Alexandre Adam

Likelihood analysis is typically limited to normally distributed noise due to the difficulty of determining the probability density function… (see more) of complex, high-dimensional, non-Gaussian, and anisotropic noise. This work presents Score-based LIkelihood Characterization (SLIC), a framework that resolves this issue by building a data-driven noise model using a set of noise realizations from observations. We show that the approach produces unbiased and precise likelihoods even in the presence of highly non-Gaussian correlated and spatially varying noise. We use diffusion generative models to estimate the gradient of the probability density of noise with respect to data elements. In combination with the Jacobian of the physical model of the signal, we use Langevin sampling to produce independent samples from the unbiased likelihood. We demonstrate the effectiveness of the method using real data from the Hubble Space Telescope and James Webb Space Telescope.

2023-11-02

NeurIPS.cc/2023/Workshop/Deep_Inverse (poster)

openreview.net

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

Alexandre Adam

Laurence Perreault-Levasseur

Yashar Hezaveh

MAX WELLING

Modeling strong gravitational lenses in order to quantify the distortions in the images of background sources and to reconstruct the mass de… (see more)nsity in the foreground lenses has been a difficult computational challenge. As the quality of gravitational lens images increases, the task of fully exploiting the information they contain becomes computationally and algorithmically more difficult. In this work, we use a neural network based on the Recurrent Inference Machine (RIM) to simultaneously reconstruct an undistorted image of the background source and the lens mass density distribution as pixelated maps. The method iteratively reconstructs the model parameters (the image of the source and a pixelated density map) by learning the process of optimizing the likelihood given the data using the physical model (a ray-tracing simulation), regularized by a prior implicitly learned by the neural network through its training data. When compared to more traditional parametric models, the proposed method is significantly more expressive and can reconstruct complex mass distributions, which we demonstrate by using realistic lensing galaxies taken from the IllustrisTNG cosmological hydrodynamic simulation.

2023-06-26

The Astrophysical Journal (published)

doi.org

arxiv.org

Beyond Gaussian Noise: A Generalized Approach to Likelihood Analysis with non-Gaussian Noise

Ronan Legin

Alexandre Adam

Yashar Hezaveh

Laurence Perreault Levasseur

Likelihood analysis is typically limited to normally distributed noise due to the difficulty of determining the probability density function… (see more) of complex, high-dimensional, non-Gaussian, and anisotropic noise. This is a major limitation for precision measurements in many domains of science, including astrophysics, for example, for the analysis of the Cosmic Microwave Background, gravitational waves, gravitational lensing, and exoplanets. This work presents Score-based LIkelihood Characterization (SLIC), a framework that resolves this issue by building a data-driven noise model using a set of noise realizations from observations. We show that the approach produces unbiased and precise likelihoods even in the presence of highly non-Gaussian correlated and spatially varying noise. We use diffusion generative models to estimate the gradient of the probability density of noise with respect to data elements. In combination with the Jacobian of the physical model of the signal, we use Langevin sampling to produce independent samples from the unbiased likelihood. We demonstrate the effectiveness of the method using real data from the Hubble Space Telescope and James Webb Space Telescope.

2023-05-31

The Astrophysical Journal Letters (published)

doi.org

arxiv.org

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

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,… (see more) 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.

2022-11-06

ArXiv (preprint)

doi.org

arxiv.org

Mila Techaide 2026

Venture Scientist Bootcamp

AI Advantage: Productivity in Public Service

Alexandre Adam

Publications

Mila Techaide 2026

Venture Scientist Bootcamp

AI Advantage: Productivity in Public Service

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Alexandre Adam

Publications