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

TL;DR

This paper introduces a Bayesian sparse regression model tailored for multivariate mixed-type responses, improving prediction accuracy and interpretability of runtime metrics in fog manufacturing systems.

Contribution

It develops a novel Bayesian sparse regression approach that handles mixed response types and models their dependencies, with applications to fog manufacturing performance prediction.

Findings

Achieves accurate prediction of runtime metrics.

Enables statistical inference on model parameters.

Demonstrates effectiveness through simulation and real case studies.

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.