Hazard Gradient Penalty for Survival Analysis
This work addresses a specific issue in survival analysis models, particularly for applications in medicine, economics, and other fields, by introducing a novel regularization technique, though it is incremental as it builds on the existing ODE framework.
The paper tackles the problem of naively applying the ODE framework to survival analysis, which can lead to fiercely changing density functions and worsen performance, by proposing a hazard gradient penalty (HGP) that regularizes the gradient of the hazard function; experimental results on three public benchmarks show that HGP outperforms other regularization methods.
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.