The Classification Tree (CT) is one of the most common models in
interpretable machine learning. Although such models are usually built with
greedy strategies, in recent years, thanks to remarkable advances in
Mixer-Integer Programming (MIP) solvers, several exact formulations of the
learning problem have been developed. In this paper, we argue that some of the
most relevant ones among these training models can be encapsulated within a
general framework, whose instances are shaped by the specification of loss
functions and regularizers. Next, we introduce a novel realization of this
framework: specifically, we consider the logistic loss, handled in the MIP
setting by a linear piece-wise approximation, and couple it with
$\ell_1$-regularization terms. The resulting Optimal Logistic Tree model
numerically proves to be able to induce trees with enhanced interpretability
features and competitive generalization capabilities, compared to the
state-of-the-art MIP-based approaches.

本研究提出了一个通用框架并构建了一种新型的最优逻辑树模型，该模型采用线性分段逼近法处理逻辑损失，并与 L1 正则项耦合，证明其能够诱导出具有更好可解释性和竞争性推广能力的树状模型，相对于现有的 MIP-based 方法。