Wilcoxon随机森林用于稳健分布预测
Wilcoxon Random Forests for Robust Distributional Prediction
- Vanderbilt University（范德堡大学）
- University of Southern California（南加州大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对生物医学有序结果中的异常值、偏态和混合类型，提出基于秩分裂的Wilcoxon随机森林，通过聚合回归树估计条件分布，在偏态或异方差下提升分位数估计与校准，并成功应用于HIV治疗后的CD4和病毒载量预测。
AI中文摘要：
随机森林（RF）是基于树的模型，能够捕捉复杂的高阶预测变量交互。在生物医学研究中，有序结果常存在异常值、偏态或连续值与有序值的混合（例如由于检测限所致）。标准RF通过平方误差针对条件均值进行分裂，对此类不规则性敏感。我们提出了一种Wilcoxon回归树，通过最大化基于秩的杂质减少来选择分裂，这等价于最大化平方Wilcoxon秩和统计量。由于该准则仅依赖于结果秩，它对单调变换具有不变性，并能自然适应连续、有序或混合结果。我们开发了Wilcoxon随机森林（WRF），通过子采样聚合Wilcoxon回归树，并使用森林加权经验CDF估计条件分布。我们在正则条件下建立了WRF分布估计量的一致性。我们使用校准诊断和连续排序概率分数评估分布预测，并定义了袋外置换变量重要性度量。模拟表明，当误差对称且同方差时，WRF的性能与标准分位数回归森林相当，而当结果偏态或异方差时，WRF在分位数估计和校准方面有所改进。我们将WRF应用于预测多中心拉丁美洲队列中抗逆转录病毒治疗启动后六个月的CD4细胞计数和HIV病毒载量，WRF改善了阈值概率估计，并适应了病毒载量检测限处的大量质量。
英文摘要：
Random forests (RF) are tree-based models that capture complex, high-order predictor interactions. In biomedical studies, ordered outcomes often have outliers, skewness, or mixtures of continuous and ordinal values (e.g., due to detection limits). Standard RF splitting targets conditional means via squared errors and is sensitive to such irregularities. We propose a Wilcoxon regression tree that selects splits by maximizing a rank-based impurity reduction, equivalent to maximizing the squared Wilcoxon rank-sum statistic. Because the criterion depends only on outcome ranks, it is invariant to monotone transformations and naturally accommodates continuous, ordinal, or mixed outcomes. We develop the Wilcoxon random forest (WRF), which aggregates Wilcoxon regression trees via subsampling and estimates conditional distributions using forest-weighted empirical CDFs. We establish consistency of the WRF distribution estimator under regularity conditions. We evaluate distributional prediction using calibration diagnostics and continuous ranked probability scores, and define an out-of-bag permutation variable-importance measure. Simulations show that the WRF performs comparably to the standard quantile regression forest when errors are symmetric and homoscedastic, and yields improved quantile estimation and calibration when outcomes are skewed or heteroscedastic. We apply the WRF to predict CD4 cell count and HIV viral load six months after antiretroviral therapy initiation in a multicenter Latin American cohort, and the WRF improves threshold probability estimation and accommodates the large mass at the viral load detection limit.
