matrices are then multiplied element-wise and the resulting matrix elements are summed. Both of these operations are also $O(N^2)$, so the overall complexity of computing the distance covariance is $O(N^2)$. The division by $n$ can be ignored as it is always cancelled out in the computation of the correlation.

To compute the distance correlation, we simply divide the distance covariance of the response with a given predictor by the square root of the distance covariance of the response with itself and by the square root of the distance covariance of the predictor with itself. On the surface, this would merely be doing three $O(N^2)$ operations with two square roots and two multiplications, but a significant amount of computation can be saved by sharing the doubly centered distance matrices. The overall complexity remains at $O(N^2)$, but there are computational savings to be done with a careful implementation.

Distance Correlation Sure Independent Screening
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The method that we are proposing to use, Distance Correlation Sure Independent Screening (DC-SIS) [@dcsis], uses the distance correlation between each predictor in isolation and the response as the importance of that predictor. Since the importance’s are independent of one another, the feature selection process involves merely sorting 