Dynamic Programming in Rank Space: Scaling Structured Inference with Low-Rank HMMs and PCFGs

Songlin Yang, Wei Liu, Kewei Tu


Abstract
Hidden Markov Models (HMMs) and Probabilistic Context-Free Grammars (PCFGs) are widely used structured models, both of which can be represented as factor graph grammars (FGGs), a powerful formalism capable of describing a wide range of models. Recent research found it beneficial to use large state spaces for HMMs and PCFGs. However, inference with large state spaces is computationally demanding, especially for PCFGs. To tackle this challenge, we leverage tensor rank decomposition (aka. CPD) to decrease inference computational complexities for a subset of FGGs subsuming HMMs and PCFGs. We apply CPD on the factors of an FGG and then construct a new FGG defined in the rank space. Inference with the new FGG produces the same result but has a lower time complexity when the rank size is smaller than the state size. We conduct experiments on HMM language modeling and unsupervised PCFG parsing, showing better performance than previous work. Our code is publicly available at https://github.com/VPeterV/RankSpace-Models.
Anthology ID:
2022.naacl-main.353
Volume:
Proceedings of the 2022 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies
Month:
July
Year:
2022
Address:
Seattle, United States
Venue:
NAACL
SIG:
Publisher:
Association for Computational Linguistics
Note:
Pages:
4797–4809
Language:
URL:
https://aclanthology.org/2022.naacl-main.353
DOI:
10.18653/v1/2022.naacl-main.353
Bibkey:
Cite (ACL):
Songlin Yang, Wei Liu, and Kewei Tu. 2022. Dynamic Programming in Rank Space: Scaling Structured Inference with Low-Rank HMMs and PCFGs. In Proceedings of the 2022 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, pages 4797–4809, Seattle, United States. Association for Computational Linguistics.
Cite (Informal):
Dynamic Programming in Rank Space: Scaling Structured Inference with Low-Rank HMMs and PCFGs (Yang et al., NAACL 2022)
Copy Citation:
PDF:
https://aclanthology.org/2022.naacl-main.353.pdf
Code
 sustcsonglin/TN-PCFG +  additional community code
Data
Penn Treebank