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.

SurvBETA: Ensemble-Based Survival Models Using Beran Estimators and Several Attention Mechanisms

Many ensemble-based models have been proposed to solve machine learning problems in the survival analysis framework, including random survival forests, the gradient boosting machine with weak survival models, ensembles of the Cox models. To extend the set of models, a new ensemble-based model called SurvBETA (the Survival Beran estimator Ensemble using Three Attention mechanisms) is proposed where the Beran estimator is used as a weak learner in the ensemble. The Beran estimator can be regarded as a kernel regression model taking into account the relationship between instances. Outputs of weak learners in the form of conditional survival functions are aggregated with attention weights taking into account the distance between the analyzed instance and prototypes of all bootstrap samples. The attention mechanism is used three times: for implementation of the Beran estimators, for determining specific prototypes of bootstrap samples and for aggregating the weak model predictions. The proposed model is presented in two forms: in a general form requiring to solve a complex optimization problem for its training; in a simplified form by considering a special representation of the attention weights by means of the imprecise Huber's contamination model which leads to solving a simple optimization problem. Numerical experiments illustrate properties of the model on synthetic data and compare the model with other survival models on real data. A code implementing the proposed model is publicly available.