We tackle the problem of building explainable recommendation systems that are based on a per-user decision tree, with decision rules that are based on single attribute values. We build the trees by applying learned regression functions to obtain the decision rules as well as the values at the leaf nodes. The regression functions receive as input the embedding of the user's training set, as well as the embedding of the samples that arrive at the current node. The embedding and the regressors are learned end-to-end with a loss that encourages the decision rules to be sparse. By applying our method, we obtain a collaborative filtering solution that provides a direct explanation to every rating it provides. With regards to accuracy, it is competitive with other algorithms. However, as expected, explainability comes at a cost and the accuracy is typically slightly lower than the state of the art result reported in the literature.