Fighting Underspecification in Symbolic Regression with Fitness Sharing

Underspecification happens when there are different plausible hypotheses for a training and validation data set that behave differently when evaluating outside the training domain or distribution. Symbolic regression algorithms are prone to underspecification because of the additional degree of freedom of having to specify the structural component of the regression model. When facing different likely alternatives, some algorithms use the Occam's razor principle of choosing the simplest alternative. But not only there is no guarantee that this is the correct decision but the definition of simplest in symbolic regression is also subjective. In this work we analyse the use diversity control mechanisms to help fight the underspecification problem by providing to the end-user multiple alternative models in a single execution. These alternative models can be used in a post-analysis process when the practitioner has additional knowledge. For this purpose, we implemented a fitness sharing mechanism in the Transformation-Interaction-Rational Symbolic Regression algorithm with a distance function that measures how different two models behave outside the domain of the training data. The results showed that this adaptation is capable of producing multiple alternatives with similar fitness but with distinct behavior outside this domain.