Learning Sparse Causal Models is not NP-hard

TL;DR

This paper demonstrates that discovering sparse causal models can be done efficiently with a modified algorithm, challenging the assumption that causal discovery is NP-hard, especially for sparse graphs.

Contribution

It introduces a modified FCI algorithm that efficiently finds causal models for sparse graphs, showing causal discovery is not necessarily NP-hard.

Findings

Causal model discovery for sparse graphs can be achieved in polynomial time.

The modified FCI algorithm is sound and complete for sparse causal graphs.

Sparse causal discovery is less computationally hard than learning minimal Bayesian networks.

Abstract

This paper shows that causal model discovery is not an NP-hard problem, in the sense that for sparse graphs bounded by node degree k the sound and complete causal model can be obtained in worst case order N^{2(k+2)} independence tests, even when latent variables and selection bias may be present. We present a modification of the well-known FCI algorithm that implements the method for an independence oracle, and suggest improvements for sample/real-world data versions. It does not contradict any known hardness results, and does not solve an NP-hard problem: it just proves that sparse causal discovery is perhaps more complicated, but not as hard as learning minimal Bayesian networks.