Interpretable Scientific Discovery with Symbolic Regression: A Review

Symbolic Regression (SR) is a rapidly growing subfield within machine learning (ML) to infer symbolic mathematical expressions from data [1, 2]. Interest in SR is being driven by the observation that it is not sufficient to only have accurate predictive models; however, it is often necessary that the learned models be interpretable [3]. A model is interpretable if the relationship between the input and output of the model can be logically or mathematically traced in a succinct manner. In other words, learnable models are interpretable if expressed as mathematical equations. As "disciplines" become increasingly data-rich and adopt ML techniques, the demand for interpretable models is likely to grow. For example, in the natural sciences (e.g., physics), mathematical models derived from first principles make it possible to reason about the underlying phenomenon in a way that is not possible with predictive models like deep neural networks. In critical disciplines like healthcare, non-interpretable models may never be allowed to be deployed - however accurate they maybe [4].