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.

翻译：许多集成模型已被提出用于解决生存分析框架下的机器学习问题，包括随机生存森林、基于弱生存模型的梯度提升机以及Cox模型的集成。为扩展模型集合，本文提出一种名为SurvBETA（基于三重注意力机制的Beran估计器生存集成模型）的新型集成模型，其中Beran估计器被用作集成中的弱学习器。Beran估计器可视为考虑实例间关系的核回归模型。弱学习器输出的条件生存函数通过注意力权重进行聚合，该权重考虑了被分析实例与所有自助样本原型之间的距离。注意力机制在三个环节被使用：实现Beran估计器、确定自助样本的特定原型以及聚合弱模型预测。所提模型以两种形式呈现：一种通用形式需要解决复杂优化问题进行训练；另一种简化形式通过采用基于不精确Huber污染模型的注意力权重特殊表示，从而转化为简单优化问题的求解。数值实验通过合成数据展示了模型特性，并在真实数据上与其他生存模型进行了比较。所提模型的实现代码已公开。