Landmark-embedded Gaussian process with applications for functional data modeling

Abstract

In practice, we often need to infer the value of a target variable from functional observation data. A challenge in this task is that the relationship between the functional data and the target variable is very complex: the target variable not only influences the shape but also the location of the functional data. In addition, due to the uncertainties in the environment, the relationship is probabilistic, that is, for a given fixed target variable value, we still see variations in the shape and location of the functional data. To address this challenge, we present a landmark-embedded Gaussian process model that describes the relationship between the functional data and the target variable. A unique feature of the model is that landmark information is embedded in the Gaussian process model so that both the shape and location information of the functional data are considered simultaneously in a unified manner. Gibbs–Metropolis–Hasting algorithm is used for model parameters estimation and target variable inference. The performance of the proposed framework is evaluated by extensive numerical studies and a case study of nano-sensor calibration.

Keywords:

• Shifting functional data
• Gaussian process
• landmark
• MCMC

Data availability

Data available on request from the authors.

Additional information

Funding

This work was supported by the National Science Foundation under grant number 1727846 and 2039268.

Notes on contributors

Jaesung Lee

Jaesung Lee received his BS degree in industrial systems and information engineering and his BFE degree in financial engineering from Korea University, Seoul, South Korea, in 2011 and his MS degree in management engineering from Korea Advanced Institute of Science and Technology (KAIST), Daejeon, South Korea, in 2013 and his MS degree in statistics from the University of Wisconsin–Madison, Madison, WI, USA in 2020. From 2013 to 2016, he was a Research Engineer at Diquest. Inc. Seoul, South Korea. In 2017, he was an engineering consultant at Gurobi Korea, Seoul, South Korea. He is currently a PhD candidate in industrial and systems engineering at the University of Wisconsin–Madison. His research interests include Bayesian statistical models, high-dimensional statistics, statistical application on quality and reliability.

Chao Wang

Chao Wang is an assistant professor in the Department of Industrial and Systems Engineering at the University of Iowa. He received his BS from the Hefei University of Technology in 2012, and MS from the University of Science and Technology of China in 2015, both in mechanical engineering, and his MS in statistics and PhD in industrial and systems engineering from the University of Wisconsin-Madison in 2018 and 2019, respectively. His research interests include statistical modeling, analysis, monitoring and control for complex systems. He is member of INFORMS, IISE, and SME.

Xiaoyu Sui

Xiaoyu Sui is currently a PhD student in the Pritzker School of Molecular Engineering at the University of Chicago. He received his bachelor’s and master’s degrees in materialogy from Tongji University, Shanghai, China. His research interests include nanoscale engineering of nanomaterials and additive manufacturing for water sensing and energy storage applications.

Shiyu Zhou

Shiyu Zhou received the BS and MS degrees in mechanical engineering from the University of Science and Technology of China, Hefei, China, in 1993 and 1996, respectively, and the master’s degree in industrial engineering and the PhD degree in mechanical engineering from the University of Michigan, Ann Arbor, MI, USA, both in 2000. He is the Vilas Distinguished Achievement Professor with the Department of Industrial and Systems Engineering, University of Wisconsin-Madison, Madison, WI, USA. His research interests include data-driven modeling, monitoring, diagnosis, and prognosis for engineering systems with particular emphasis on manufacturing and after-sales service systems.

Junhong Chen

Junhong Chen is currently Crown Family Professor of Molecular Engineering at Pritzker School of Molecular Engineering, The University of Chicago and Lead Water Strategist and Senior Scientist at Argonne National Laboratory. Prof. Chen received his PhD in mechanical engineering from University of Minnesota and was a postdoctoral scholar in chemical engineering at California Institute of Technology. His research interest focuses on molecular engineering of 2D nanomaterials, hybrid nanomaterials, chemical and biological sensors, and energy devices.