Operator-induced structural variable selection for identifying materials genes

In the emerging field of materials informatics, a fundamental task is to identify physicochemically meaningful descriptors, or materials genes, which are engineered from primary variables and a set of elementary algebraic operators through compositions. Standard practice directly analyzes the high-dimensional candidate predictor space in a linear model; statistical analyses are then substantially hampered by the daunting challenge posed by the astronomically large number of correlated predictors with limited sample size. We formulate this problem as variable selection with operator-induced structure (OIS), and propose a new method to achieve unconventional dimension reduction by utilizing the geometry embedded in OIS. Although the model remains linear, we iterate nonparametric variable selection for effective dimension reduction. This enables variable selection based on ab initio primary variables, leading to a method that is orders of magnitude faster than existing methods, with improved accuracy. An OIS screening property for variable selection with OIS is introduced; interestingly, finite sample assessment indicates that the employed Bayesian Additive Regression Trees (BART)-based variable selection method enjoys this property under the simulation settings. Numerical studies show the superiority of the proposed method, which continues to exhibit robust performance when the dimension of engineered features is out of reach of existing methods. Our analysis to single-atom catalysis identifies physical descriptors that explain the binding energy of metal-support pairs with high explanatory power, leading to interpretable insights to guide the prevention of a notorious problem called sintering and aid catalysis design.