predictions from the test set. For kNN, we use a similar search technique (described in §\[sec:knn\]) and find that using $k=12$ gives the minimum MSE on the validation set. The kNN test set results below are derived using this value.

A set of 2D histograms in $N_{gal,true}$ versus $N_{gal,predicted}$ from our test set is shown in Figure \[fig:milall\]. The top panel shows the SVM result and the bottom panel shows the kNN result. One can see that in both cases, the MSE is dramatically improved over the base MSE which indicates that the ML algorithms are learning some information about $N_{gal}$ from the input features as expected. The MSE values from the 2 different methods are very similar and hence SVM and kNN appear to be equally good for inferring $N_{gal}$ from halo features. However, we note that upon careful inspection of the 2D histograms, one sees that there is a slight bias towards under-predicting $N_{gal}$ which is discussed more below.

ML algorithms appear to match the expected distribution of $N_{halo}$ as a function of $N_{gal}$ quite well as shown in Figure \[fig:mildist\]. The panels show histograms where the $y$-axes correspond to the fraction of halos with $N_{gal}$ and the 