  Updating machine learning models with new information usually improves their
predictive performance, yet, in many applications, it is also desirable to
avoid changing the model predictions too much. This property is called
stability. In most cases when stability matters, so does explainability. We
therefore focus on the stability of an inherently explainable machine learning
method, namely regression trees. We aim to use the notion of empirical
stability and design algorithms for updating regression trees that provide a
way to balance between predictability and empirical stability. To achieve this,
we propose a regularization method, where data points are weighted based on the
uncertainty in the initial model. The balance between predictability and
empirical stability can be adjusted through hyperparameters. This
regularization method is evaluated in terms of loss and stability and assessed
on a broad range of data characteristics. The results show that the proposed
update method improves stability while achieving similar or better predictive
performance. This shows that it is possible to achieve both predictive and
stable results when updating regression trees.
