Distribution inference from early-stage stationary data streams by transfer learning

Abstract

Data streams are prevalent in current manufacturing and service systems where real-time data arrive progressively. A quick distribution inference from such data streams at their early stages is extremely useful for prompt decision making in many industrial applications. For example, a quality monitoring scheme can be quickly started if the process data distribution is available and the optimal inventory level can be determined early once the customer demand distribution is estimated. To this end, this article proposes a novel online recursive distribution inference method for stationary data streams that can respond as soon as the streaming data are generated and update as regularly as the data accumulate. A major challenge is that the data size might be too small to produce an accurate estimation at the early stage of data streams. To solve this, we resort to an instance-based transfer learning approach which integrates a sufficient amount of auxiliary data from similar processes or products to aid the distribution inference in our target task. Particularly, the auxiliary data are reweighted automatically by a density ratio fitting model with a prior-belief-guided regularization term to alleviate data scarcity. Our proposed distribution inference method also possesses an efficient online algorithm with recursive formulas to update upon every incoming data point. Extensive numerical simulations and real case studies verify the advantages of the proposed method.

Keywords:

• Data sharing
• density ratio estimation
• instance transfer
• prior information
• small data

Acknowledgments

The authors greatly acknowledge the valuable comments provided by the department editor, associate editor and two anonymous referees that have resulted in great improvements of this article.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China under Grants 71931006, 71772147; the National Key R&D Program of China under Grant 2019YFB1704100; the Fellowship of China Postdoctoral Science Foundation under Grant 2020M673430; the Hong Kong RGC General Research Funds under Grants 16216119, 16201718; the Science & Technology Innovation Team Plan of Shaanxi Province under Project S2020-ZC-TD-0083; the Youth Innovation Team of Shaanxi Universities “Big data and Business Intelligent Innovation Team”; and the Fundamental Research Funds for the Central Universities.

Notes on contributors

Kai Wang

Kai Wang is currently an assistant professor in the Department of Operations Management & Industrial Engineering, School of Management, at the Xi’an Jiaotong University, Xi’an, China. He received his PhD degree in the industrial engineering and logistics management in 2018 from the HKUST, Hong Kong, and his bachelor’s degree in industrial engineering in 2014 from Xi’an Jiaotong University, Shaanxi, China. His research focuses on industrial big data analytics, machine learning and transfer learning, statistical process control and monitoring.

Jian Li

Jian Li is an associate professor in the School of Management, Xi’an Jiaotong University, China. He received his BS degree in automation from Tsinghua University, Beijing, China, and his PhD degree in industrial engineering and decision analytics from the Hong Kong University of Science and Technology, Hong Kong. His current research interests include quality management and quality engineering, Six Sigma implementation, and statistical process control.

Fugee Tsung

Fugee Tsung is a Chair Professor in the Department of Industrial Engineering and Decision Analytics (IEDA), Director of the Quality and Data Analytics Lab (QLab), at the Hong Kong University of Science and Technology (HKUST), Hong Kong, China. He is a Fellow of the American Society for Quality, Fellow of the American Statistical Association, Academician of the International Academy for Quality, and Fellow of the Hong Kong Institution of Engineers. He received both his MSc and PhD from the University of Michigan, Ann Arbor, and his BSc from the National Taiwan University. His research interests include quality analytics in advanced manufacturing and service processes, industrial big data and statistical process control, monitoring, and diagnosis.