Operator-Induced Structural Variable Selection for Identifying Materials Genes
针对材料信息学中从初级特征和代数算子组合中识别有物理化学意义的描述符（材料基因）的问题，提出一种利用算子诱导结构几何进行非参数变量选择的方法，比现有方法快数个数量级且精度更高，并在单原子催化分析中识别出解释金属-载体结合能的物理描述符。
In the emerging field of materials informatics, a fundamental task is to identify physicochemically meaningful descriptors, or materials genes, which are engineered from primary features 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 features, leading to a method that is orders of magnitude faster than existing methods, with improved accuracy. To select the nonparametric module, we discuss a desired performance criterion that is uniquely induced by variable selection with OIS; in particular, we propose to employ a Bayesian Additive Regression Trees (BART)-based variable selection method. Numerical studies show superiority of the proposed method, which continues to exhibit robust performance when the input dimension is out of reach of existing methods. Our analysis of 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.