# DAVIDSTUTZ

Check out our latest research on weakly-supervised 3D shape completion.
10thMAY2015

Louppe et al. discuss the Mean Decrease Impurity (MDI) variable importance measure and derive several theoretical properties. Given a forest of $T$ randomized trees, each expecting $D$-dimensional input $x = (x_1, \ldots, x_D)$, the Mean Decrease Impurity variable importance for dimension $d$ is computed as:
$MDI(x_d) = \frac{1}{T} \sum_{t = 1}^T \sum_{s(v) = x_n} \frac{N_v}{N} \Delta i(v)$(1)
where $N$ is the total number of examples, $N_v$ is the number of examples reaching inner node $v$ and $\Delta i(v)$ is the impurity decrease achieved at node $v$. Here, the second sum in equation (1) runs over all inner nodes $v$ in tree $t$ where feature dimension $d$ is selected as split feature.