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Causal discovery methods seek to identify causal relations between randomvariables from purely observational data, as opposed to actively collectedexperimental data where an experimenter intervenes on a subset of correlates.One of the seminal works in this area is the Inferred Causation algorithm,which guarantees successful causal discovery under the assumption of aconditional independence (CI) oracle: an oracle that can states whether tworandom variables are conditionally independent given another set of randomvariables. Practical implementations of this algorithm incorporate statisticaltests for conditional independence, in place of a CI oracle. In this paper, weanalyze the sample complexity of causal discovery algorithms without a CIoracle: given a certain level of confidence, how many data points are neededfor a causal discovery algorithm to identify a causal structure? Furthermore,our methods allow us to quantify the value of domain expertise in terms of datasamples. Finally, we demonstrate the accuracy of these sample rates withnumerical examples, and quantify the benefits of sparsity priors and knowncausal directions.

On the Sample Complexity of Causal Discovery and the Value of Domain Expertise