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Causal Discovery Using Regression-Based Conditional Independence Tests

Last modified: 2017-02-12

#### Abstract

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.#### Keywords

Causality discovery; Conditional independent test; Regression

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