  The Potential Outcome Framework (POF) plays a prominent role in the field of
causal inference. Most causal inference models based on the POF (CIMs-POF) are
designed for eliminating confounding bias and default to an underlying
assumption of Confounding Covariates. This assumption posits that the
covariates consist solely of confounders. However, the assumption of
Confounding Covariates is challenging to maintain in practice, particularly
when dealing with high-dimensional covariates. While certain methods have been
proposed to differentiate the distinct components of covariates prior to
conducting causal inference, the consequences of treating non-confounding
covariates as confounders remain unclear. This ambiguity poses a potential risk
when conducting causal inference in practical scenarios. In this paper, we
present a unified graphical framework for the CIMs-POF, which greatly enhances
the comprehension of these models' underlying principles. Using this graphical
framework, we quantitatively analyze the extent to which the inference
performance of CIMs-POF is influenced when incorporating various types of
non-confounding covariates, such as instrumental variables, mediators,
colliders, and adjustment variables. The key findings are: in the task of
eliminating confounding bias, the optimal scenario is for the covariates to
exclusively encompass confounders; in the subsequent task of inferring
counterfactual outcomes, the adjustment variables contribute to more accurate
inferences. Furthermore, extensive experiments conducted on synthetic datasets
consistently validate these theoretical conclusions.
