The linear random forest algorithm and its advantages in machine learning assisted logging regression modeling

Direct measurements of formation properties such as the shale volume, porosity, permeability, and fluid saturation are often accompanied by expensive cost and are time-consuming too. Well logging inversion provides an alternative way for the determination of formation properties. Compared to traditional theoretical models or formalized empirical fitted models, machine learning assisted logging regression modeling is more accurate and objective. Several machine learning regression algorithms such as neural networks, support vector regression, fuzzy logic, k nearest neighbors regression, multivariate adaptive regression spline, and random forest have already been applied. In this article, we present the Linear Random Forest algorithm and investigate its application in logging regression modeling. By systematic comparison with 8 other algorithms including least squared linear regression, neural networks, epsilon support vector regression, k nearest neighbors regression, regression tree, regression random forest, gradient descent boosted trees, and linear decision tree, the advantage of linear random forest in performance is confirmed by 24 real-world tasks from 7 different areas. Deeper discussions reveal that the advantages of linear random forest source from its strong learning ability, robustness, and feasibility of the hypothesis space. Through our study, the superiority of linear random forest for logging regression modeling is substantiated, which provides a more reasonable way for the further practices of logging regression modeling.