Survival Analysis as Imprecise Classification with Trainable Kernels

Abstract: Survival analysis is a fundamental tool for modeling time-to-event data in healthcare, engineering, and finance, where censored observations pose significant challenges. While traditional methods like the Beran estimator offer nonparametric solutions, they often struggle with the complex data structures and heavy censoring. This paper introduces three novel survival models, iSurvM (the imprecise Survival model based on Mean likelihood functions), iSurvQ (the imprecise Survival model based on the Quantiles of likelihood functions), and iSurvJ (the imprecise Survival model based on the Joint learning), that combine imprecise probability theory with attention mechanisms to handle censored data without parametric assumptions. The first idea behind the models is to represent censored observations by interval-valued probability distributions for each instance over time intervals between events moments. The second idea is to employ the kernel-based Nadaraya-Watson regression with trainable attention weights for computing the imprecise probability distribution over time intervals for the entire dataset. The third idea is to consider three decision strategies for training, which correspond to the proposed three models. Experiments on synthetic and real datasets demonstrate that the proposed models, especially iSurvJ, consistently outperform the Beran estimator from the accuracy and computational complexity points of view. Codes implementing the proposed models are publicly available.