problem of subhalo finding which is a required step in any SHAM-based approach; like HOD-based models, our proposed ML techniques operate on the parent halo itself.

The learning process is accomplished by “training” the algorithm on a set of training data where $Y$ is known. The learned mapping can then be applied to a test set of $\mathbf{X}$ values with known $Y$ to verify its accuracy. If the learned relationship appears robust, it can be applied to a set of $\mathbf{X}$ with unknown $Y$ to make predictions.

In testing the accuracy of the predicted values, we draw on the mean-squared-error (MSE) defined as $$\mathrm{MSE} = \frac{\sum_{i=1}^{N} 
\label{eqn:mse}
(Y_{i,test,true} - Y_{i,test,predicted})^2}{N}$$ where $N$ is the number of test data points. This effectively measures a combination of variance (the scatter in the predicted values) and bias (how different from truth the predicted values are).

Support Vector Machines {#sec:svm}
-----------------------

Support Vector Machines (SVMs) work by mapping the features $\mathbf{X}$ to a higher dimensional-space and attempting to separate them into regions that map onto specific $Y$ values using a set of hyperplanes [@CV95]. In its original form, it is a classification scheme but can be generalized to a regression algorithm [@Dea97].

The general 