Process Modeling and Prediction With Large Number of High-Dimensional Variables Using Functional Regression

Learning the relationship between a response variable (e.g., a quality characteristic) and a set of predictors (e.g., process variables) is of special importance in process modeling, prediction, and optimization. In many applications, not only is the number of these variables large but these variables are also high-dimensional (HD) (e.g., they are represented by waveform signals). This high dimensionality requires a systematic approach to both modeling the relationship between the variables and removing the noninformative input variables. This article proposes a functional regression method in which an HD response is estimated and predicted through a set of informative and noninformative HD covariates. For this purpose, the functional regression coefficients are expanded through a set of low-dimensional smooth basis functions. In order to estimate the low-dimensional set of parameters, a penalized loss function with both smoothing and group lasso penalties is defined. The block coordinate decent (BCD) method is employed to develop a computationally tractable algorithm for minimizing the loss function. Through simulations and case studies, the performance of the proposed method is evaluated and compared with benchmarks. The results illustrate the advantage of the proposed method over the benchmarks.