Faithfulness and Intervention-Only Causal Discovery

Bijan Mazaheri, Jiaqi Zhang, Caroline Uhler

Keywords: interventions, causal discovery, faithfulness

TL;DR: We provide a milder faithfulness condition for interventions and provide an algorithm that only uses interventions to learn a causal structure.

Abstract: Causal discovery seeks to learn a network describing the causal dependencies between observed variables. Constraint-based causal discovery makes use of conditional independence properties to narrow the space of possible causal networks down to a Markov equivalence class, which consists of adjacency information (e.g., $A$ causes $B$ or $B$ causes $A$, but we might not know the direction). Score-based causal discovery differs algorithmically, but also relies on statistical properties of the observed distribution to determine adjacency. A critical assumption for both approaches is faithfulness --- a requirement that causally linked variables exhibit statistical dependence. Previous works have shown faithfulness to be a strong and restrictive assumption, especially in the finite sample regime. While interventions are usually utilized to orient causal edges, the results of these orientations also contain adjacency-specific information that is generally not utilized. In particular, we show that faithfulness violations can be resolved using interventions. To formalize this notion, we provide a mild assumption that we call intervention-adjacency (IA) faithfulness and build intervention-only causal discovery algorithms that are provably consistent under this assumption. We also specify equivalence classes when the identification criteria are not met due to limitations in the scope of interventions, which may be further resolved via conditional independence testing. Our results provide new insights into the power of online learning and learning by doing.

Submission Number: 12