Online Learning Approach for Survival Analysis
This work addresses the need for real-time adaptation in survival analysis, which is incremental as it applies existing optimization methods to a new context.
The authors tackled the problem of survival analysis in dynamic environments by introducing an online learning framework that adapts to censored data in real time, achieving non-asymptotic convergence guarantees and logarithmic stochastic regret through algorithms like Online Newton Step.
We introduce an online mathematical framework for survival analysis, allowing real time adaptation to dynamic environments and censored data. This framework enables the estimation of event time distributions through an optimal second order online convex optimization algorithm-Online Newton Step (ONS). This approach, previously unexplored, presents substantial advantages, including explicit algorithms with non-asymptotic convergence guarantees. Moreover, we analyze the selection of ONS hyperparameters, which depends on the exp-concavity property and has a significant influence on the regret bound. We propose a stochastic approach that guarantees logarithmic stochastic regret for ONS. Additionally, we introduce an adaptive aggregation method that ensures robustness in hyperparameter selection while maintaining fast regret bounds. The findings of this paper can extend beyond the survival analysis field, and are relevant for any case characterized by poor exp-concavity and unstable ONS. Finally, these assertions are illustrated by simulation experiments.