Connor Stone

Gabriel Missael Barco, Alexandre Adam, Connor Stone et al. · mila

Bayesian inference for inverse problems hinges critically on the choice of priors. In the absence of specific prior information, population-level distributions can serve as effective priors for parameters of interest. With the advent of machine learning, the use of data-driven population-level distributions (encoded, e.g., in a trained deep neural network) as priors is emerging as an appealing alternative to simple parametric priors in a variety of inverse problems. However, in many astrophysical applications, it is often difficult or even impossible to acquire independent and identically distributed samples from the underlying data-generating process of interest to train these models. In these cases, corrupted data or a surrogate, e.g. a simulator, is often used to produce training samples, meaning that there is a risk of obtaining misspecified priors. This, in turn, can bias the inferred posteriors in ways that are difficult to quantify, which limits the potential applicability of these models in real-world scenarios. In this work, we propose addressing this issue by iteratively updating the population-level distributions by retraining the model with posterior samples from different sets of observations, and we showcase the potential of this method on the problem of background image reconstruction in strong gravitational lensing when score-based models are used as data-driven priors. We show that, starting from a misspecified prior distribution, the updated distribution becomes progressively closer to the underlying population-level distribution, and the resulting posterior samples exhibit reduced bias after several updates.

Alexandre Adam, Connor Stone, Connor Bottrell et al.

Examining the detailed structure of galaxy populations provides valuable insights into their formation and evolution mechanisms. Significant barriers to such analysis are the non-trivial noise properties of real astronomical images and the point spread function (PSF) which blurs structure. Here we present a framework which combines recent advances in score-based likelihood characterization and diffusion model priors to perform a Bayesian analysis of image deconvolution. The method, when applied to minimally processed \emph{Hubble Space Telescope} (\emph{HST}) data, recovers structures which have otherwise only become visible in next-generation \emph{James Webb Space Telescope} (\emph{JWST}) imaging.

Michael J. Smith, James E. Geach, Ryan A. Jackson et al.

We show that a Denoising Diffusion Probabalistic Model (DDPM), a class of score-based generative model, can be used to produce realistic mock images that mimic observations of galaxies. Our method is tested with Dark Energy Spectroscopic Instrument (DESI) grz imaging of galaxies from the Photometry and Rotation curve OBservations from Extragalactic Surveys (PROBES) sample and galaxies selected from the Sloan Digital Sky Survey. Subjectively, the generated galaxies are highly realistic when compared with samples from the real dataset. We quantify the similarity by borrowing from the deep generative learning literature, using the `Fréchet Inception Distance' to test for subjective and morphological similarity. We also introduce the `Synthetic Galaxy Distance' metric to compare the emergent physical properties (such as total magnitude, colour and half light radius) of a ground truth parent and synthesised child dataset. We argue that the DDPM approach produces sharper and more realistic images than other generative methods such as Adversarial Networks (with the downside of more costly inference), and could be used to produce large samples of synthetic observations tailored to a specific imaging survey. We demonstrate two potential uses of the DDPM: (1) accurate in-painting of occluded data, such as satellite trails, and (2) domain transfer, where new input images can be processed to mimic the properties of the DDPM training set. Here we `DESI-fy' cartoon images as a proof of concept for domain transfer. Finally, we suggest potential applications for score-based approaches that could motivate further research on this topic within the astronomical community.