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Posterior samples of source galaxies in strong gravitational lenses with score-based priors
Alexandre Adam · Adam Coogan · Nikolay Malkin · Ronan Legin · Laurence Perreault-Levasseur · Yashar Hezaveh · Yoshua Bengio

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.

Author Information

Alexandre Adam (Université de Montréal)
Adam Coogan (Ciela Institute (Université de Montréal & Mila))
Nikolay Malkin (Mila / Université de Montréal)
Ronan Legin (University of Montreal)
Laurence Perreault-Levasseur (Université de Montréal)
Yashar Hezaveh (Université de Montréal)
Yoshua Bengio (Mila / U. Montreal)

Yoshua Bengio is Full Professor in the computer science and operations research department at U. Montreal, scientific director and founder of Mila and of IVADO, Turing Award 2018 recipient, Canada Research Chair in Statistical Learning Algorithms, as well as a Canada AI CIFAR Chair. He pioneered deep learning and has been getting the most citations per day in 2018 among all computer scientists, worldwide. He is an officer of the Order of Canada, member of the Royal Society of Canada, was awarded the Killam Prize, the Marie-Victorin Prize and the Radio-Canada Scientist of the year in 2017, and he is a member of the NeurIPS advisory board and co-founder of the ICLR conference, as well as program director of the CIFAR program on Learning in Machines and Brains. His goal is to contribute to uncover the principles giving rise to intelligence through learning, as well as favour the development of AI for the benefit of all.

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