Fast Training of Support Vector Machines for Survival Analysis

Survival analysis is a commonly used technique to identify important predictors of adverse events and develop guidelines for patient’s treatment in medical research. When applied to large amounts of patient data, efficient optimization routines become a necessity. We propose efficient training algorithms for three kinds of linear survival support vector machines: 1) ranking-based, 2) regression-based, and 3) combined ranking and regression. We perform optimization in the primal using truncated Newton optimization and use order statistic trees to lower computational costs of training. We employ the same optimization technique and extend it for non-linear models too. Our results demonstrate the superiority of our proposed optimization scheme over existing training algorithms, which fail due to their inherently high time and space complexities when applied to large datasets. We validate the proposed survival models on 6 real-world datasets, and show that pure ranking-based approaches outperform regression and hybrid models.