Multi-Model Variational Bayesian Approaches for Causality Analysis

Abstract

Causality analysis using data-driven models helps in the construction of graphical models that illustrate the interaction among the variables of a process system. A majority of industrial processes operate in multiple operating modes and thus the measurements from these processes exhibit multi-modal characteristics. However, the literature for causality analysis is skewed towards analyzing unimodal processes. In this work, we propose an approach for causality analysis in multi-modal systems.\par Granger causality analysis is one of the widely popular methods for causality analysis. Classical techniques for multivariate Granger causality analysis rely on significance tests on parameters of vector autoregressive (VAR) models or vector moving average (VMA) models of the actual unimodal processes. In this work, we propose a Granger causality analysis technique with multi-modal VAR models. Our technique relies on variational Bayesian analysis of multi-modal VAR models. It imposes a soft constraint through Normal-Gamma priors on multi-modal VAR model parameters. This soft constraint ensures that the causal graphs extracted from different modes are consistent while allowing the strengths of interaction to vary across modes. Our approach also provides a single metric to assess the significance of each causal interaction in multi-modal systems. We illustrate the proposed algorithm using both simulation and industrial data. Furthermore, Bayesian network based approach for Granger causality analysis in multi-mode systems can handle data with outliers. The performance of the robust method is also tested using simulation and industrial process data.