I am new to the domain of symbolic regression and found the article to constitute a well-written and interesting introduction to it. Yet, I kept wondering to what extent the presented approach can really help interpreting complex black box functions. In the final example, it is clear that the results are fairly simple and interpretable while delivering a moderate loss in prectivity compared to the crude algorithm. But in more generality, I still don't see how combinations of Bessel functions and alike will help most practitioners. Which leads us to a question that to the best of my understanding was somehow underinvestigated here, namely some more systematic approach on how to tune the complexity of the metamodel, and maybe explore the Pareto front of simplicity versus predictivity.

The reviewers agreed that this paper presents a valuable contribution; they appreciated the quality of the writing, the overall motivation of interpretability of the models, and the proposed approach to use gradient descent to learn symbolic models. The primary shortcomings that the discussion focused around were some of the limited evaluation included in the paper, and the justification of the proposed models as being "interpretable". The response was useful in addressing some of these concerns.

Understanding the predictions of a machine learning model can be as crucial as the model's accuracy in many application domains. However, the black-box nature of most highly-accurate (complex) models is a major hindrance to their interpretability. To address this issue, we introduce the symbolic metamodeling framework -- a general methodology for interpreting predictions by converting "black-box" models into "white-box" functions that are understandable to human subjects. A symbolic metamodel is a model of a model, i.e., a surrogate model of a trained (machine learning) model expressed through a succinct symbolic expression that comprises familiar mathematical functions and can be subjected to symbolic manipulation. We parameterize symbolic metamodels using Meijer G-functions -- a class of complex-valued contour integrals that depend on scalar parameters, and whose solutions reduce to familiar elementary, algebraic, analytic and closed-form functions for different parameter settings.

As an Applied Data Scientist at Civis, I implemented the latest data science research to solve real-world problems. We recently worked with a global tool manufacturing company to reduce churn among their most loyal customers. A newly proposed tool, called SHAP (SHapley Additive exPlanation) values, allowed us to build a complex time-series XGBoost model capable of making highly accurate predictions for which customers were at risk, while still allowing for an individual-level interpretation of the factors that made each of these customers more or less likely to churn. To understand why this is important, we need to take a closer look at the concepts of model accuracy and interpretability. Until recently, we always had to choose between an accurate model that was hard to interpret, or a simple model that was easy to explain but sacrificed some accuracy.

Understanding the predictions of a machine learning model can be as crucial as the model's accuracy in many application domains. However, the black-box nature of most highly-accurate (complex) models is a major hindrance to their interpretability. To address this issue, we introduce the symbolic metamodeling framework -- a general methodology for interpreting predictions by converting "black-box" models into "white-box" functions that are understandable to human subjects. A symbolic metamodel is a model of a model, i.e., a surrogate model of a trained (machine learning) model expressed through a succinct symbolic expression that comprises familiar mathematical functions and can be subjected to symbolic manipulation. We parameterize symbolic metamodels using Meijer G-functions -- a class of complex-valued contour integrals that depend on scalar parameters, and whose solutions reduce to familiar elementary, algebraic, analytic and closed-form functions for different parameter settings.

As an Applied Data Scientist at Civis, I implement the latest data science research to solve real-world problems. We recently worked with a global tool manufacturing company to reduce churn among their most loyal customers. A newly proposed tool, called SHAP (SHapley Additive exPlanation) values, allowed us to build a complex time-series XGBoost model capable of making highly accurate predictions for which customers were at risk, while still allowing for an individual-level interpretation of the factors that made each of these customers more or less likely to churn. To understand why this is important, we need to take a closer look at the concepts of model accuracy and interpretability. Until recently, we always had to choose between an accurate model that was hard to interpret, or a simple model that was easy to explain but sacrificed some accuracy.