Uncertain Priors for Graphical Causal Models: A Multi-Objective Optimization Perspective

Learning graphical causal models from observational data can effectively elucidate the underlying causal mechanism behind the variables. In the context of limited datasets, modelers often incorporate prior knowledge, which is assumed to be correct, as a penalty in single-objective optimization. However, this approach struggles to adapt complex and uncertain priors effectively. This paper introduces UpCM, which tackles the issue from a multi-objective optimization perspective. Instead of focusing exclusively on the DAG as the optimization goal, UpCM methodically evaluate the effect of uncertain priors on specific structures, merging data-driven and knowledge-driven objectives. Utilizing the MOEA/D framework, it achieve a balanced trade-off between these objectives. Furthermore, since uncertain priors may introduce erroneous constraints, resulting in PDAGs lacking consistent extensions, the minimal non-consistent extension is explored. This extension, which separately incorporates positive and negative constraints, aims to approximate the true causality of the PDAGs. Experimental results demonstrate that UpCM achieves significant structural accuracy improvements compared to baseline methods. It reduces the SHD by 7.94%, 13.23%, and 12.8% relative to PC_stable, GES, and MAHC, respectively, when incorporating uncertain priors. In downstream inference tasks, UpCM outperforms domain-expert knowledge graphs, owing to its ability to learn explainable causal relationships that balance data-driven evidence with prior knowledge.