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We explore the feasibility of learning the connection between SDSS galaxiesand ELUCID subhaloes with random forest (RF). ELUCID is a constrained $N$-bodysimulation constructed using the matter density field of SDSS. Based on anSDSS-ELUCID matched catalogue, we build RF models that predict $M_r$ magnitude,colour, stellar mass $M_*$, and specific star formation rate (sSFR) withseveral subhalo properties. While the RF can predict $M_r$ and $M_*$ withreasonable accuracy, the prediction accuracy of colour and sSFR is low, whichcould be due to the mismatch between galaxies and subhaloes. To test this, weshuffle the galaxies in subhaloes of narrow mass bins in the localneighbourhood using galaxies of a semi-analytic model (SAM) and the TNGhydrodynamic simulation. We find that the shuffling only slightly reduces thecolour prediction accuracy in SAM and TNG, which is still considerably higherthan that of the SDSS. This suggests that the true connection between SDSScolour and subhalo properties could be weaker than that in the SAM and TNGwithout the mismatch effect. We also measure the Pearson correlationcoefficient between galaxy properties and the subhalo properties in SDSS, SAM,and TNG. Similar to the RF results, we find that the colour-subhalo correlationin SDSS is lower than both the SAM and TNG. We also show that thegalaxy-subhalo correlations depend on subhalo mass in the galaxy formationmodels. Advanced surveys with more fainter galaxies will provide new insightsinto the galaxy-subhalo relation in the real Universe.

Connection Between SDSS Galaxies and ELUCID Subhaloes in the Eye of Machine Learning