Comparison of symbolic regression algorithms in Star/galaxy/quasar separation

Abstract

This work investigates symbolic regression (SR) as an interpretable alternative to black-box machine learning for the classification of stars, galaxies, and quasars in the Sloan Digital Sky Survey Data Release 17 (SDSS DR17). We conduct a systematic comparative study of four state-of-the-art SR frameworks: {\tt PySR}, Exhaustive Symbolic Regression ({\tt ESR}) with MDL-based selection, Physical Symbolic Optimization ({\tt PhySO}) using deep reinforcement learning, and Multi-View Symbolic Regression ({\tt MvSR}). By deriving compact analytic functions (complexity $\le$ 10) on a representative training subset and subsequently evaluating them via an 80,000-sample 5-fold cross-validation threshold optimization phase and a subsequent 10,000-sample unseen hold-out test set, we map spectroscopic redshift ($z$) to continuous classification scores. Our results demonstrate that these low-complexity expressions achieve high predictive reliability, with {\tt MvSR} reaching a cross-validation Cohen's Kappa of 0.8956 (0.8876 on the hold-out set) and {\tt PhySO} achieving exceptional parametric stability ($\sigma <0.002$). We note however that the resulting equations returned by Symbolic regression are purely empirical and no physical significance should be ascribed to these equations.

23 pages, 32 figures. Accepted for publication in Astronomy and Computing

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