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

arXiv: https://arxiv.org/abs/2506.11416 · HTML: https://mlsanity.com/paper/2506.11416/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 29 references that are in the map.
- First posted on arXiv 13 Jun 2025.

## Builds on (most cited first, 2 of 2)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [OSQP: An Operator Splitting Solver for Quadratic Programs](https://mlsanity.com/paper/1711.08013/) (2017)

## Abstract (arXiv)

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.