Bayesian Sparse Regression for Mixed Multi-Responses with Application to Runtime Metrics Prediction in Fog Manufacturing

Abstract

Fog manufacturing can greatly enhance traditional manufacturing systems through distributed Fog computation units, which are governed by predictive computational workload offloading methods under different Industrial Internet architectures. It is known that the predictive offloading methods highly depend on accurate prediction and uncertainty quantification of runtime performance metrics, containing multivariate mixed-type responses (i.e., continuous, counting, binary). In this work, we propose a Bayesian sparse regression for multivariate mixed responses to enhance the prediction of runtime performance metrics and to enable the statistical inferences. The proposed method considers both group and individual variable selection to jointly model the mixed types of runtime performance metrics. The conditional dependency among multiple responses is described by a graphical model using the precision matrix, where a spike-and-slab prior is used to enable the sparse estimation of the graph. The proposed method not only achieves accurate prediction, but also makes the predictive model more interpretable with statistical inferences on model parameters and prediction in the Fog manufacturing. A simulation study and a real case example in a Fog manufacturing are conducted to demonstrate the merits of the proposed model.

KEYWORDS:

• Graphical model
• Mixed responses
• Spike-and-slab prior
• Variable selection

Supplementary Materials

The supplementary materials for this article contain the following: (a) detailed derivation of full-conditional distributions; (b) detailed performance comparison in numerical study; (c) detailed full factorial design for sensitivity study of prior settings; and (d) data and R implementation of the proposed BS-MRMR method for numerical study.

Acknowledgments

The authors would like to sincerely thank the editor, associate editor, and two referees for their insightful and constructive comments for helping improve the article.

Disclosure Statement

The authors report that there are no competing interests to declare.

Additional information

Funding

Deng’s research was supported by the National Science Foundation CISE Expedition (CCF-1918770) and Virginia Tech Data Science Faculty Fellowship. Kang’s research was supported by the Natural Science Foundation of Liaoning Province (2022-MS-179).