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Statistical learning with a large number of rare binary features is commonlyencountered in analyzing electronic health records (EHR) data, especially inthe modeling of disease onset with prior medical diagnoses and procedures.Dealing with the resulting highly sparse and large-scale binary feature matrixis notoriously challenging as conventional methods may suffer from a lack ofpower in testing and inconsistency in model fitting while machine learningmethods may suffer from the inability of producing interpretable results orclinically-meaningful risk factors. To improve EHR-based modeling and utilizethe natural hierarchical structure of disease classification, we propose atree-guided feature selection and logic aggregation approach for large-scaleregression with rare binary features, in which dimension reduction is achievedthrough not only a sparsity pursuit but also an aggregation promoter with thelogic operator of ``or''. We convert the combinatorial problem into a convexlinearly-constrained regularized estimation, which enables scalable computationwith theoretical guarantees. In a suicide risk study with EHR data, ourapproach is able to select and aggregate prior mental health diagnoses asguided by the diagnosis hierarchy of the International Classification ofDiseases. By balancing the rarity and specificity of the EHR diagnosis records,our strategy improves both prediction and model interpretation. We identifyimportant higher-level categories and subcategories of mental health conditionsand simultaneously determine the level of specificity needed for each of themin predicting suicide risk.

Tree-Guided Rare Feature Selection and Logic Aggregation with Electronic Health Records Data