for predicting $Y$ from $\mathbf{X}$. A simple approach to this is forward feature selection which relies on an initial comparison to the base MSE, or the MSE calculated by taking all $Y_{i,test,predicted}
= \langle Y_{train} \rangle$ in Equation (\[eqn:mse\]), i.e. $$\mathrm{Base \; MSE} = \frac{\sum_{i=1}^{N} 
(Y_{i,test,true} - \langle Y_{train} \rangle )^2}{N}$$ This is just the MSE one would obtain by doing the most naive thing: predicting all $Y$ values to be the mean $Y$ of the training set (denoted as $\langle Y_{train} \rangle$ above.

Forward feature selection starts by training an ML algorithm to predict $Y$ using only a single feature. We repeat this for each individual feature and calculate its MSE value from a test set. If the minimum MSE is less than the base MSE, then we are doing better than the naive prediction, indicating that the features do contain information that is correlated with and can help us predict $Y$. We then “select” the feature that produced the minimum MSE and individually add each other feature to it and repeat the train/test procedure to calculate MSE values. At the end of this round, if the minimum MSE is smaller than the minimum MSE in the previous step, 