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

TL;DR

This study compares four symbolic regression algorithms for classifying stars, galaxies, and quasars in SDSS DR17, demonstrating that low-complexity models can achieve high accuracy and interpretability in astrophysical classification tasks.

Contribution

It provides a systematic comparison of four advanced symbolic regression frameworks for astrophysical classification, highlighting their effectiveness and interpretability.

Findings

MvSR achieved a Cohen's Kappa of 0.8948.

PhySO demonstrated parametric stability with $\sigma < 0.002$.

Models matched traditional baselines while offering transparent, concise boundaries.

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 $\leq 10$) on a representative training subset and subsequently evaluating them via a 5-fold stratified cross-validation protocol on 100,000 spectroscopically confirmed objects, 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 Cohen's Kappa of 0.8948 and {\tt PhySO} achieving exceptional parametric stability ($\sigma < 0.002$). We show that these models not only match the performance of traditional baselines but also provide a transparent, mathematically concise characterization of the astrophysical boundaries separating galactic and extragalactic populations.