Ensemble-Based Survival Models with the Self-Attended Beran Estimator Predictions

Survival analysis predicts the time until an event of interest, such as failure or death, but faces challenges due to censored data, where some events remain unobserved. Ensemble-based models, like random survival forests and gradient boosting, are widely used but can produce unstable predictions due to variations in bootstrap samples. To address this, we propose SurvBESA (Survival Beran Estimators Self-Attended), a novel ensemble model that combines Beran estimators with a self-attention mechanism. Unlike traditional methods, SurvBESA applies self-attention to predicted survival functions, smoothing out noise by adjusting each survival function based on its similarity to neighboring survival functions. We also explore a special case using Huber's contamination model to define attention weights, simplifying training to a quadratic or linear optimization problem. Numerical experiments show that SurvBESA outperforms state-of-the-art models. The implementation of SurvBESA is publicly available.

Survival Concept-Based Learning Models

Concept-based learning enhances prediction accuracy and interpretability by leveraging high-level, human-understandable concepts. However, existing CBL frameworks do not address survival analysis tasks, which involve predicting event times in the presence of censored data -- a common scenario in fields like medicine and reliability analysis. To bridge this gap, we propose two novel models: SurvCBM (Survival Concept-based Bottleneck Model) and SurvRCM (Survival Regularized Concept-based Model), which integrate concept-based learning with survival analysis to handle censored event time data. The models employ the Cox proportional hazards model and the Beran estimator. SurvCBM is based on the architecture of the well-known concept bottleneck model, offering interpretable predictions through concept-based explanations. SurvRCM uses concepts as regularization to enhance accuracy. Both models are trained end-to-end and provide interpretable predictions in terms of concepts. Two interpretability approaches are proposed: one leveraging the linear relationship in the Cox model and another using an instance-based explanation framework with the Beran estimator. Numerical experiments demonstrate that SurvCBM outperforms SurvRCM and traditional survival models, underscoring the importance and advantages of incorporating concept information. The code for the proposed algorithms is publicly available.