In this paper, we consider the problem of estimating all possible causal effects from observational data with two types of background knowledge: direct causal information and non-ancestral information. Following the IDA framework, we first provide locally valid orientation rules for maximal partially directed acyclic graphs (PDAGs), which are widely used to represent background knowledge. Based on the proposed rules, we present a fully local algorithm to estimate all possible causal effects with direct causal information. Furthermore, we consider non-ancestral information and prove that it can be equivalently transformed into direct causal information, meaning that we can also locally estimate all possible causal effects with non-ancestral information. The test results on both synthetic and real-world data sets show that our methods are efficient and stable.
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