Extreme Deconvolution Reimagined: Conditional Densities via Neural Networks and an Application in Quasar Classification

Density estimation is a fundamental problem that arises in many areas of astronomy, with applications ranging from selecting quasars using color distributions to characterizing stellar abundances. Astronomical observations are inevitably noisy; however, the density of a noise-free feature is often the desired outcome. The extreme-deconvolution (XD) method can be used to deconvolve the noise and obtain noise-free density estimates by fitting a mixture of Gaussians to data where each sample has non-identical (heteroscedastic) Gaussian noise. However, XD does not generalize to cases where some feature dimensions have highly non-Gaussian distribution, and no established method exists to overcome this limitation. We introduce a possible solution using neural networks to perform Gaussian mixture modeling of the Gaussian-like dimensions conditioned on those non-Gaussian features. The result is the CondXD algorithm, a generalization of XD that performs noise-free conditional density estimation. We apply CondXD to a toy model and find that it is more accurate than other approaches. We further test our method on a real-world high redshift quasar versus contaminant classification problem. Specifically, we estimate noise-free densities in flux-ratio (i.e., color) space for contaminants, conditioned on their magnitude. Our results are comparable to the existing method, which divides the samples into magnitude bins and applies XD separately in each bin, and our method is approximately ten times faster. Overall, our method has the potential to significantly improve estimating conditional densities and enable new discoveries in astronomy.