Low‐Dimensional Controls on Oceanic Basalt Geochemistry Revealed by Regression‐Based Machine Learning Models

Abstract The low dimensionality of basalt geochemical data has long been inferred but has not been quantitatively evaluated from the relationships among elemental contents. We developed regression‐based machine learning models and examined the relationships among elemental contents for basalts. We applied an extended gradient boosting algorithm (natural gradient boosting), which allows predictions with associated probability distributions, to a training data set of global basalt compositions, including midocean ridge, ocean island, and volcanic arc basalts. From four input elements (Th, Nb, Zr, and Ti), the trained models can successfully predict the contents of 12 trace elements (Rb, Ba, U, La, Ce, Pb, Sr, P, Nd, Y, Yb, and Lu; R 2 > 0.7) and 5 major elements (SiO 2 , MgO, Na 2 O, CaO, and K 2 O; R 2 > 0.67). The adopted model interpretation techniques quantitatively identified key input features for output element estimations, such as similar elemental incompatibility (e.g., Th‐Rb contents) and elemental ratios/products involving different incompatible elements (e.g., Zr/Th ratios for Yb contents). This is consistent with well‐established geochemical principles related to elemental incompatibility and tectonic setting and was achieved without prior geochemical knowledge of the samples. On a projection of a reduced two‐dimensional map constructed from the four input elements, numerical variations of the identified key input features were correlated with the output contents. Given the successfully constructed regression‐based models based on only four input elements, basalt geochemical data have a low dimensionality. Moreover, our approach can potentially provide a more comprehensive understanding of the link between basalt geochemistry and geological processes.