Unbiased and Efficient Sampling of Dependency Trees
This work solves a bias issue in dependency tree sampling for computational linguistics, offering incremental improvements in efficiency and correctness.
The paper addresses the bias in Wilson-RC, a fast algorithm for sampling dependency trees with replacement, by proposing two unbiased alternatives and introducing two more efficient algorithms for sampling without replacement, reducing runtime to O(kn^3).
Most computational models of dependency syntax consist of distributions over spanning trees. However, the majority of dependency treebanks require that every valid dependency tree has a single edge coming out of the ROOT node, a constraint that is not part of the definition of spanning trees. For this reason all standard inference algorithms for spanning trees are suboptimal for inference over dependency trees. Zmigrod et al. (2021b) proposed algorithms for sampling with and without replacement from the dependency tree distribution that incorporate the single-root constraint. In this paper we show that their fastest algorithm for sampling with replacement, Wilson-RC, is in fact producing biased samples and we provide two alternatives that are unbiased. Additionally, we propose two algorithms (one incremental, one parallel) that reduce the asymptotic runtime of algorithm for sampling k trees without replacement to O(kn3). These algorithms are both asymptotically and practically more efficient.