Estimating Output Variance of a Regressing Tree Model: A Case Study of Concrete Strength Prediction

Model trees combine the strengths of two interpretable models-namely, decision trees and multiple linear regression-to handle complex nonlinear problems, making them a popular machine learning strategy in civil engineering. Analyzing the error terms between predicted and target outputs is the standard method for evaluating the model's accuracy. However, the model does not explain the variance associated with the predicted output for a given set of inputs, which may be deemed insufficient in many civil engineering applications. This research proposes a framework that combines error propagation theory with the model tree algorithm to quantify the variance of the model predicted output and provide explainable artificial intelligence (XAI) for engineering applications. A metric based on the variance estimate is proposed to decide whether the model predicted output is acceptable. A concrete strength prediction model is presented to demonstrate the application of the proposed methodology.