A Bayesian Convolutional Neural Network for Robust Galaxy Ellipticity Regression

Cosmic shear estimation is an essential scientific goal for large galaxy\nsurveys. It refers to the coherent distortion of distant galaxy images due to\nweak gravitational lensing along the line of sight. It can be used as a tracer\nof the matter distribution in the Universe. The unbiased estimation of the\nlocal value of the cosmic shear can be obtained via Bayesian analysis which\nrelies on robust estimation of the galaxies ellipticity (shape) posterior\ndistribution. This is not a simple problem as, among other things, the images\nmay be corrupted with strong background noise. For current and coming surveys,\nanother central issue in galaxy shape determination is the treatment of\nstatistically dominant overlapping (blended) objects. We propose a Bayesian\nConvolutional Neural Network based on Monte-Carlo Dropout to reliably estimate\nthe ellipticity of galaxies and the corresponding measurement uncertainties. We\nshow that while a convolutional network can be trained to correctly estimate\nwell calibrated aleatoric uncertainty, -- the uncertainty due to the presence\nof noise in the images -- it is unable to generate a trustworthy ellipticity\ndistribution when exposed to previously unseen data (i.e. here, blended\nscenes). By introducing a Bayesian Neural Network, we show how to reliably\nestimate the posterior predictive distribution of ellipticities along with\nrobust estimation of epistemic uncertainties. Experiments also show that\nepistemic uncertainty can detect inconsistent predictions due to unknown\nblended scenes.\n