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
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