Semi-supervised Variational Autoencoders for Regression: Application to Soft Sensors.

We present the development of a semi-supervised regression method using variational autoencoders (VAE) for soft sensing of process quality variables. Recently, use of VAEs was proposed for regression applications based on variational inference. In this work, We extend this approach of supervised VAEs for regression to make it learn from both labelled and unlabelled data leading to a semi-supervised VAE for regression (SSVAER) formulation. The probabilistic regressor resulting from the variational approach makes it possible to estimate the variance of the predictions simultaneously, which provides a means for online uncertainty quantification for soft sensors. We provide an extensive comparative study of SSVAER with previously proposed semi-supervised learning methods on two soft sensing benchmark problems using fixed-size datasets, where we vary the percentage of labelled data available for training. In these experiments, SSVAER achieves the lowest test errors in 11 of the 20 studied cases, compared to other methods where the second best method gets 4 lowest test errors out of the 20.