Penalized Matrix Regression for Two-Dimensional Variable Selection
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The root-cause diagnostics for product quality defects in multistage manufacturing processes often requires us to simultaneously identify the crucial stages and variables. To satisfy this requirement, this paper proposes a novel penalized matrix regression methodology for two-dimensional variable selection. The method regresses a matrix-based predictor against a scalar-based response variable using a generalized linear model. The rows and columns of the regression coefficient matrix are simultaneously penalized to inspire sparsity. To estimate the parameters, we develop a block coordinate proximal descent (BCPD) optimization algorithm, which cyclically solves two sub optimization problems, both of which have closed-form solutions. A simulation study and data from a real-world application are used to validate the effectiveness of the proposed method.
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