Bayesian model selection for reducing bloat and overfitting in genetic programming for symbolic regression

When performing symbolic regression using genetic programming, overfitting and bloat can negatively impact generalizability and interpretability of the resulting equations as well as increase computation times. A Bayesian fitness metric is introduced and its impact on bloat and overfitting during population evolution is studied and compared to common alternatives in the literature. The proposed approach was found to be more robust to noise and data sparsity in numerical experiments, guiding evolution to a level of complexity appropriate to the dataset. Further evolution of the population resulted not in overfitting or bloat, but rather in slight simplifications in model form. The ability to identify an equation of complexity appropriate to the scale of noise in the training data was also demonstrated. In general, the Bayesian model selection algorithm was shown to be an effective means of regularization which resulted in less bloat and overfitting when any amount of noise was present in the training data.

The efficacy of a Genetic Programming (GP) [1] solution is often characterized by its (1) fitness, i.e. ability to perform a training task, (2) complexity, and (3) generalizability, i.e. ability to perform its task in an unseen scenario. Bloat is a common phenomenon for GP in which continued training results in significant increases in complexity with minimal improvements in fitness. There are several theories for the prevalence of bloat in GP which postulate possible evolutionary benefits of bloat [2]; however, for most practical purposes bloat is a hindrance rather than a benefit. For example, bloated solutions are less interpretable and more computationally expensive. Overfitting is another common phenomena in GP and the broader machine learning field. Overfitting occurs when continued training results in better fitness but reduced generalizability.