Structural learning of functional directed graphical models with incomplete signals

Abstract

Functional directed graph model (DGM) learning has been widely used to analyze complex systems. Most existing works assume that the functional signals are complete, which in reality is not true. To address this problem, in this study, a framework for DGM learning with incomplete signals is proposed. Specifically, a penalty term that integrates information from the graph structure is added to the Maximum Margin Matrix Factorization (MMMF) objective function. The proposed method can be used with a known structure to estimate the functional relationship between nodes or with an unknown structure to estimate the relationship together with the graph structure. Numerical experiments and a real-world case study of monocrystalline silicone manufacturing are performed to verify the effectiveness of the proposed method when the signal matrices are incomplete.

Keywords:

• Functional directed graph models
• function-to-function regression
• graph learning
• missing data
• signal completion

Disclosure statement

No potential conflict of interest was reported by the authors.

Data availability statement

Due to the nature of this research, participants of this study did not agree for their data to be shared publicly, so supporting data is not available.

Additional information

Funding

This work was funded by the Key Program of National Science Foundation of China under Grant No. 71932006.