Entropic causal inference is a framework for inferring the causal direction between two categorical variables from observational data. The central assumption is that the amount of unobserved randomness in the system is not too large. This unobserved randomness is measured by the entropy of the exogenous variable in the underlying structural causal model, which governs the causal relation between the observed variables. Kocaoglu et al. conjectured that the causal direction is identifiable when the entropy of the exogenous variable is not too large. In this paper, we prove a variant of their conjecture.

Entropic causal inference is a recent framework for learning the causal graph between two variables from observational data by finding the information-theoretically simplest structural explanation of the data, i.e., the model with smallest entropy. In our work, we first extend the causal graph identifiability result in the two-variable setting under relaxed assumptions. We then show the first identifiability result using the entropic approach for learning causal graphs with more than two nodes. Our approach utilizes the property that ancestrality between a source node and its descendants can be determined using the bivariate entropic tests. We provide a sound sequential peeling algorithm for general graphs that relies on this property. We also propose a heuristic algorithm for small graphs that shows strong empirical performance. We rigorously evaluate the performance of our algorithms on synthetic data generated from a variety of models, observing improvement over prior work. Finally we test our algorithms on real-world datasets.

Entropic causal inference is a framework for inferring the causal direction between two categorical variables from observational data. The central assumption is that the amount of unobserved randomness in the system is not too large. This unobserved randomness is measured by the entropy of the exogenous variable in the underlying structural causal model, which governs the causal relation between the observed variables. Kocaoglu et al. conjectured that the causal direction is identifiable when the entropy of the exogenous variable is not too large. In this paper, we prove a variant of their conjecture.

As quantum computing and networking nodes scale-up, important open questions arise on the causal influence of various sub-systems on the total system performance. These questions are related to the tomographic reconstruction of the macroscopic wavefunction and optimizing connectivity of large engineered qubit systems, the reliable broadcasting of information across quantum networks as well as speed-up of classical causal inference algorithms on quantum computers. A direct generalization of the existing causal inference techniques to the quantum domain is not possible due to superposition and entanglement. We put forth a new theoretical framework for merging quantum information science and causal inference by exploiting entropic principles. First, we build the fundamental connection between the celebrated quantum marginal problem and entropic causal inference. Second, inspired by the definition of geometric quantum discord, we fill the gap between classical conditional probabilities and quantum conditional density matrices. These fundamental theoretical advances are exploited to develop a scalable algorithmic approach for quantum entropic causal inference. We apply our proposed framework to an experimentally relevant scenario of identifying message senders on quantum noisy links. This successful inference on a synthetic quantum dataset can lay the foundations of identifying originators of malicious activity on future multi-node quantum networks. We unify classical and quantum causal inference in a principled way paving the way for future applications in quantum computing and networking.