Non-Count Symmetries in Boolean & Multi-Valued Prob. Graphical Models
This work addresses a bottleneck in efficient inference for probabilistic graphical models, particularly for researchers and practitioners in AI and machine learning, by enabling the exploitation of previously missed symmetries, though it is incremental as it builds on existing lifted inference methods.
The paper tackles the limitation of existing lifted inference algorithms in probabilistic graphical models, which only identify count symmetries, by introducing the first algorithms to compute non-count symmetries in both Boolean-valued and multi-valued domains, resulting in substantial computational gains in MCMC experiments.
Lifted inference algorithms commonly exploit symmetries in a probabilistic graphical model (PGM) for efficient inference. However, existing algorithms for Boolean-valued domains can identify only those pairs of states as symmetric, in which the number of ones and zeros match exactly (count symmetries). Moreover, algorithms for lifted inference in multi-valued domains also compute a multi-valued extension of count symmetries only. These algorithms miss many symmetries in a domain. In this paper, we present first algorithms to compute non-count symmetries in both Boolean-valued and multi-valued domains. Our methods can also find symmetries between multi-valued variables that have different domain cardinalities. The key insight in the algorithms is that they change the unit of symmetry computation from a variable to a variable-value (VV) pair. Our experiments find that exploiting these symmetries in MCMC can obtain substantial computational gains over existing algorithms.