A Robust Independence Test for Constraint-Based Learning of Causal Structure
This addresses an incremental improvement for researchers in causal discovery, specifically mitigating issues in constraint-based algorithms when databases are small or incomplete.
The paper tackles the problem of unreliable conditional-independence tests in constraint-based causal structure learning by introducing a new robust test that combines Bayesian learning, Bayesian network inference, and classical hypothesis testing. The result is improved reliability in recovering structural features, smaller KL-Divergence in networks, and reduced stalling probability, especially with more nodes or fewer records.
Constraint-based (CB) learning is a formalism for learning a causal network with a database D by performing a series of conditional-independence tests to infer structural information. This paper considers a new test of independence that combines ideas from Bayesian learning, Bayesian network inference, and classical hypothesis testing to produce a more reliable and robust test. The new test can be calculated in the same asymptotic time and space required for the standard tests such as the chi-squared test, but it allows the specification of a prior distribution over parameters and can be used when the database is incomplete. We prove that the test is correct, and we demonstrate empirically that, when used with a CB causal discovery algorithm with noninformative priors, it recovers structural features more reliably and it produces networks with smaller KL-Divergence, especially as the number of nodes increases or the number of records decreases. Another benefit is the dramatic reduction in the probability that a CB algorithm will stall during the search, providing a remedy for an annoying problem plaguing CB learning when the database is small.