Prediction Intervals and Confidence Regions for Symbolic Regression Models based on Likelihood Profiles

TL;DR

This paper introduces a method for calculating likelihood profiles to quantify uncertainty in symbolic regression models, enhancing interpretability and decision-making, which has been overlooked in genetic programming literature.

Contribution

It details the calculation of likelihood profiles for symbolic regression and demonstrates their usefulness through examples with different algorithms and datasets.

Findings

Likelihood profiles reveal model limitations.

They assist in informed post-prediction decisions.

The method is applicable across multiple symbolic regression algorithms.

Abstract

Symbolic regression is a nonlinear regression method which is commonly performed by an evolutionary computation method such as genetic programming. Quantification of uncertainty of regression models is important for the interpretation of models and for decision making. The linear approximation and so-called likelihood profiles are well-known possibilities for the calculation of confidence and prediction intervals for nonlinear regression models. These simple and effective techniques have been completely ignored so far in the genetic programming literature. In this work we describe the calculation of likelihood profiles in details and also provide some illustrative examples with models created with three different symbolic regression algorithms on two different datasets. The examples highlight the importance of the likelihood profiles to understand the limitations of symbolic regression models and to help the user taking an informed post-prediction decision.