We introduce ECSEL, an explainable classification method that learns formal expressions in the form of signomial equations, motivated by the observation that many symbolic regression benchmarks admit compact signomial structure. ECSEL directly constructs a structural, closed-form expression that serves as both a classifier and an explanation. On standard symbolic regression benchmarks, our method recovers a larger fraction of target equations than competing state-of-the-art approaches while requiring substantially less computation. Leveraging this efficiency, ECSEL achieves classification accuracy competitive with established machine learning models without sacrificing interpretability. Further, we show that ECSEL satisfies some desirable properties regarding global feature behavior, decision-boundary analysis, and local feature attributions. Experiments on benchmark datasets and two real-world case studies i.e., e-commerce and fraud detection, demonstrate that the learned equations expose dataset biases, support counterfactual reasoning, and yield actionable insights.

翻译：我们提出ECSEL，一种可解释的分类方法，其通过学习符号方程形式的解析表达式实现分类。该方法的提出源于我们观察到许多符号回归基准问题具有紧凑的符号结构特性。ECSEL直接构建结构化的闭式表达式，该表达式同时兼具分类器与解释器的功能。在标准符号回归基准测试中，相较于当前最先进的竞争方法，本方法能以显著更少的计算量恢复更高比例的目标方程。凭借这一高效特性，ECSEL在保持可解释性的同时，达到了与成熟机器学习模型相当的分类准确率。此外，我们证明ECSEL在全局特征行为、决策边界分析和局部特征归因方面满足若干理想性质。在基准数据集及两个实际案例（即电子商务与欺诈检测）上的实验表明，学习得到的方程能够揭示数据集偏差、支持反事实推理，并产生可操作的洞见。