Decision trees are a popular family of models due to their attractive properties such as interpretability and ability to handle heterogeneous data. Concurrently, missing data is a prevalent occurrence that hinders performance of machine learning models. As such, handling missing data in decision trees is a well studied problem. In this paper, we tackle this problem by taking a probabilistic approach. At deployment time, we use tractable density estimators to compute the expected prediction of our models. At learning time, we fine-tune parameters of already learned trees by minimizing their expected prediction loss w.r.t. our density estimators. We provide brief experiments showcasing effectiveness of our methods compared to few baselines.
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