio et al 2023). However, depending on specific scientific requirements, the conventional forward modeling approach would still be favorable for a subset of all the new lenses.…”