Adam Coogan
Gather.town id
DM07
Poster Title
Precision searches for subhalos in strong lensing images with targeted inference networks
Institution
GRAPPA, University of Amsterdam
Abstract (short summary)
Robustly inferring the properties of a dark matter subhalo in a strong lensing image requires marginalizing over uncertainties in the main lens mass and source light distributions. This is an extremely difficult problem due to the high dimensionality of lensing observations. Here we present a new multi-stage method for performing subhalo inference that combines the strengths of parametric lensing models and simulation-based inference (SBI), a tool that leverages neural networks to directly obtain marginal posteriors from observations. In the first stage, we use our novel Gaussian process-inspired lensing model to closely fit an observation, obtaining approximate posteriors for all model parameters. We use the obtained posteriors to generate variations of the target image with different subhalo realizations. In the second stage we train a targeted inference network on these images to produce precision posteriors for the subhalo's parameters using the technique of neural likelihood-to-evidence estimation. The final inference is performed by applying the trained network to the original observation of interest. We present results of a mock analysis showing we can accurately reconstruct a subhalo's position and mass in a realistic, high-resolution observation, marginalizing over more than 100,000 lens and source parameters. The whole analysis can be performed rapidly using a single graphical processing unit and scales rather favorably (linearly) with models complexity.
Plain text (extended) Summary
First panel: the goal and the problem. Our goal is to infer the properties of individual dark matter subhalos in strong galaxy-galaxy lenses. This amounts to computing posteriors for quantities such as the subhalo's position and mass, marginalized over nuisance parameters characterizing the source, lens and potentially other light subhalos. This marginalization is extremely difficult to perform because modeling high-quality observations requires many thousands of parameters, and the likelihood can have many degenerate minima. In this setting established techniques like MCMC and nested sampling are intractable, since they require sampling the joint posterior over subhalo and nuisance parameters.
Second panel: a machine learning solution. Neural likelihood-to-evidence ratio estimation rephrases marginal posterior inference as an equivalent classification problem. In this approach, a neural network is provided pairs of images and subhalo parameters and trained to distinguish whether they come from one of two classes, A or B. For samples from class A, the subhalo parameters were sampled from the prior and used to generate an image. For samples from class B, the subhalo parameters were not used to generate the image -- instead, they are just a random sample from the prior. Through training, the neural network approaches the optimal classifier, which uses the ratio of the posterior of the subhalo parameters given an image to the prior for those parameters. This means the network learns a function equivalent to the marginal posterior we wanted to compute. The marginalization over nuisance parameters is accomplished by randomly sampling them while generating training data.
Third panel: targeted inference. While the marginalization should formally run over all possible values of the nuisance parameters, the vast majority are inconsistent with any given observation. Our strategy instead is to target the inference by only using nuisance parameters compatible with the observation. We are able to accomplish this using a new lensing model we developed, described in detail by Konstantin Karchev's poster. In brief, the model is differentiable and uses an approximate Gaussian process source with variational hyperparameter optimization. It enables fitting a variational posterior for roughly 100,000 source and lens parameters using gradient-based optimization. The figure shows we are able to fit high-resolution observations down to the noise level with this lens model. We then sample from the variational posterior to generate training data for the neural network that looks similar to the observation.
Fourth panel: results. We set up an analysis of high-resolution mock images containing a single subhalo with mass between 10 to the 8.5 and 10 to the 10.5 solar masses, randomly positioned on the image. After the initial fitting step, we generate targeted training data for the posterior inference network. To perform the final inference, we apply the network to the observation. As the figure shows, we find it gives accurate marginal posteriors for the subhalo's position and mass, which are marginalized over all 174,458 source and lens parameters. These results used a simple inference network trained on just 10,000 samples, so we expect there is room to improve performance.
In Noemi Anau Montel's talk, she will discuss our work in progress on extending the analysis to the parameters of a population of perturbers.
Second panel: a machine learning solution. Neural likelihood-to-evidence ratio estimation rephrases marginal posterior inference as an equivalent classification problem. In this approach, a neural network is provided pairs of images and subhalo parameters and trained to distinguish whether they come from one of two classes, A or B. For samples from class A, the subhalo parameters were sampled from the prior and used to generate an image. For samples from class B, the subhalo parameters were not used to generate the image -- instead, they are just a random sample from the prior. Through training, the neural network approaches the optimal classifier, which uses the ratio of the posterior of the subhalo parameters given an image to the prior for those parameters. This means the network learns a function equivalent to the marginal posterior we wanted to compute. The marginalization over nuisance parameters is accomplished by randomly sampling them while generating training data.
Third panel: targeted inference. While the marginalization should formally run over all possible values of the nuisance parameters, the vast majority are inconsistent with any given observation. Our strategy instead is to target the inference by only using nuisance parameters compatible with the observation. We are able to accomplish this using a new lensing model we developed, described in detail by Konstantin Karchev's poster. In brief, the model is differentiable and uses an approximate Gaussian process source with variational hyperparameter optimization. It enables fitting a variational posterior for roughly 100,000 source and lens parameters using gradient-based optimization. The figure shows we are able to fit high-resolution observations down to the noise level with this lens model. We then sample from the variational posterior to generate training data for the neural network that looks similar to the observation.
Fourth panel: results. We set up an analysis of high-resolution mock images containing a single subhalo with mass between 10 to the 8.5 and 10 to the 10.5 solar masses, randomly positioned on the image. After the initial fitting step, we generate targeted training data for the posterior inference network. To perform the final inference, we apply the network to the observation. As the figure shows, we find it gives accurate marginal posteriors for the subhalo's position and mass, which are marginalized over all 174,458 source and lens parameters. These results used a simple inference network trained on just 10,000 samples, so we expect there is room to improve performance.
In Noemi Anau Montel's talk, she will discuss our work in progress on extending the analysis to the parameters of a population of perturbers.
URL
https://adam-coogan.github.io/
Poster file