Non-Count Symmetries in Boolean & Multi-Valued Prob. Graphical Models
Ankit Anand, Ritesh Noothigattu, Parag Singla, Mausam
Abstract
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.
BibTeX
@InProceedings{pmlr-v54-anand17a,
title = {{Non-Count Symmetries in Boolean & Multi-Valued Prob. Graphical Models}},
author = {Anand, Ankit and Noothigattu, Ritesh and Singla, Parag and Mausam, },
booktitle = {Proceedings of the 20th International Conference on Artificial Intelligence and Statistics},
pages = {1541--1549},
year = {2017},
editor = {Singh, Aarti and Zhu, Jerry},
volume = {54},
series = {Proceedings of Machine Learning Research},
month = {20--22 Apr},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v54/anand17a/anand17a.pdf},
url = {https://proceedings.mlr.press/v54/anand17a.html},
abstract = {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.}
}