Neural Diffusion Processes for Physically Interpretable Survival Prediction
This addresses survival analysis in complex systems by offering interpretable models without assuming proportional hazards, though it is incremental as it combines existing stochastic process theory with deep learning.
The paper tackled survival prediction by coupling deep neural networks with first hitting time distributions from stochastic process theory, achieving predictive accuracy on par with state-of-the-art methods while providing physically interpretable parameters.
We introduce DeepFHT, a survival-analysis framework that couples deep neural networks with first hitting time (FHT) distributions from stochastic process theory. Time to event is represented as the first passage of a latent diffusion process to an absorbing boundary. A neural network maps input variables to physically meaningful parameters including initial condition, drift, and diffusion, within a chosen FHT process such as Brownian motion, both with drift and driftless. This yields closed- form survival and hazard functions and captures time-varying risk without assuming proportional- hazards. We compare DeepFHT with Cox regression using synthetic and real-world datasets. The method achieves predictive accuracy on par with the state-of-the-art approach, while maintaining a physics- based interpretable parameterization that elucidates the relation between input features and risk. This combination of stochastic process theory and deep learning provides a principled avenue for modeling survival phenomena in complex systems