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

TL;DR

This paper analyzes the sample complexity of causal discovery algorithms without a conditional independence oracle, quantifies the value of domain expertise, and demonstrates how priors and known directions improve efficiency.

Contribution

It provides the first detailed analysis of sample complexity in observational causal discovery without an oracle and quantifies the benefits of domain knowledge and priors.

Findings

Sample complexity bounds for causal discovery algorithms.

Quantification of domain expertise value in reducing data requirements.

Numerical validation of theoretical sample rates.

Abstract

Causal discovery methods seek to identify causal relations between random variables from purely observational data, as opposed to actively collected experimental 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 a conditional independence (CI) oracle: an oracle that can states whether two random variables are conditionally independent given another set of random variables. Practical implementations of this algorithm incorporate statistical tests for conditional independence, in place of a CI oracle. In this paper, we analyze the sample complexity of causal discovery algorithms without a CI oracle: given a certain level of confidence, how many data points are needed for a causal discovery algorithm to identify a causal structure? Furthermore, our methods allow us to quantify the value of domain expertise in terms of data samples. Finally, we demonstrate the accuracy of these sample rates with numerical examples, and quantify the benefits of sparsity priors and known causal directions.