Lifting Factor Graphs with Some Unknown Factors for New Individuals
This work addresses a specific challenge in probabilistic graphical models for researchers in AI and machine learning, representing an incremental improvement by extending lifting techniques to handle unknown factors.
The paper tackles the problem of performing probabilistic inference in factor graphs with unknown factors by introducing the LIFAGU algorithm, which identifies indistinguishable subgraphs to transfer known potentials to unknown ones, ensuring well-defined semantics and enabling lifted inference.
Lifting exploits symmetries in probabilistic graphical models by using a representative for indistinguishable objects, allowing to carry out query answering more efficiently while maintaining exact answers. In this paper, we investigate how lifting enables us to perform probabilistic inference for factor graphs containing unknown factors, i.e., factors whose underlying function of potential mappings is unknown. We present the Lifting Factor Graphs with Some Unknown Factors (LIFAGU) algorithm to identify indistinguishable subgraphs in a factor graph containing unknown factors, thereby enabling the transfer of known potentials to unknown potentials to ensure a well-defined semantics of the model and allow for (lifted) probabilistic inference. We further extend LIFAGU to incorporate additional background knowledge about groups of factors belonging to the same individual object. By incorporating such background knowledge, LIFAGU is able to further reduce the ambiguity of possible transfers of known potentials to unknown potentials.