Decision trees are widely used due to their interpretability and efficiency, but they struggle in regression tasks that require reliable extrapolation and well-calibrated uncertainty. Piecewise-constant leaf predictions are bounded by the training targets and often become overconfident under distribution shift. We propose a single-tree Bayesian model that extends VSPYCT by equipping each leaf with a GP predictor. Bayesian oblique splits provide uncertainty-aware partitioning of the input space, while GP leaves model local functional behaviour and enable principled extrapolation beyond the observed target range. We present an efficient inference and prediction scheme that combines posterior sampling of split parameters with \gls{gp} posterior predictions, and a gating mechanism that activates GP-based extrapolation when inputs fall outside the training support of a leaf. Experiments on benchmark regression tasks show improvements in the predictive performance compared to standard variational oblique trees, and substantial performance gains in extrapolation scenarios.

翻译：决策树因其可解释性和高效性而被广泛使用，但在需要可靠外推和良好校准不确定性的回归任务中表现不佳。分段常数叶节点预测受限于训练目标，在分布偏移下常变得过度自信。我们提出一种单树贝叶斯模型，通过为每个叶节点配备高斯过程预测器来扩展VSPYCT。贝叶斯倾斜分割提供了输入空间的不确定性感知划分，而高斯过程叶节点则建模局部函数行为，并支持基于原理的超出观测目标范围的外推。我们提出一种高效的推断与预测方案，该方案结合了分割参数的后验采样与高斯过程后验预测，并采用门控机制在输入超出叶节点训练支持域时激活基于高斯过程的外推。在基准回归任务上的实验表明，相较于标准变分倾斜树，该方法在预测性能上有所提升，并在外推场景中取得显著的性能增益。