E-INSPIRE - II. Finding relics from wide-sky multi-band surveys: A proof-of-concept machine learning regression algorithm

Abstract

In this second paper of the E-INSPIRE series, we train a machine-learning-based regression on $\sim430$ nearby ($z<0.5$) ultra-compact massive galaxies (UCMGs) with spectroscopically inferred kinematics, stellar population parameters and a measured ``degree of relicness&#39;&#39; (DoR). Our goal is to investigate how robustly the spectroscopically inferred DoR can be statistically reconstructed from observable galaxy properties, and to explore the potential applicability of this framework to future wide-area surveys. We test several regression algorithms finding that Support Vector Regression (SVR) provides the best performance. We explore multiple input feature configurations, from a minimal set including only age and metallicity to more comprehensive ones incorporating stellar population parameters, kinematics, structural properties, and the associated uncertainties. All tested models achieve similarly high performance on the training set ($R^2\ge0.81$), except for the minimal configuration ($R^2\sim0.78$). When evaluated on an independent INSPIRE sample of 52 UCMGs, the predictive power remains robust, although with increased model-to-model variation. The DoR distribution shows three regimes, with low (DoR$<0.3$) and high (DoR$>0.6$) values sparsely populated, leading to mild regression shrinkage toward intermediate values. However, this behaviour enables a conservative selection strategy: galaxies with predicted DoR$\ge0.6$ are strongly biased toward genuine extreme relics, making them prime targets for follow-up observations. This proof-of-concept confirms that the spectroscopically inferred DoR is robustly connected to observable stellar population and kinematical properties, and provides a first step toward future relic-candidate selection strategies in large photometric and spectroscopic surveys.