Redshift prediction of Fermi-LAT gamma-ray sources using CatBoost gradient boosting decision trees

The determination of distance is fundamental in astrophysics. Gamma-ray sources are poorly characterized in this sense, as the limited angular resolution and poor photon-count statistics in gamma-ray astronomy makes it difficult to associate them to a multiwavelength object with known redshift. Taking the 1794 active galactic nuclei (AGNs) with known redshift from the Fermi-LAT latest AGN catalog, 4LAC-DR3, we employ machine learning techniques to predict the distance of the rest of AGNs based on their spectral and spatial properties. The state-of-the-art CatBoost algorithm reaches an average 0.56 R2 score with 0.46 root-mean-squared error (RMSE), predicting an average redshift value of $z_{avg}=0.63$, with a maximum $z_{max}=1.97$. We use the SHAP explainer package to gain insights into the variables influence on the outcome, and also study the extragalactic bakground light (EBL) implications. In a second part, we use this regression model to predict the redshift of the unassociated sample of the latest LAT point-source catalog, 4FGL-DR3, using the results of a previous paper to determine the possible AGNs within them.