# Hazard Gradient Penalty for Survival Analysis

arXiv: https://arxiv.org/abs/2205.13717 · HTML: https://mlsanity.com/paper/2205.13717/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 48 references that are in the map.
- First posted on arXiv 27 May 2022.

## Builds on (most cited first, 15 of 15)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Virtual Adversarial Training: A Regularization Method for Supervised and Semi-Supervised Learning](https://mlsanity.com/paper/1704.03976/) (2017)
- [Which Training Methods for GANs do actually Converge?](https://mlsanity.com/paper/1801.04406/) (2018)
- [DeepSurv: Personalized Treatment Recommender System Using A Cox Proportional Hazards Deep Neural Network](https://mlsanity.com/paper/1606.00931/) (2016)
- [On Neural Differential Equations](https://mlsanity.com/paper/2202.02435/) (2022)
- [Time-to-Event Prediction with Neural Networks and Cox Regression](https://mlsanity.com/paper/1907.00825/) (2019)
- [Adversarial Time-to-Event Modeling](https://mlsanity.com/paper/1804.03184/) (2018)
- [X-CAL: Explicit Calibration for Survival Analysis](https://mlsanity.com/paper/2101.05346/) (2021)
- [Inverse-Weighted Survival Games](https://mlsanity.com/paper/2111.08175/) (2021)
- [Real-time Prediction of COVID-19 related Mortality using Electronic Health Records](https://mlsanity.com/paper/2008.13412/) (2020)
- [Survival Analysis via Ordinary Differential Equations](https://mlsanity.com/paper/2009.03449/) (2020)
- [A General Framework for Survival Analysis and Multi-State Modelling](https://mlsanity.com/paper/2006.04893/) (2020)

## Abstract (arXiv)

Survival analysis appears in various fields such as medicine, economics, engineering, and business. Recent studies showed that the Ordinary Differential Equation (ODE) modeling framework unifies many existing survival models while the framework is flexible and widely applicable. However, naively applying the ODE framework to survival analysis problems may model fiercely changing density function which may worsen the model's performance. Though we can apply L1 or L2 regularizers to the ODE model, their effect on the ODE modeling framework is barely known. In this paper, we propose hazard gradient penalty (HGP) to enhance the performance of a survival analysis model. Our method imposes constraints on local data points by regularizing the gradient of hazard function with respect to the data point. Our method applies to any survival analysis model including the ODE modeling framework and is easy to implement. We theoretically show that our method is related to minimizing the KL divergence between the density function at a data point and that of the neighborhood points. Experimental results on three public benchmarks show that our approach outperforms other regularization methods.