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

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.

READ FULL TEXT
research
07/19/2021

Predicting Friction System Performance with Symbolic Regression and Genetic Programming with Factor Variables

Friction systems are mechanical systems wherein friction is used for for...
research
07/22/2021

Hash-Based Tree Similarity and Simplification in Genetic Programming for Symbolic Regression

We introduce in this paper a runtime-efficient tree hashing algorithm fo...
research
06/13/2022

Symbolic Regression for Space Applications: Differentiable Cartesian Genetic Programming Powered by Multi-objective Memetic Algorithms

Interpretable regression models are important for many application domai...
research
09/28/2021

Cluster Analysis of a Symbolic Regression Search Space

In this chapter we take a closer look at the distribution of symbolic re...
research
04/07/2020

Robust inference for nonlinear regression models from the Tsallis score: application to Covid-19 contagion in Italy

We discuss an approach for fitting robust nonlinear regression models, w...
research
05/18/2023

Generalised likelihood profiles for models with intractable likelihoods

Likelihood profiling is an efficient and powerful frequentist approach f...
research
04/12/2022

Automated Learning of Interpretable Models with Quantified Uncertainty

Interpretability and uncertainty quantification in machine learning can ...

Please sign up or login with your details

Forgot password? Click here to reset