Conventional decision trees have a number of favorable properties, including a small computational footprint, interpretability, and the ability to learn from little training data. However, they lack a key quality that has helped fuel the deep learning revolution: that of being end-to-end trainable. Kontschieder et al. (ICCV, 2015) have addressed this deficit, but at the cost of losing a main attractive trait of decision trees: the fact that each sample is routed along a small subset of tree nodes only. We here present an end-to-end learning scheme for deterministic decision trees and decision forests. Thanks to a new model and expectation–maximization training scheme, the trees are fully probabilistic at train time, but after an annealing process become deterministic at test time. In experiments we explore the effect of annealing visually and quantitatively, and find that our method performs on par or superior to standard learning algorithms for oblique decision trees and forests. We further demonstrate on image datasets that our approach can learn more complex split functions than common oblique ones, and facilitates interpretability through spatial regularization.

中文翻译：

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决策树和森林的端到端学习

传统的决策树具有许多有利的特性，包括计算量小、可解释性以及从少量训练数据中学习的能力。然而，它们缺乏有助于推动深度学习革命的关键品质：端到端可训练。Kontschieder 等人。(ICCV, 2015) 已经解决了这个缺陷，但代价是失去了决策树的一个主要有吸引力的特征：每个样本仅沿着树节点的一个小子集路由的事实。我们在这里提出了一种用于确定性决策树和决策森林的端到端学习方案。由于新模型和期望最大化训练方案，这些树在训练时完全是概率性的，但在退火过程之后在测试时变得确定性。在实验中，我们在视觉上和定量上探索了退火的效果，并发现我们的方法与倾斜决策树和森林的标准学习算法相当或优于标准学习算法。我们在图像数据集上进一步证明，我们的方法可以学习比普通倾斜函数更复杂的分裂函数，并通过空间正则化促进可解释性。