A Langevin-like Sampler for Discrete Distributions

Ruqi Zhang, Xingchao Liu, Qiang Liu
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:26375-26396, 2022.

Abstract

We propose discrete Langevin proposal (DLP), a simple and scalable gradient-based proposal for sampling complex high-dimensional discrete distributions. In contrast to Gibbs sampling-based methods, DLP is able to update all coordinates in parallel in a single step and the magnitude of changes is controlled by a stepsize. This allows a cheap and efficient exploration in the space of high-dimensional and strongly correlated variables. We prove the efficiency of DLP by showing that the asymptotic bias of its stationary distribution is zero for log-quadratic distributions, and is small for distributions that are close to being log-quadratic. With DLP, we develop several variants of sampling algorithms, including unadjusted, Metropolis-adjusted, stochastic and preconditioned versions. DLP outperforms many popular alternatives on a wide variety of tasks, including Ising models, restricted Boltzmann machines, deep energy-based models, binary neural networks and language generation.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-zhang22t, title = {A {L}angevin-like Sampler for Discrete Distributions}, author = {Zhang, Ruqi and Liu, Xingchao and Liu, Qiang}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {26375--26396}, year = {2022}, editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan}, volume = {162}, series = {Proceedings of Machine Learning Research}, month = {17--23 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v162/zhang22t/zhang22t.pdf}, url = {https://proceedings.mlr.press/v162/zhang22t.html}, abstract = {We propose discrete Langevin proposal (DLP), a simple and scalable gradient-based proposal for sampling complex high-dimensional discrete distributions. In contrast to Gibbs sampling-based methods, DLP is able to update all coordinates in parallel in a single step and the magnitude of changes is controlled by a stepsize. This allows a cheap and efficient exploration in the space of high-dimensional and strongly correlated variables. We prove the efficiency of DLP by showing that the asymptotic bias of its stationary distribution is zero for log-quadratic distributions, and is small for distributions that are close to being log-quadratic. With DLP, we develop several variants of sampling algorithms, including unadjusted, Metropolis-adjusted, stochastic and preconditioned versions. DLP outperforms many popular alternatives on a wide variety of tasks, including Ising models, restricted Boltzmann machines, deep energy-based models, binary neural networks and language generation.} }
Endnote
%0 Conference Paper %T A Langevin-like Sampler for Discrete Distributions %A Ruqi Zhang %A Xingchao Liu %A Qiang Liu %B Proceedings of the 39th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Kamalika Chaudhuri %E Stefanie Jegelka %E Le Song %E Csaba Szepesvari %E Gang Niu %E Sivan Sabato %F pmlr-v162-zhang22t %I PMLR %P 26375--26396 %U https://proceedings.mlr.press/v162/zhang22t.html %V 162 %X We propose discrete Langevin proposal (DLP), a simple and scalable gradient-based proposal for sampling complex high-dimensional discrete distributions. In contrast to Gibbs sampling-based methods, DLP is able to update all coordinates in parallel in a single step and the magnitude of changes is controlled by a stepsize. This allows a cheap and efficient exploration in the space of high-dimensional and strongly correlated variables. We prove the efficiency of DLP by showing that the asymptotic bias of its stationary distribution is zero for log-quadratic distributions, and is small for distributions that are close to being log-quadratic. With DLP, we develop several variants of sampling algorithms, including unadjusted, Metropolis-adjusted, stochastic and preconditioned versions. DLP outperforms many popular alternatives on a wide variety of tasks, including Ising models, restricted Boltzmann machines, deep energy-based models, binary neural networks and language generation.
APA
Zhang, R., Liu, X. & Liu, Q.. (2022). A Langevin-like Sampler for Discrete Distributions. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:26375-26396 Available from https://proceedings.mlr.press/v162/zhang22t.html.

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