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Data dimensionality is becoming an increasing challenge in causal inference. For example, there is currently much interest in learning network structure from observational data for use in statistical genetics, microbiomics, social network applications etc. If a large number of potential confounders are available, the discovery of plausible DAG structures is itself a major hurdle to correct adjustment for confounding, and reliance on subject matter expertise may be unreliable. One strategy for causal structure discovery is based on the `PC algorithm' that performs sequential hypothesis testing for dependence and structure simplification and orientation. However, this algorithm is largely heuristic, and not designed for large dimensional data. This theme will investigate new approaches to causal structure discovery, with a focus on high dimensional settings and current issues in network inference.