Neural Causal Models under Markov Equivalence

Neural causal models can simulate interventions in complex, high-dimensional settings, but typically require a known causal graph. Observational data, however, generally identifies only a Markov equivalence class of graphs, represented by a CPDAG, and causal queries may vary across DAGs in that class. We introduce \textit{Masked Neural Causal Models }(NCMs), a provably expressive nonparametric framework for simulating and bounding interventional queries over all models compatible with a given CPDAG given observational data. We give an optimization objective in the space of Masked NCMs that asymptotically recovers the true bounds of the causal effect. To enable this optimization in practice, we introduce an attention-based architecture and a novel optimization strategy that recovers highly accurate bounds in discrete nonparametric settings.