biniLasso: Automated cut-point detection via sparse cumulative binarization

We present biniLasso and its sparse variant (sparse biniLasso), novel methods for prognostic analysis of high-dimensional survival data that enable detection of multiple cut-points per feature. Our approach leverages the Cox proportional hazards model with two key innovations: (1) a cumulative binarization scheme with $L_1$-penalized coefficients operating on context-dependent cut-point candidates, and (2) for sparse biniLasso, additional uniLasso regularization to enforce sparsity while preserving univariate coefficient patterns. These innovations yield substantially improved interpretability, computational efficiency (4-11x faster than existing approaches), and prediction performance. Through extensive simulations, we demonstrate superior performance in cut-point detection, particularly in high-dimensional settings. Application to three genomic cancer datasets from TCGA confirms the methods' practical utility, with both variants showing enhanced risk prediction accuracy compared to conventional techniques.