特征重要性的计算是维度约简的一种方法，对于随机森林，通常可以用基尼指数（Gini index）或者袋外数据（OOB）错误率作为评价指标来衡量。

基于Gini指数的评价

接着我们看看sklearn中是怎样实现的：

scikit-learn-master/sklearn/tree

cpdef compute_feature_importances(self, normalize=True):
        """Computes the importance of each feature (aka variable)."""
        cdef Node* left
        cdef Node* right
        cdef Node* nodes = self.nodes
        cdef Node* node = nodes
        cdef Node* end_node = node + self.node_count

        cdef double normalizer = 0.

        cdef np.ndarray[np.float64_t, ndim=1] importances
        importances = np.zeros((self.n_features,))
        cdef DOUBLE_t* importance_data = <DOUBLE_t*>importances.data

        with nogil:
            while node != end_node:
                if node.left_child != _TREE_LEAF:
                    # ... and node.right_child != _TREE_LEAF:
                    left = &nodes[node.left_child]
                    right = &nodes[node.right_child]

                    importance_data[node.feature] += (
                        node.weighted_n_node_samples * node.impurity -
                        left.weighted_n_node_samples * left.impurity -
                        right.weighted_n_node_samples * right.impurity)
                node += 1

        importances /= nodes[0].weighted_n_node_samples

        if normalize:
            normalizer = np.sum(importances)

            if normalizer > 0.0:
                # Avoid dividing by zero (e.g., when root is pure)
                importances /= normalizer

        return importances

基于袋外估计的评价:

在评价oob中第j个特征时，替换\(X_ij\)为随机排列，然后得到第j个特征的重要性。