Better Simulations for Validating Causal Discovery with the DAG-Adaptation of the Onion Method

TL;DR

This paper introduces the DAG-adaptation of the Onion (DaO) simulation method, which generates more realistic linear causal models by focusing on correlation matrices, aiming to standardize and improve validation of causal discovery algorithms.

Contribution

The paper presents a novel simulation design for causal discovery validation that emphasizes correlation matrix distribution, along with methods for sampling DAGs with specific degree distributions.

Findings

DaO produces more realistic causal models.

Compared to existing methods, DaO offers more consistent validation benchmarks.

Provides open-source implementations in Python and R.

Abstract

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.