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.

翻译：在新兴的材料信息学领域，一项基本任务是识别物理化学上有意义的描述符，即材料基因，这些描述符是通过对原始特征和一组基本代数算子进行组合而构建的。标准做法直接在线性模型中分析高维候选预测因子空间；然而，统计分析受到天文数字般数量且样本量有限的相互关联预测因子所带来的严峻挑战的严重阻碍。我们将该问题表述为带有算子诱导结构（OIS）的变量选择，并提出一种新方法，通过利用OIS中嵌入的几何结构来实现非传统降维。尽管模型保持线性，但我们通过迭代非参数变量选择来实现有效的降维。这使得能够基于从头计算的原始特征进行变量选择，从而得到一种比现有方法快数个数量级且精度更高的方法。为了选择非参数模块，我们讨论了一种由OIS变量选择唯一引发的理想性能准则；具体而言，我们建议采用基于贝叶斯加性回归树（BART）的变量选择方法。数值研究表明所提方法具有优越性，当输入维度超出现有方法的处理范围时，该方法仍表现出稳健性能。我们对单原子催化的分析识别出物理描述符，这些描述符以高解释力解释了金属-载体对的结合能，从而提供了可解释的见解，以指导预防一种称为烧结的棘手问题并辅助催化设计。