Variational Bayesian Approach for Causality and Contemporaneous Correlation Features Inference in Industrial Process...

Area of Science:

• Statistics
• Machine Learning
• Econometrics

Background:

• Multivariate processes often exhibit complex causal relationships and contemporaneous correlations.
• Identifying these relationships is crucial for accurate modeling and prediction.
• Existing methods may struggle to simultaneously address both causal inference and feature selection.

Purpose of the Study:

• To propose a novel hybrid model for simultaneously mining causal connections and identifying features driving contemporaneous correlations.
• To develop a robust parameter estimation and model reduction technique for complex multivariate systems.

Main Methods:

• Combining Vector Auto-Regressive Exogenous (VARX) and Factor Analysis (FA) models.
• Employing hierarchical prior distributions for regularization and pruning of model parameters.
• Utilizing Variational Bayesian Expectation Maximization (VBEM) for parameter estimation.
• Implementing a systematic model reduction strategy based on a relevance criterion.

Main Results:

• The proposed hybrid model effectively identifies significant causal connections and contemporaneous correlations.
• Parameter regularization successfully prunes irrelevant features, leading to parsimonious models.
• The model reduction technique refines complex models into simpler, interpretable structures.

Conclusions:

• The hybrid VARX-FA model offers a powerful approach for analyzing multivariate processes.
• The method provides a principled way to perform causal discovery and feature selection simultaneously.
• Demonstrated effectiveness through simulations and an industrial case study.