Causal Network Inference by Optimal Causation Entropy

The broad abundance of time series data, which is in sharp contrast to limited knowledge of the underlying network dynamic processes that produce such observations, calls for an general and efficient method of causal network inference. Here we develop mathematical theory of Causation Entropy, a model-free information-theoretic statistic designed for causality inference. We prove that for a given node in the network, the collection of its direct causal neighbors forms the minimal set of nodes that maximizes Causation Entropy, a result we refer to as the Optimal Causation Entropy Principle. This principle guides us to further develop computational and data efficient algorithms for causal network inference. Analytical and numerical results for Gaussian processes on large random networks highlight that inference by Optimal Causation Entropy outperforms previous leading methods including Conditional Granger Causality and Transfer Entropy. Interestingly, our numerical results also indicate that the number of samples required for accurate inference depends strongly on network characteristics such as the density of links and information diffusion rate and not on the number of nodes.