We thank the reviewers for giving positive and insightful evaluations of our paper. Specific responses are given below. We will discuss these in our paper. Future work could replace Eureqa inside our framework with more sophisticated SR backends. This Eureqa alternative is optimized for rediscovering existing equations by, e.g., This approach does not seem applicable for discovering new equations so we chose Eureqa.

In contrast, decision tree models are known more robust to overfitting, and also more efficient.

Decision trees have been widely used as classifiers in many machine learning applications thanks to their lightweight and interpretable decision process.

The Rashomon set is the set of these all almost-optimal models. Rashomon sets can be large in size and complicated in structure, particularly for highly nonlinear function classes that allow complex interaction terms, such as decision trees.

Then f (x) = p( Y | x), provided that p (x) > 0. Proof. Since the GeDT is deterministic, it has at most one non-zero child. Before proving Theorem 2 we need to introduce some background. We are now ready to prove Theorem 2. Proof. (see also proof of Theorem 1). Here, we assume for simplicity that all variables are continuous.

Regression (PR) trees, that adapt to the smoothness of the prediction function relating input and output variables while preserving the interpretability of the prediction and being robust to noise. In PR trees, an observation is associated to all regions of a tree through a probability distribution that reflects how far the observation is to a region.

Performance Data Set which serve to show the usability of our implementation in practice. Section J explains the binarization process for real-valued decision trees and high-level queries. We review the definition of first-order logic (FO) over vocabularies consisting only of relations. If x,y are variables, then x = y is an FO-formula over σ . This proof requires some background in model theory.