Version 2: Corresponds to the v34 of the 4FGL-DR4 Fermi-LAT catalog. It is related to the published version of the paper https://arxiv.org/abs/2401.04565. The file4FGL-DR4_v34_4classes_GMM_no_bcu_spp_no_coord_features_prob_cat_v2.csvcontain classification of Fermi-LAT sources into 4 classes (dominated by bll, fsrq, psr, and msp physical classes) and correspond to the main analysis in the published version of the paper (no coordinate features, no bcu or spp sources). The corresponding file4FGL-DR4_v34_4classes_GMM_no_bcu_spp_no_coord_features_summary_v2.csvcontains the summary of the classification and the definition of the classes. The files remaining files 4FGL-DR4_v34_4classes_GMM_no_bcu_spp_no_coord_features_weighted_prob_cat_v2.csv4FGL-DR4_v34_4classes_GMM_no_bcu_spp_no_coord_features_weighted_summary_v2.csv4FGL-DR4_v34_6classes_GMM_no_coord_features_prob_cat_v2.csv4FGL-DR4_v34_6classes_GMM_no_coord_features_summary_v2.csv4FGL-DR4_v34_6classes_GMM_no_coord_features_weighted_prob_cat_v2.csv4FGL-DR4_v34_6classes_GMM_no_coord_features_weighted_summary_v2.csvcorrespond to different test cases considered in Appendix A of https://arxiv.org/abs/2401.04565. For details see the description to Version 1 of the files below. This version of the files is also used for comparison with the prior shift model in https://arxiv.org/abs/2412.04675. Version 1: These are catalogs with probabilistic classification of the Fermi-LAT 4FGL-DR4 sources used in https://arxiv.org/abs/2401.04565. The classification is performed similarly to https://zenodo.org/doi/10.5281/zenodo.8140548with the following differences: Coordinate features (Glat and Glon) are not used as input features. Some versions of the catalogs below do not have sources with uncertain associations in the training (bcu and spp classes in 4FGL-DR4). Files ending with "prob_cat" contain the class probabilities and corresopnding statistical uncertainties for all 4FGL-DR4 sources together with input features and source names. sin(GLAT), cos(GLON), sin(GLON) are included for convenience but are not used in training. Files ending with "summary" contain definition of the classes in terms of the groups of physical classes in 4FGL-DR4 and the predicted source counts for associated and unassociated sources. The files 4FGL-DR4_5classes_GMM_no_bcu_spp_no_coord_features_prob_cat_v1.csv4FGL-DR4_5classes_GMM_no_bcu_spp_no_coord_features_summary_v1.csv correspond to the main analysis in https://arxiv.org/abs/2401.04565: 5 classes and no bcu, spp, or unk sources in training. The files 4FGL-DR4_5classes_GMM_no_bcu_spp_no_coord_features_weighted_prob_cat_v1.csv4FGL-DR4_5classes_GMM_no_bcu_spp_no_coord_features_weighted_summary_v1.csv are similar to the main analysis results but include a weighting in training to account for the covariate shift, e.g., the differences in the distribution of associated and unassociated sources. More details on the weighting can be found in https://arxiv.org/abs/2307.09584. The weighted training is used as a check of systematic uncertainties in Appendix A of https://arxiv.org/abs/2401.04565. The files 4FGL-DR4_6classes_GMM_no_coord_features_prob_cat_v1.csv4FGL-DR4_6classes_GMM_no_coord_features_summary_v1.csv4FGL-DR4_6classes_GMM_no_coord_features_weighted_prob_cat_v1.csv4FGL-DR4_6classes_GMM_no_coord_features_weighted_summary_v1.csv contain respectively unweighted and weighted training with 6 classes, where bcu and spp sources are included in training (unk sources are not included in training). The groups are similar to the groups in https://arxiv.org/abs/2307.09584, but the coordinate features are not used in training. These catalogs are also used to estimate systematic uncertainties in Appendix A of https://arxiv.org/abs/2401.04565.