Causal Discovery Using Regression-Based Conditional Independence Tests

No. 1: Thirty-First AAAI Conference On Artificial Intelligence

Volume

Proceedings of the AAAI Conference on Artificial Intelligence, 31

AAAI Technical Track: Knowledge Representation and Reasoning

Conditional independence (CI) testing is an important tool in causal discovery. Generally, by using CI tests, a set of Markov equivalence classes w.r.t. the observed data can be estimated by checking whether each pair of variables x and y is d-separated, given a set of variables Z. Due to the curse of dimensionality, CI testing is often difficult to return a reliable result for high-dimensional Z. In this paper, we propose a regression-based CI test to relax the test of x _ y|Z to simpler unconditional independence tests of x _ f(Z) _ y_g(Z), and x_f(Z) _ Z or y_g(Z) _ Z under the assumption that the data-generating procedure follows additive noise models (ANMs). When the ANM is identifiable, we prove that x _ f(Z) _ y _ g(Z) _ x _ y|Z. We also show that 1) f and g can be easily estimated by regression, 2) our test is more powerful than the state-of-the-art kernel CI tests, and 3) existing causal learning algorithms can infer much more causal directions by using the proposed method.

10.1609/aaai.v31i1.10698