EDC: Equation Discovery for Classification

TL;DR

This paper introduces EDC, a novel symbolic equation discovery framework for binary classification that finds interpretable analytical functions defining decision boundaries, outperforming existing methods in accuracy and flexibility.

Contribution

The paper presents a new ED-based classification method, EDC, with a configurable grammar for discovering interpretable decision boundary equations, advancing symbolic regression techniques into classification tasks.

Findings

EDC outperforms current ED-based classifiers in accuracy.

The proposed grammar captures complex decision boundaries effectively.

EDC achieves performance comparable to state-of-the-art classifiers.

Abstract

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.