SCRBenchmark: A Benchmarking Library for Shape-Constrained Regression

Shape-constrained regression aims to fit regression models that adhere to specific constraints regarding the expected shape of the parametric model. Commonly studied constraints include convexity, concavity, symmetry, and monotonicity. These constraints can be used to enforce the desired behavior or incorporate prior knowledge about the studied phenomena, guiding the fitting process towards a more realistic solution. These are particularly useful to ensure proper behavior when extrapolating beyond the training data in cases where only limited training data is available. Also, this helps to reduce the influence of noise, mitigating overfitting. There has been a growing interest in shape-constrained regression, however, no established benchmark currently exists. As a result, many studies lack a direct comparison between methods or focus solely on practical applications. To address this gap, we propose an adaptation of the Feynman benchmark suite for symbolic regression as a general benchmark for shape-constrained regression. The Feynman benchmark suite is an appropriate choice because it is derived from physical phenomena where shape constraints naturally occur. In this benchmark, we evaluate model accuracy, the number of violated constraints, and model behavior when extrapolating data and handling noise. Additionally, we provide a Python interface to facilitate the evaluation of any regression model.