这篇论文给PRTrees加了直接处理缺失值的能力，不用先插补。在缺数据多的场景下比CART更准，关键还保持树模型好解释。
该论文将概率回归树（PRTrees）扩展为可直接处理缺失预测变量，无需预先插补。提出了三种策略：均匀概率法、部分观测法和降维平滑法，均保持概率守恒和边际兼容性。在多个真实数据集上与经典回归树CART对比，结果显示填充策略对预测性能影响最大。当数据缺失比例较高时，所提方法常优于CART，同时保留树模型的解释性。
Handling Missing Data in Probabilistic Regression Trees
Probabilistic Regression Trees (PRTrees) are a smooth and consistent alternative to classical regression trees, producing continuous predictions through probabilistic split assignments. This paper extends the PRTree framework to accommodate missing predictor values directly during tree construction, eliminating the need for prior imputation. Three strategies are proposed, each exploiting the available information differently: a uniform-probability approach, a partial-observation approach, and a dimension-reduced smoothing approach. These modifications are defined to preserve the fundamental probabilistic properties of the original methodology, including probability conservation and marginal compatibility, under arbitrary patterns of missing covariate values. The proposed methods are evaluated on several real-world datasets exhibiting different levels of missingness and are compared with classical regression trees. The results show that the effectiveness of probabilistic tree construction depends strongly on the treatment of missing observations. Across the considered datasets, the fill strategy emerged as the dominant modeling component, often exerting a larger influence on predictive performance than either the smoothing distribution or the proxy-selection criterion. In datasets where a substantial proportion of observations contained missing predictor values, the proposed methods frequently outperformed CART, while maintaining the interpretability and flexibility of tree-based models.