Online Learning Approach for Survival Analysis
Camila Fernandez Pierre Gaillard Joseph de Vilmarest Olivier Wintenberger
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.