Estimating possible causal effects with latent variables via adjustment and novel rule orientation

Causal effect estimation from observational data is a fundamental task in artificial intelligence and has been widely studied given known causal relations. However, in the presence of latent confounders, only a part of causal relations can be identified from observational data, characterized by a partial ancestral graph (PAG), where some causal relations are indeterminate. In such cases, the causal effect is often unidentifiable, as there could be super-exponential number of potential causal graphs consistent with the identified PAG but associated with different causal effects. In this paper, we target on set determination within a PAG, i.e., determining the set of possible causal effects of a specified variable X on another variable Y via covariate adjustment. We develop the first set determination method that does not require enumerating any causal graphs. Furthermore, we present two novel orientation rules for incorporating structural background knowledge (BK) into a PAG, which facilitate the identification of additional causal relations given BK. Notably, we show that these rules can further enhance the efficiency of our set determination method, as certain transformed edges during the procedure can be interpreted as BK and enable the rules to reveal further causal information. Theoretically and empirically, we demonstrate that our set determination methods can yield the same results as the enumeration-based method with super-exponentially less computational complexity.