Efficient Sampling of Dependency Structure

Ran Zmigrod, Tim Vieira, Ryan Cotterell


Abstract
Probabilistic distributions over spanning trees in directed graphs are a fundamental model of dependency structure in natural language processing, syntactic dependency trees. In NLP, dependency trees often have an additional root constraint: only one edge may emanate from the root. However, no sampling algorithm has been presented in the literature to account for this additional constraint. In this paper, we adapt two spanning tree sampling algorithms to faithfully sample dependency trees from a graph subject to the root constraint. Wilson (1996(’s sampling algorithm has a running time of O(H) where H is the mean hitting time of the graph. Colbourn (1996)’s sampling algorithm has a running time of O(Nˆ3), which is often greater than the mean hitting time of a directed graph. Additionally, we build upon Colbourn’s algorithm and present a novel extension that can sample K trees without replacement in O(K Nˆ3 + Kˆ2 N) time. To the best of our knowledge, no algorithm has been given for sampling spanning trees without replacement from a directed graph.
Anthology ID:
2021.emnlp-main.824
Original:
2021.emnlp-main.824v1
Version 2:
2021.emnlp-main.824v2
Volume:
Proceedings of the 2021 Conference on Empirical Methods in Natural Language Processing
Month:
November
Year:
2021
Address:
Online and Punta Cana, Dominican Republic
Venue:
EMNLP
SIG:
Publisher:
Association for Computational Linguistics
Note:
Pages:
10558–10569
Language:
URL:
https://aclanthology.org/2021.emnlp-main.824
DOI:
10.18653/v1/2021.emnlp-main.824
Bibkey:
Cite (ACL):
Ran Zmigrod, Tim Vieira, and Ryan Cotterell. 2021. Efficient Sampling of Dependency Structure. In Proceedings of the 2021 Conference on Empirical Methods in Natural Language Processing, pages 10558–10569, Online and Punta Cana, Dominican Republic. Association for Computational Linguistics.
Cite (Informal):
Efficient Sampling of Dependency Structure (Zmigrod et al., EMNLP 2021)
Copy Citation:
PDF:
https://aclanthology.org/2021.emnlp-main.824.pdf
Video:
 https://aclanthology.org/2021.emnlp-main.824.mp4
Code
 rycolab/treesample