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The SVR-Tree classifier is the minimizer of the weighted average of signed tree impurity and surface-to-volume ratio. Letting $\mathscr{T}$ be the collection of possible trees, the SVR-Tree classifier is formally defined as $$\label{Tree Impu}
\hat{T} = \operatorname*{argmin}_{T\in\mathscr{T}}[\tilde{I}_\alpha(T,\mathbb{P}_n) + \lambda_n r(T)],$$ where $\lambda_n$ is a penalty. The unknown probability measure $\mathbb{P}$ is replaced with the empirical measure $\mathbb{P}_n$ that assigns mass $1/n$ to each training sample $(X_i, Y_i), 1\le i\le n$. Unfortunately, without restricting the space of trees $\mathscr{T}$, optimization problem (\[Tree Impu\]) is intractable. In the following subsection, we introduce an iterative greedy search algorithm that limits the size of $\mathscr{T}$ in each step to efficiently obtain a tree having provably good performance.

The SVR-Tree Algorithm
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The SVR-Tree Algorithm is designed to find a nearly optimal SVR-Tree classifier. SVR-Tree proceeds in a greedy manner. We begin with the root node. At each step, we operate on one leaf node of the current tree, partitioning it into two new leaf nodes by finding the solution of (\[Tree Impu\]). The node to partition at each step is uniquely specified by a breadth-first searching order. After partitioning, the tree is updated and the node to partition in the next step will 