A Langevin-like Sampler for Discrete Distributions

This repository contains code for the paper A Langevin-like Sampler for Discrete Distributions, accepted in International Conference on Machine Learning (ICML), 2022.

@article{zhang2022langevinlike,
  title={A Langevin-like Sampler for Discrete Distributions},
  author={Zhang, Ruqi and Liu, Xingchao and Liu, Qiang},
  journal={International Conference on Machine Learning},
  year={2022}
}

Introduction

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 the 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.

Dependencies

• PyTorch 1.9.1
• torchvision 0.10.1

Usage

Sampling From Ising Models

Please run

python ising_sample.py

Sampling From Restricted Boltzmann Machines

Please run

python rbm_sample.py

Learning Ising Models

Run bash generate_data.sh to generate the data, then learn the Ising model by running

python pcd.py --sampler=<SAMPLER>

• SAMPLER — Specify which sampler to use.
  dmala: discrete Metropolis-adjusted Langevin algorithm;
  dula: discrete unadjusted Langevin algorithm

Use plt_pcd to plot the results of log RMSE with respect to the number of iterations and the runtime.

Learning Deep EBMs

The datasets can be found here.

To learn the EBM, run bash ebm.sh and to evaluate the learned EBM using AIS, run ais.sh.

Binary Bayesian Neural Networks

See

./BinaryBNN

A Toy Example For Categorical Sampling

See

./CategoricalExample

References

• This repo is built upon the GWG repo