Stochastic Beams and Where To Find Them: The Gumbel-Top-k Trick for Sampling Sequences Without Replacement
Wouter Kool, Herke Van Hoof, Max Welling
Abstract
The well-known Gumbel-Max trick for sampling from a categorical distribution can be extended to sample $k$ elements without replacement. We show how to implicitly apply this ’Gumbel-Top-$k$’ trick on a factorized distribution over sequences, allowing to draw exact samples without replacement using a Stochastic Beam Search. Even for exponentially large domains, the number of model evaluations grows only linear in $k$ and the maximum sampled sequence length. The algorithm creates a theoretical connection between sampling and (deterministic) beam search and can be used as a principled intermediate alternative. In a translation task, the proposed method compares favourably against alternatives to obtain diverse yet good quality translations. We show that sequences sampled without replacement can be used to construct low-variance estimators for expected sentence-level BLEU score and model entropy.
BibTeX
@InProceedings{pmlr-v97-kool19a,
title = {Stochastic Beams and Where To Find Them: The {G}umbel-Top-k Trick for Sampling Sequences Without Replacement},
author = {Kool, Wouter and Van Hoof, Herke and Welling, Max},
booktitle = {Proceedings of the 36th International Conference on Machine Learning},
pages = {3499--3508},
year = {2019},
editor = {Chaudhuri, Kamalika and Salakhutdinov, Ruslan},
volume = {97},
series = {Proceedings of Machine Learning Research},
month = {09--15 Jun},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v97/kool19a/kool19a.pdf},
url = {https://proceedings.mlr.press/v97/kool19a.html},
abstract = {The well-known Gumbel-Max trick for sampling from a categorical distribution can be extended to sample $k$ elements without replacement. We show how to implicitly apply this ’Gumbel-Top-$k$’ trick on a factorized distribution over sequences, allowing to draw exact samples without replacement using a Stochastic Beam Search. Even for exponentially large domains, the number of model evaluations grows only linear in $k$ and the maximum sampled sequence length. The algorithm creates a theoretical connection between sampling and (deterministic) beam search and can be used as a principled intermediate alternative. In a translation task, the proposed method compares favourably against alternatives to obtain diverse yet good quality translations. We show that sequences sampled without replacement can be used to construct low-variance estimators for expected sentence-level BLEU score and model entropy.}
}