Optimal Pattern Detection Tree for Symbolic Rule-Based Classification

Learning systems based on IF-THEN rule representations readily offer interpretability, making them a crucial focus in contemporary AI research. A key objective for such rule sets is to achieve both high discriminative power and interpretability. While existing state-of-the-art algorithms implicitly prioritize predictive accuracy, they often fall short on one or more quality metrics that ensure interpretability, such as coverage and parsimony of rule sets. Motivated by this, this paper propose the development of CDPR, which aims to create highly accurate and interpretable rule sets for classification problems. To the best of our knowledge, this represents the first attempt to establish such an approach. In this study, we introduce two algorithms rooted in submodular maximization, which not only provide provable guarantees on coverage but also yield rule sets that are both discriminative and parsimonious. We empirically demonstrate that rule sets learned through our approaches achieve higher accuracy and interpretability and has more than a 2.5-fold improvement in average coverage rates when compared to the next best algorithm.

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.

Ensuring model reliability in Explainable AI requires a global assessment of the hypothesis space. We propose a formal framework for the exhaustive analysis of optimal and near-optimal decision trees, called Algebraic Decision Tree Counting (ADTC). Inspired by Algebraic Model Counting (AMC) in knowledge representation, ADTC reformulates diverse analytical tasks, such as optimization, counting, and sampling, into a unified sum-of-products computation over a semiring $R$. While the hypothesis space of decision trees is doubly exponential with respect to the maximum depth $Δ$, our dynamic programming algorithm achieves $O^*(n^{O(Δ)})$ time complexity in the number of features $n$, where $O^*$ suppresses polynomial factors. To handle complex constraints consisting of multiple tree metrics, we introduce model behavior tensors that aggregate semiring values via convolution products over a tensor semiring. This algebraic approach efficiently constructs a model profile that captures the global landscape and trade-offs between criteria such as accuracy, size, and fairness. We demonstrate the utility of our software, emtrees, on real-world datasets, illustrating how ADTC facilitates evidence-based model selection in sensitive domains.