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Discovering the causal relationship via recovering the directed acyclic graph(DAG) structure from the observed data is a well-known challengingcombinatorial problem. When there are latent variables, the problem becomeseven more difficult. In this paper, we first propose a DAG structure recoveringalgorithm, which is based on the Cholesky factorization of the covariancematrix of the observed data. The algorithm is fast and easy to implement andhas theoretical grantees for exact recovery. On synthetic and real-worlddatasets, the algorithm is significantly faster than previous methods andachieves the state-of-the-art performance. Furthermore, under the equal errorvariances assumption, we incorporate an optimization procedure into theCholesky factorization based algorithm to handle the DAG recovering problemwith latent variables. Numerical simulations show that the modified "Cholesky +optimization" algorithm is able to recover the ground truth graph in most casesand outperforms existing algorithms.

Recovering Linear Causal Models with Latent Variables via Cholesky Factorization of Covariance Matrix