Better Simulations for Validating Causal Discovery with the DAG-Adaptation of the Onion Method
This addresses the problem of inconsistent performance evaluations in causal discovery research, offering a potential universal benchmark, though it is incremental as it builds on existing simulation critiques.
The paper tackles the lack of standardized simulation designs for validating causal discovery algorithms in linear models by proposing the DAG-adaptation of the Onion (DaO) method, which uniformly samples correlation matrices consistent with DAGs and is implemented in Python and R.
The number of artificial intelligence algorithms for learning causal models from data is growing rapidly. Most ``causal discovery'' or ``causal structure learning'' algorithms are primarily validated through simulation studies. However, no widely accepted simulation standards exist and publications often report conflicting performance statistics -- even when only considering publications that simulate data from linear models. In response, several manuscripts have criticized a popular simulation design for validating algorithms in the linear case. We propose a new simulation design for generating linear models for directed acyclic graphs (DAGs): the DAG-adaptation of the Onion (DaO) method. DaO simulations are fundamentally different from existing simulations because they prioritize the distribution of correlation matrices rather than the distribution of linear effects. Specifically, the DaO method uniformly samples the space of all correlation matrices consistent with (i.e. Markov to) a DAG. We also discuss how to sample DAGs and present methods for generating DAGs with scale-free in-degree or out-degree. We compare the DaO method against two alternative simulation designs and provide implementations of the DaO method in Python and R: https://github.com/bja43/DaO_simulation. We advocate for others to adopt DaO simulations as a fair universal benchmark.