# Efficient Sampling of Dependency Structures

arXiv: https://arxiv.org/abs/2109.06521 · HTML: https://mlsanity.com/paper/2109.06521/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 43 references that are in the map.
- First posted on arXiv 14 Sep 2021.

## Builds on (most cited first, 7 of 7)

- [Deep Biaffine Attention for Neural Dependency Parsing](https://mlsanity.com/paper/1611.01734/) (2016)
- [MaskGAN: Better Text Generation via Filling in the______](https://mlsanity.com/paper/1801.07736/) (2018)
- [Incremental Sampling Without Replacement for Sequence Models](https://mlsanity.com/paper/2002.09067/) (2020)
- [Efficient Computation of Expectations under Spanning Tree Distributions](https://mlsanity.com/paper/2008.12988/) (2020)
- [Please Mind the Root: Decoding Arborescences for Dependency Parsing](https://mlsanity.com/paper/2010.02550/) (2020)
- [Neural Probabilistic Model for Non-projective MST Parsing](https://mlsanity.com/paper/1701.00874/) (2017)
- [Monte Carlo Syntax Marginals for Exploring and Using Dependency Parses](https://mlsanity.com/paper/1804.06004/) (2018)

## Abstract (arXiv)

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(N3), 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 N3 + K2 N) time. To the best of our knowledge, no algorithm has been given for sampling spanning trees without replacement from a directed graph.