Semi-supervised variational Bayesian Student’s t mixture regression and robust inferential sensor application

Abstract

Data-driven inferential sensor has been widely adopted to estimate key quality relevant variables. However, industrial dataset usually presents many characteristics such as nonlinearity, non-Gaussianity, insufficiency of labeled samples, contamination of outliers, etc. These intractable characteristics have rendered significant difficulties in developing high-performance inferential sensor. This paper deals with these issues in the probabilistic way by proposing a robust semi-supervised variational Bayesian Student’s t mixture regression (referred to as the ‘SSVBSMR’). Specifically, in the SSVBSMR, the nonlinear and non-Gaussian characteristics are handled by Bayesian finite mixture models (FMM), and the Student’s t distribution is employed to constitute the components of FMM, which makes the SSVBSMR robust against outliers. In addition, the SSVBSMR exploits unlabeled samples to remedy the insufficiency of labeled samples. Furthermore, the SSVBSMR treats all model parameters as stochastic rather than deterministic such that the model selection can be automatically and efficiently completed and some limitations of the maximum likelihood method (such as overfitting and singular covariance) can be alleviated. A variational Bayesian expectation–maximization-based learning algorithm is also developed to train the SSVBSMR. Two cases are carried out to investigate the performance of the SSVBSMR, and the results demonstrate its effectiveness and feasibility compared to several state-of-the-art methods.