Table 1.

Comparison of the fundamental causal discovery methods reviewed in this paper.

	PC	FCI	GES	LiNGAM/PNL/ANM
Faithfulness assumption required?	Yes	Yes	Some weaker condition required (not totally clear yet)	No
Specific assumptions on data distributions required?	No	No	Yes (usually assumes linear-Gaussian models or multinomial distributions)	Yes
Properly handle confounders?	No	Yes	No	No
Output	Markov equivalence class	Partial ancestral graph	Markov equivalence class	DAG as well as causal model (under the respective identifiability conditions)
Remark on practical issues	Confounder in the linear, non-Gaussian case Hoyer et al. (2008); feedback in linear cases Lacerda et al. (2008); Sanchez-Romero et al. (2019); measurement error Zhang et al. (2017a); non-stationary times series or heterogeneous multiple data sets Huang et al. (2017); Zhang et al. (2017b); missing data Tu et al. (2019); subsampled or aggregated time series Danks and Plis (2013); Gong* et al. (2015); Gong et al. (2017), etc.