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

TL;DR

This study compares a machine learning approach using an autoencoder CNN with a traditional maximum-likelihood estimator for determining galaxy cluster masses from galaxy distributions, demonstrating improved accuracy with the ML method.

Contribution

The paper introduces a novel application of an autoencoder CNN for cluster mass estimation and compares its performance against the conventional MLE, highlighting the ML approach's superior accuracy.

Findings

AE-CNN achieves lower rms scatter (0.10 dex) than MLE (0.16 dex) in predicting true cluster masses.

AE-CNN maintains robust performance across different input types, including velocities and distances.

The ML method effectively handles inhomogeneous biases like Malmquist bias.

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.