ArXiv

Handling Missing Data in Probabilistic Regression Trees

2026-08-06 · 15:54 UTC ·Taiane Schaedler Prass, Alisson Silva Neimaier, Guilherme Pumi ·1 min read
Authors
Taiane Schaedler Prass, Alisson Silva Neimaier, Guilherme Pumi
Categories
stat.ML, cs.LG
arXiv
https://arxiv.org/abs/2608.06195v1
PDF
https://arxiv.org/pdf/2608.06195v1

Brief

The paper adapts Probabilistic Regression Trees to natively handle missing predictors by introducing three split-assignment strategies (uniform-probability, partial-observation, and dimension-reduced smoothing) that retain probability conservation and marginal compatibility for arbitrary missing patterns. Experiments on multiple real-world datasets show method performance depends on missing-data handling, with the proposed approaches often beating CART when missingness is high. Only the abstract was available for this summary.

Why it matters

The paper extends Probabilistic Regression Trees (PRTrees) to handle missing predictor values directly during tree construction via three strategies: a uniform-probability approach, a partial-observation approach, and a dimension-reduced smoothing approach.

Key details

  • The extensions are defined to preserve key probabilistic properties (probability conservation and marginal compatibility) under arbitrary missing-covariate patterns; empirical tests on multiple real-world datasets show effectiveness depends strongly on the missing-data treatment, with the proposed methods frequently outperforming CART when missingness is substantial.
  • The authors report that the 'fill' strategy emerged as the dominant modeling component—often exerting larger influence on predictive performance than the smoothing distribution or proxy-selection criterion; authors: Taiane Schaedler Prass, Alisson Silva Neimaier, Guilherme Pumi (arXiv:2608.06195v1, 2026-08-06).
Source evidence

Abstract

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.

Comment: Theoretical background for the companion paper, arXiv:2510.03634