Random Survival Forests Incorporated by the Nadaraya-Watson Regression

Abstract

An attention-based random survival forest (Att-RSF) is presented in the paper. The first main idea behind this model is to adapt the Nadaraya-Watson kernel regression to the random survival forest so that the regression weights or kernels can be regarded as trainable attention weights under important condition that predictions of the random survival forest are represented in the form of functions, for example, the survival function and the cumulative hazard function. Each trainable weight assigned to a tree and a training or testing example is defined by two factors: by the ability of corresponding tree to predict and by the peculiarity of an example which falls into a leaf of the tree. The second main idea behind Att-RSF is to apply the Huber's contamination model to represent the attention weights as the linear function of the trainable attention parameters. The Harrell's C-index (concordance index) measuring the prediction quality of the random survival forest is used to form the loss function for training the attention weights. The C-index jointly with the contamination model lead to the standard quadratic optimization problem for computing the weights, which has many simple algorithms for its solution. Numerical experiments with real datasets containing survival data illustrate Att-RSF.