MetaSR: A Meta-Learning Approach to Fitness Formulation for Frequency-Aware Symbolic Regression
Abstract: State-of-the-art Symbolic Regression (SR) algorithms employ evolutionary techniques to fulfill the task of generating a concise mathematical expression that fulfills an objective. A common objective is to fit to a dataset of input-output pairs, in which the faithfulness of a predicted output to the actual output is used as the fitness measure (e.g., R-squared). In many datasets, among the candidate expressions evaluated, there tends to be a large number of pseudo-expressions, referring to expressions that achieve high fitness but do not resemble the ground-truth equation. These pseudo-expressions decrease the equation recovery rate of SR algorithms. To formulate novel fitness measures that function as better discriminators of the ground-truth equation, we introduce a novel meta-learning approach to SR, MetaSR, in which we utilize SR itself to discover new fitness measures that can be complex combinations of existing base measures. In this paper, we focus on frequency-aware symbolic regression, where the fitness can depend on the frequency domain. We show that our new fitness measures better discriminate the ground-truth equation from other equations and demonstrate the improved performance of our method against existing algorithms.
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