as the difference between the relevance (\[eq:r\]) and the redundancy (\[eq:d\]): $$\Phi(D,R) = D - R
    \label{eq:phi}$$

or, alternatively, as their quotient. This represents the difference of their logs: $$\Phi(D,R) = \frac{D}{R}$$

Minimum Redundancy-Maximum Relevance Computation
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To perform the mRMR feature selection, we used the `pymrmr` package in Python, which uses C code via Cython to do the computations efficiently and in parallel. Estimating the mutual information of continuous data in (\[eq:i\]) is a difficult and ongoing problem. Since it is a double integral (or reduced to a double sum), the computational complexity is typically some multiple of $O(N^2)$ depending on the way the included predictors are handled since $X$ and $Y$ could each be multivariate. This method of computing mutual information is then applied to computing the relevance (\[eq:d\]) and redundancy (\[eq:r\]).

Best subset selection using this criterion is as difficult as with other criteria, so a greedy forward stepwise selection is done instead. Since this method adds a single predictor at a time, we only need to compute the differential of (\[eq:phi\]) to select the best change. Thus, computing the change in relevance due to adding a given predictor effectively amounts to computing the mutual information of 