This paper aims to improve Advanced Color Passing (ACP), a state-of-the-art algorithm that compresses propositional factorization models for efficient lifted inference in probabilistic graphical models representing indistinguishable objects and their relationships. ACP groups factors with similar distributions. An approximate version uses the hyperparameter ε to group factors that differ by less than $(1\pm ε)$. However, finding an appropriate ε value is difficult and requires extensive trial and error, and the model varies significantly depending on the ε value, reducing interpretability. Therefore, this paper presents a hierarchical approach without a hyperparameter. This method efficiently computes a hierarchy of ε values to create a model hierarchy. That is, factors grouped at a specific ε value continue to be grouped at higher ε values. This hierarchy of ε values is then followed by a hierarchy of error bounds. The ε value for ACP is selected based on a balance between compression and accuracy, thereby improving interpretability across different models.
