论文标题
基于似然曲线的符号回归模型的预测间隔和置信区域
Prediction Intervals and Confidence Regions for Symbolic Regression Models based on Likelihood Profiles
论文作者
论文摘要
符号回归是一种非线性回归方法，通常通过诸如遗传编程等进化计算方法执行。量化回归模型的不确定性对于模型和决策的解释很重要。线性近似和所谓的似然谱是非线性回归模型计算置信度和预测间隔的众所周知的可能性。到目前为止，这些简单有效的技术在遗传编程文献中已被完全忽略。在这项工作中，我们在详细信息中描述了似然概况的计算，并提供了一些说明性示例，其中有两个不同的符号回归算法创建的模型。这些示例强调了可能性概况的重要性，即了解符号回归模型的局限性并帮助用户做出明智的预测后决策。
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.
