Supervised Latent Variable Model with Gaussian Inner Structure for Dynamic PROCESS

Abstract

Supervised multivariate statistical techniques are important tools for modeling the relationship between variables in dynamic processes. To building the dynamic relationship between variables, a supervised dynamic latent variable (LV) model with Gaussian inner structure is proposed to extract explicit LVs from the process and quality data with high collinearity. The outer dynamic latent structure gains stronger prediction ability by paying attention to both the variance and covariance of data while extracting LVs from the process and quality data. As a Gaussian process, the inner model is directly estimated as a function that is searched for within an infinite-dimensional space, such that an inner model with appropriate model order is obtained. Besides, the properties of the inner structure, such as exponential stability and smoothness, are integrated into the process of identifying the Gaussian model. As a result, the prediction capability of the proposed supervised LV model is enhanced. What's more, it is easy to interpret the results obtained by the proposed model as the dynamic LVs are directly extracted from the original process and quality data matrices rather than the augmented data matrices. The efficiency of the proposed model is demonstrated by modeling the glycemic dynamics of people with type 1 diabetes.