  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.
