Semidefinite tests for latent causal structures
This provides a computationally efficient method for testing latent causal structures, which is a fundamental problem in causal inference for researchers and practitioners.
The paper tackles the problem of testing whether a probability distribution is compatible with a given Bayesian network in causal inference, specifically for models where correlations arise from latent variables, and shows that this can be done efficiently using semidefinite programming, contrasting with more complex algebraic geometric methods.
Testing whether a probability distribution is compatible with a given Bayesian network is a fundamental task in the field of causal inference, where Bayesian networks model causal relations. Here we consider the class of causal structures where all correlations between observed quantities are solely due to the influence from latent variables. We show that each model of this type imposes a certain signature on the observable covariance matrix in terms of a particular decomposition into positive semidefinite components. This signature, and thus the underlying hypothetical latent structure, can be tested in a computationally efficient manner via semidefinite programming. This stands in stark contrast with the algebraic geometric tools required if the full observable probability distribution is taken into account. The semidefinite test is compared with tests based on entropic inequalities.