SURVFIT: Doubly Sparse Rule Learning for Survival Data.

Survival data analysis has been leveraged in medical research to study disease morbidity and mortality, and to discover significant bio-markers affecting them. A crucial objective in studying high dimensional medical data is the development of inherently interpretable models that can efficiently capture sparse underlying signals while retaining a high predictive accuracy. Recently developed rule ensemble models have been shown to effectively accomplish this objective; however, they are computationally expensive when applied to survival data and do not account for sparsity in the number of variables included in the generated rules. To address these gaps, we present SURVFIT, a "doubly sparse" rule extraction formulation for survival data. This doubly sparse method can induce sparsity both in the number of rules and in the number of variables involved in the rules. Our method has the computational efficiency needed to realistically solve the problem of rule-extraction from survival data if we consider both rule sparsity and variable sparsity, by adopting a quadratic loss function with an overlapping group regularization. Further, a systematic rule evaluation framework that includes statistical testing, decomposition analysis and sensitivity analysis is provided. We demonstrate the utility of SURVFIT via experiments carried out on a synthetic dataset and a sepsis survival dataset from MIMIC-III.