Node Splitting SVMs for Survival Trees Based on an L2-Regularized Dipole Splitting Criteria

TL;DR

This paper introduces a new node-splitting SVM method for survival trees that enables non-linear partitioning of survival data, improving flexibility and predictive power over existing methods.

Contribution

It extends previous dipole splitting criteria by incorporating kernel methods with ridge regularization, allowing non-linear splits in survival trees.

Findings

Non-linear splits achieve similar predictive power as linear ones.

Non-linear trees are often smaller than traditional trees.

The method is effective on real and simulated datasets.

Abstract

This paper proposes a novel, node-splitting support vector machine (SVM) for creating survival trees. This approach is capable of non-linearly partitioning survival data which includes continuous, right-censored outcomes. Our method improves on an existing non-parametric method, which uses at most oblique splits to induce survival regression trees. In the prior work, these oblique splits were created via a non-SVM approach, by minimizing a piece-wise linear objective, called a dipole splitting criterion, constructed from pairs of covariates and their associated survival information. We extend this method by enabling splits from a general class of non-linear surfaces. We achieve this by ridge regularizing the dipole-splitting criterion to enable application of kernel methods in a manner analogous to classical SVMs. The ridge regularization provides robustness and can be tuned. Using various kernels, we induce both linear and non-linear survival trees to compare their sizes and predictive powers on real and simulated data sets. We compare traditional univariate log-rank splits, oblique splits using the original dipole-splitting criterion and a variety of non-linear splits enabled by our method. In these tests, trees created by non-linear splits, using polynomial and Gaussian kernels show similar predictive power while often being of smaller sizes compared to trees created by univariate and oblique splits. This approach provides a novel and flexible array of survival trees that can be applied to diverse survival data sets.