Estimating cluster masses: a comparative study between machine learning and maximum likelihood

Abstract

We compare an autoencoder convolutional neural network (AE-CNN) with a conventional maximum-likelihood estimator (MLE) for inferring cluster virial masses, $M_v$, directly from the galaxy distribution around clusters, without identifying members or interlopers. The AE-CNN is trained on mock galaxy catalogues, whereas the MLE assumes that clusters of similar mass share the same phase-space galaxy profile. Conceptually, the MLE returns an unbiased estimate of $\log M_v$ at fixed true mass, whereas the AE-CNN approximates the posterior mean, so the true $\log M_v$ is unbiased at fixed estimate. Using MDPL2 mock clusters with redshift space number density as input, the AE-CNN attains an rms scatter of $0.10\,\textrm{dex}$ between predicted and true $\log M_v$, compared with $0.16\,\textrm{dex}$ for the MLE. With inputs based on mean peculiar velocities, binned in redshift space or observed distance, the AE-CNN achieves scatters of $0.12\,\textrm{dex}$ and $0.16\,\textrm{dex}$, respectively, despite strong inhomogeneous Malmquist bias.