Machine learning methods provide a powerful approach for analyzing longitudinal data in which repeated measurements are observed for a subject over time. We boost multivariate trees to fit a novel flexible semi-nonparametric marginal model for longitudinal data. In this model, features are assumed to be nonparametric, while feature-time interactions are modeled semi-nonparametrically utilizing P-splines with estimated smoothing parameter. In order to avoid overfitting, we describe a relatively simple in sample cross-validation method which can be used to estimate the optimal boosting iteration and which has the surprising added benefit of stabilizing certain parameter estimates. Our new multivariate tree boosting method is shown to be highly flexible, robust to covariance misspecification and unbalanced designs, and resistant to overfitting in high dimensions. Feature selection can be used to identify important features and feature-time interactions. An application to longitudinal data of forced 1-second lung expiratory volume (FEV1) for lung transplant patients identifies an important feature-time interaction and illustrates the ease with which our method can find complex relationships in longitudinal data.

中文翻译：

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纵向数据的增强多元树

机器学习方法提供了一种强大的方法来分析纵向数据，其中随着时间的推移观察对象的重复测量。我们增强多元树以适应纵向数据的新颖灵活的半非参数边际模型。在此模型中，假设特征是非参数的，而特征-时间交互是利用带有估计平滑参数的 P 样条进行半非参数建模的。为了避免过度拟合，我们描述了一种相对简单的样本交叉验证方法，该方法可用于估计最佳的提升迭代，并且具有稳定某些参数估计的令人惊讶的额外好处。我们新的多元树增强方法被证明是高度灵活的，对协方差错误指定和不平衡设计具有鲁棒性，并且能够抵抗高维度的过度拟合。特征选择可用于识别重要特征和特征时间交互。对肺移植患者用力 1 秒肺呼气量 (FEV1) 纵向数据的应用确定了重要的特征-时间交互作用，并说明了我们的方法可以轻松地找到纵向数据中的复杂关系。