Attention and self-attention in random forests

New models of random forests jointly using the attention and self-attention mechanisms are proposed for solving the regression problem. The models can be regarded as extensions of the attention-based random forest whose idea stems from applying a combination of the Nadaraya–Watson kernel regression and the Huber’s contamination model to random forests. The self-attention aims to capture dependencies of the tree predictions and to remove noise or anomalous predictions in the random forest. The self-attention module is trained jointly with the attention module for computing weights. It is shown that the training process of attention weights is reduced to solving a single quadratic or linear optimization problem. Three modifications of the self-attention are proposed and compared. A specific multi-head self-attention for the random forest is also considered. Heads of the self-attention are obtained by changing its tuning parameters including the kernel parameters and the contamination parameter of models. The proposed modifications of the attention and self-attention combinations are verified and compared with other random forest models by using several datasets. The code implementing the corresponding algorithms is publicly available.