Partial Information Decomposition for Causal Discovery With Application to Internet of Things

Jessica E. Liang

Abstract: Causal discovery is fundamental to science because the concept can be used for predictions of the consequences of actions. Information theory for causal discovery has become an active area of current research. In this article, we offer an analysis of the most popular four relations in causal discovery, and develop a necessary condition for causal discovery using interaction information with physical meaning from partial information decomposition (PID), i.e., the redundant information needs to be greater than the synergetic information. We further develop this necessary condition into a necessary and sufficient condition by incorporating a conditional mutual information. This makes causal discovery interpretable using PID. Simulation results show that our causal discovery algorithm performs very effectively for single-input single-output (SISO), multiple-input single-output (MISO), and multiple-input multiple-output (MIMO) Internet of Things (IoT) systems. The causal relations of input signals, channels, received signals, and output signals are discovered. The proposed approach is compared against the greedy equivalence search (GES) and greedy interventional equivalence search (GIES) algorithms in IoT causal discovery. Future work on extending this algorithm using $\mathcal {V}$ -Information is also discussed.