Continuous Bayesian Model Selection for Multivariate Causal Discovery
This addresses the challenge of poor performance in real-world causal discovery for researchers and practitioners, though it is incremental as it extends a bivariate approach to the multivariate case.
The paper tackles the problem of multivariate causal discovery by proposing a scalable Bayesian model selection algorithm that relaxes restrictive assumptions, showing it is competitive without requiring infeasible conditions.
Current causal discovery approaches require restrictive model assumptions in the absence of interventional data to ensure structure identifiability. These assumptions often do not hold in real-world applications leading to a loss of guarantees and poor performance in practice. Recent work has shown that, in the bivariate case, Bayesian model selection can greatly improve performance by exchanging restrictive modelling for more flexible assumptions, at the cost of a small probability of making an error. Our work shows that this approach is useful in the important multivariate case as well. We propose a scalable algorithm leveraging a continuous relaxation of the discrete model selection problem. Specifically, we employ the Causal Gaussian Process Conditional Density Estimator (CGP-CDE) as a Bayesian non-parametric model, using its hyperparameters to construct an adjacency matrix. This matrix is then optimised using the marginal likelihood and an acyclicity regulariser, giving the maximum a posteriori causal graph. We demonstrate the competitiveness of our approach, showing it is advantageous to perform multivariate causal discovery without infeasible assumptions using Bayesian model selection.