Interpretability in Symbolic Regression: a benchmark of Explanatory
  Methods using the Feynman data set
Guilherme Seidyo Imai Aldeia Fabricio Olivetti de Franca
In some situations, the interpretability of the machine learning models plays
a role as important as the model accuracy. Interpretability comes from the need
to trust the prediction model, verify some of its properties, or even enforce
them to improve fairness. Many model-agnostic explanatory methods exists to
provide explanations for black-box models. In the regression task, the
practitioner can use white-boxes or gray-boxes models to achieve more
interpretable results, which is the case of symbolic regression. When using an
explanatory method, and since interpretability lacks a rigorous definition,
there is a need to evaluate and compare the quality and different explainers.
This paper proposes a benchmark scheme to evaluate explanatory methods to
explain regression models, mainly symbolic regression models. Experiments were
performed using 100 physics equations with different interpretable and
non-interpretable regression methods and popular explanation methods,
evaluating the performance of the explainers performance with several
explanation measures. In addition, we further analyzed four benchmarks from the
GP community. The results have shown that Symbolic Regression models can be an
interesting alternative to white-box and black-box models that is capable of
returning accurate models with appropriate explanations. Regarding the
explainers, we observed that Partial Effects and SHAP were the most robust
explanation models, with Integrated Gradients being unstable only with
tree-based models. This benchmark is publicly available for further
experiments.