Directed Acyclic Graphs With Tears

TL;DR

This paper introduces DAGs with Tears, a novel method for learning directed acyclic graphs in industrial processes that combines mix-integer programming with prior knowledge to overcome limitations of existing NOTEARs-based approaches.

Contribution

The paper proposes a new DAG learning method based on mix-integer programming that addresses gradient-based optimization issues and incorporates prior knowledge for industrial applications.

Findings

The proposed method effectively learns DAGs with guaranteed acyclicity.

Numerical and industrial case studies demonstrate the method's superiority.

The approach integrates prior knowledge to enhance practical structure learning.

Abstract

Bayesian network is a frequently-used method for fault detection and diagnosis in industrial processes. The basis of Bayesian network is structure learning which learns a directed acyclic graph (DAG) from data. However, the search space will scale super-exponentially with the increase of process variables, which makes the data-driven structure learning a challenging problem. To this end, the DAGs with NOTEARs methods are being well studied not only for their conversion of the discrete optimization into continuous optimization problem but also their compatibility with deep learning framework. Nevertheless, there still remain challenges for NOTEAR-based methods: 1) the infeasible solution results from the gradient descent-based optimization paradigm; 2) the truncation operation to promise the learned graph acyclic. In this work, the reason for challenge 1) is analyzed theoretically, and a novel method named DAGs with Tears method is proposed based on mix-integer programming to alleviate challenge 2). In addition, prior knowledge is able to incorporate into the new proposed method, making structure learning more practical and useful in industrial processes. Finally, a numerical example and an industrial example are adopted as case studies to demonstrate the superiority of the developed method.