Predicting galaxy bias using machine learning

¹ Departamento de Física, Universidad Técnica Federico Santa María, Av. España 1680, Valparaíso, Chile
² HEP Division, Argonne National Laboratory, 9700 South Cass Avenue, Lemont, IL, 60439, USA
³ Berkeley Center for Cosmological Physics, University of California, Berkeley, 341 Campbell Hall, Berkeley, CA, 94720, U.S.A.
⁴ Physics Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA, 94720, U.S.A.
⁵ Departamento de Física Matemática, Instituto de Física, Universidade de São Paulo, Rua do Matão 1371, CEP 05508-090, São Paulo, Brazil
⁶ Universidad Andres Bello, Facultad de Ciencias Exactas, Departamento de Fisica y Astronomia, Instituto de Astrofisica, Fernandez Concha 700, Las Condes, Santiago RM, Chile
⁷ Independent Researcher., Camino El Pino 68D, 38208, La Laguna, Spain

^★ Corresponding authors: This email address is being protected from spambots. You need JavaScript enabled to view it. ; This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 2 February 2026
Accepted: 4 May 2026

Abstract

Context. Understanding how galaxies trace the underlying matter density field is essential for characterizing the influence of the large-scale structure on galaxy formation, being therefore a key ingredient in observational cosmology. This connection, commonly described through the galaxy bias, b, can be studied effectively using machine-learning (ML) techniques, which offer strong predictive capabilities and can capture nonlinear relationships in high-dimensional data. Recent work has also highlighted the need for probabilistic methods to properly account for the intrinsic stochasticity of this connection.

Aims. We aim to incorporate the linear bias parameter assigned to individual galaxies into a ML framework, quantify its dependence on various halo and environmental properties, and evaluate whether different algorithms can accurately predict this parameter and reproduce the scatter in several bias relations.

Methods. We use data from the IllustrisTNG300 magnetohydrodynamical simulation, including the distance to different cosmic web structures computed with DisPerSE. These data are complemented with an object-by-object estimator of the large-scale linear bias (b_i), providing the individual contribution of each galaxy to the bias of the entire population. Our ML framework uses three models to predict b_i: a random forest regressor, a single-output neural network and a probabilistic method (normalizing flows).

Results. We recover the full hierarchy of galaxy bias dependencies, showing that the most informative features are the overdensities, particularly δ₈, followed by the distances to cosmic-web structures and selected internal halo properties, most notably the formation redshift (z_1/2). We also demonstrate that normalizing flows clearly outperform deterministic methods in predicting galaxy bias, including its joint distributions with galaxy properties, owing to their ability to capture the intrinsic variance associated with the stochastic nature of the matter-halo-galaxy connection. Our ML framework provides a foundation for future efforts to measure the individual bias with upcoming spectroscopic surveys.