we again select the feature that produced this minimum MSE and repeat the previous procedure. At each step if adding in an additional feature decreases the minimum MSE further, we continue. Otherwise we stop and deem the remaining features as not having much predictive power beyond the “selected” features.

Such feature selection schemes are useful for identifying the halo parameters that are most relevant to inferring $N_{gal}$.

Results {#sec:results}
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As described in § \[sec:data\], our tests use a sample of 395,832 halos from the Millennium simulation to assess the machine learning algorithms detailed in the preceding section. We randomly split this halo sample into three equal parts and use the first part for training, the second part for validation and the third part for testing. The base MSE of the test set is $\sim0.505$. We first look at the results obtained through training the ML algorithms on all 6 halo features.

As mentioned in §\[sec:svm\], we do a grid-search to find the SVM training parameters ($C$, $\gamma$ and kernel) that return the minimum MSE on the validation set. This procedure selected the rbf kernel with $C=1000$ and $\gamma=0.0001$. We then use the SVM trained using these values to make 