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

arXiv: https://arxiv.org/abs/2210.04811 · HTML: https://mlsanity.com/paper/2210.04811/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 36 references that are in the map.
- First posted on arXiv 10 Oct 2022.

## Builds on (most cited first, 5 of 5)

- [Scaling It Up: Stochastic Search Structure Learning in Graphical Models](https://mlsanity.com/paper/1505.01687/) (2015)
- [Bayesian Nonparametric Modeling for Multivariate Ordinal Regression](https://mlsanity.com/paper/1408.1027/) (2014)
- [Sparse Estimation of Multivariate Poisson Log-Normal Models from Count Data](https://mlsanity.com/paper/1602.07337/) (2016)
- [Multivariate Regression of Mixed Responses for Evaluation of Visualization Designs](https://mlsanity.com/paper/2004.02051/) (2020)
- [A Generative Approach to Joint Modeling of Quantitative and Qualitative Responses](https://mlsanity.com/paper/2102.09448/) (2021)

## Abstract (arXiv)

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.