A Novel Semi-Supervised Sparse Bayesian Regression Based on Variational Inference for Industrial Datasets With Incomplete Outputs

The acquired industrial data often contain missing outputs because of the irregularities of complicated industrial environment, which make the outputs of the training dataset incomplete. In this paper, a semi-supervised sparse Bayesian regression model is proposed for dealing with the incomplete outputs problem by employing a variational inference technique. Within the settings of specific hierarchical priors over the missing outputs, in this paper, we derive the posterior probability distribution over the uncertain variables including the missing outputs. Given that the posterior distribution is not analytically tractable, a hybrid learning procedure is designed for combining the variational inference with a gradient-based method to obtain optimal approximate posteriors. To verify the performance of the proposed method, a number of comparative experiments are conducted and analyzed by using the datasets (including artificial and real world ones) coming with different proportions of missing outputs. Compared to the existing semi-supervised regression approaches, we demonstrated the effectiveness of the proposed method.