Interpretable Fuzzy Rule-Based Regression Extension for Ex-Fuzzy Library

Interpretable classification often requires more than accurate predictions for real-life deployment: models should be transparent about the evidence behind their decisions and abstain when they cannot decide reliably. We introduce Fast Evidential Rule Learning (FERL), a method that learns interpretable, accurate fuzzy rule models whose outputs are evidential. Unlike post-hoc calibration, FERL's belief, plausibility, and abstention capabilities arise directly from the fuzzy memberships in a single deterministic pass, with no auxiliary head, held-out set, or repeated inference. Our theoretical analysis further shows that FERL is Lipschitz stable, which means that its evidential outputs vary smoothly with the input. Against state-of-the-art rule learners, FERL is statistically significantly more accurate across a 30 tabular-dataset benchmark ($+2.6\%$ average accuracy over the second best). Its native set predictions attain the best utility-discounted accuracy among credal classifiers ($u_{65}/u_{80}=0.80/0.83$ vs.\ $0.79/0.80$ for the naive credal classifier), at higher set coverage ($0.92$ vs.\ $\le0.82$). FERL also matches dedicated out-of-distribution detectors on tabular near-OOD detection ($77.7$ vs.\ $77.4$ AUROC for the strongest baseline). Under detector-class-disjoint concept-bottleneck evaluation, its it is within $2.3$ AUROC points of the strongest dedicated detector on both CUB and AwA2, while attaining the best AwA2 AUPR-Out ($68.3$) and novel-class rejection ($57.2$), while being able to name which attributes are anomalous.

The field of machine learning is subject to an increasing interest in models that are not only accurate but also interpretable and robust, thus allowing their end users to understand and trust AI systems. This paper presents a novel method for learning a set of optimal quantile regression trees. The advantages of this method are that (1) it provides predictions about the complete conditional distribution of a target variable without prior assumptions on this distribution; (2) it provides predictions that are interpretable; (3) it learns a set of optimal quantile regression trees without compromising algorithmic efficiency compared to learning a single tree.

Interpretable machine learning is essential in high-stakes domains where decision-making requires accountability, transparency, and trust. While rule-based models offer global and exact interpretability, learning rule sets that simultaneously achieve high predictive performance and low, human-understandable complexity remains challenging. To address this, we introduce TT-Sparse, a flexible neural building block that leverages differentiable truth tables as nodes to learn sparse, effective connections. A key contribution of our approach is a new soft TopK operator with straight-through estimation for learning discrete, cardinality-constrained feature selection in an end-to-end differentiable manner. Crucially, the forward pass remains sparse, enabling efficient computation and exact symbolic rule extraction. As a result, each node (and the entire model) can be transformed exactly into compact, globally interpretable DNF/CNF Boolean formulas via Quine-McCluskey minimization. Extensive empirical results across 28 datasets spanning binary, multiclass, and regression tasks show that the learned sparse rules exhibit superior predictive performance with lower complexity compared to existing state-of-the-art methods.