Statistical learning with a large number of rare binary features is commonly encountered in analyzing electronic health records (EHR) data, especially in the modeling of disease onset with prior medical diagnoses and procedures. Dealing with the resulting highly sparse and large-scale binary feature matrix is notoriously challenging as conventional methods may suffer from a lack of power in testing and inconsistency in model fitting while machine learning methods may suffer from the inability of producing interpretable results or clinically-meaningful risk factors. To improve EHR-based modeling and utilize the natural hierarchical structure of disease classification, we propose a tree-guided feature selection and logic aggregation approach for large-scale regression with rare binary features, in which dimension reduction is achieved through not only a sparsity pursuit but also an aggregation promoter with the logic operator of ``or''. We convert the combinatorial problem into a convex linearly-constrained regularized estimation, which enables scalable computation with theoretical guarantees. In a suicide risk study with EHR data, our approach is able to select and aggregate prior mental health diagnoses as guided by the diagnosis hierarchy of the International Classification of Diseases. By balancing the rarity and specificity of the EHR diagnosis records, our strategy improves both prediction and model interpretation. We identify important higher-level categories and subcategories of mental health conditions and simultaneously determine the level of specificity needed for each of them in predicting suicide risk.

翻译：统计学习处理大量罕见二元特征在电子健康档案数据分析中普遍存在，尤其在利用既往医疗诊断和程序进行疾病发病建模时。应对由此产生的高稀疏大规模二元特征矩阵极具挑战性：传统方法可能在检验中缺乏统计效力且模型拟合不一致，而机器学习方法则难以生成可解释结果或具有临床意义的危险因素。为改进基于电子健康档案的建模并利用疾病分类的自然层次结构，我们提出一种树引导的特征选择与逻辑聚合方法，用于大规模罕见二元特征回归。该方法不仅通过稀疏性追求实现降维，还利用“或”逻辑运算符构建聚合促进器。我们将组合优化问题转化为凸线性约束正则化估计，该估计支持可扩展计算并具有理论保证。在基于电子健康档案的自杀风险研究中，该方法能依据《国际疾病分类》诊断层级，选择并聚合既往心理健康诊断记录。通过平衡电子健康档案诊断记录的罕见性与特异性，我们的策略同时提升了预测性能与模型可解释性。研究识别出心理健康状况的重要高级类别与子类别，并同步确定了预测自杀风险时所需的具体细分粒度。