用符号方程发现方法实现可解释的二分类,自动找出决策边界形状。
EDC: Equation Discovery for Classification
- 基于符号回归思想,通过可配置语法生成简洁解析函数描述分类边界。
- 在真实与人工数据上超越现有符号分类方法,性能接近主流分类模型。
- 支持自定义领域表达式,适合需要可解释性的科研与工业场景。
方程发现技术在回归任务中表现优异,能提取简洁且可解释的模型(符号回归)。本文提出一种基于方程发现的新型二分类框架EDC,能够找到规模可控的解析函数,精确刻画决策边界的形状与位置。在人工数据和真实数据上的大量实验表明,EDC不仅能发现目标方程的结构,还能准确估计参数,其性能优于当前最先进的基于方程发现的分类方法,并达到主流二分类模型的水平。我们设计了一种中等复杂度的语法,包含线性、二次、指数项及两特征乘积项(可捕捉异或类依赖关系),生成的超曲面具备良好灵活性但不易过拟合。该语法可配置,支持引入特定领域表达式以满足实际需求。
原文摘要 · Abstract (English)
Equation Discovery techniques have shown considerable success in regression tasks, where they are used to discover concise and interpretable models (\textit{Symbolic Regression}). In this paper, we propose a new ED-based binary classification framework. Our proposed method EDC finds analytical functions of manageable size that specify the location and shape of the decision boundary. In extensive experiments on artificial and real-life data, we demonstrate how EDC is able to discover both the structure of the target equation as well as the value of its parameters, outperforming the current state-of-the-art ED-based classification methods in binary classification and achieving performance comparable to the state of the art in binary classification. We suggest a grammar of modest complexity that appears to work well on the tested datasets but argue that the exact grammar -- and thus the complexity of the models -- is configurable, and especially domain-specific expressions can be included in the pattern language, where that is required. The presented grammar consists of a series of summands (additive terms) that include linear, quadratic and exponential terms, as well as products of two features (producing hyperbolic curves ideal for capturing XOR-like dependencies). The experiments demonstrate that this grammar allows fairly flexible decision boundaries while not so rich to cause overfitting.
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