the list and choosing the $k$ features with highest importance. The user is then able to either select an arbitrary number of features or combine this feature importance ordering with a model-specific stepwise selection algorithm.

This method is “naive” because the redundancies between predictors are ignored similarly to the Naive Bayes Classifier. This implies an assumption that the predictors are independent, and thus have a distance correlation among any set predictors of 0. In the language of [@feature], by assuming the redundancy ($R$) is zero, we need to only optimize the relevance ($D$). Thus, our goal is to optimize a new criterion $\Phi^*$ as in (\[eq:phi\]) with respect to a Naive Distance Correlation sense of redundancy $R^*$ and relevance $D^*$: $$\max \Phi^* = D^* - R^*
    \label{eq:phistar}$$

Our independence assumption leads to $R^* = 0$, and our definition of relevance using distance correlation from (\[eq:dcorr\]) implies the following: $$D^*(S,c) = \frac{1}{|S|}\sum_{X_{\cdot i} \in S} \mathscr{R}^2(X_{\cdot i}, c)$$

DC-SIS Computation
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To do this screening, we use the distance correlation algorithm described above between the response and each predictor independently. This provides a feature quality rating for each predictor with a computational complexity of $O(N^2)$. We can then sort the feature 