[ArXiv]

Authors: Sergey Samsonov, Evgeny Lagutin, Marylou Gabrié, Alain Durmus, Alexey Naumov, Eric Moulines.

Abstract: In the present paper we study an Explore-Exploit Markov chain Monte Carlo strategy (Ex2MCMC) that combines local and global samplers showing that it enjoys the advantages of both approaches. We prove V-uniform geometric ergodicity of Ex2MCMC without requiring a uniform adaptation of the global sampler to the target distribution. We also compute explicit bounds on the mixing rate of the Explore-Exploit strategy under realistic conditions. Moreover, we also analyze an adaptive version of the strategy (FlEx2MCMC) where a normalizing flow is trained while sampling to serve as a proposal for global moves. We illustrate the efficiency of Ex2MCMC and its adaptive version on classical sampling benchmarks as well as in sampling high-dimensional distributions defined by Generative Adversarial Networks seen as Energy Based Models.

• Ex2MCMC: Local-Global MCMC kernels: the best of both worlds (NeurIPS 2022) [Paper]
  • Implementation of Ex2MCMC, FlEx2MCMC and experiments
    • Sampling from GAN as Energy-Based Model with MCMC
    • Algorithms
    • Quick start
    • Requirements
    • Installation
    • Checkpoints
    • Usage
      • Experiments with synthetic distributions:
      • Experiments with GANs on MNIST dataset
      • Experiments with GANs on CIFAR10 dataset
      • Sampling and FID computation
    • Results
      • FID and Inception Score (CIFAR10)
      • Energy landscape approximation (MNIST)
      • Sampling trajectories (CIFAR10)
    • Citation

Metrics:

Samples from SNGAN with FlEx2MCMC:

Ex²MCMC:

FlEx²MCMC:

pip install ex2mcmc
pip install git+https://github.com/kwotsin/mimicry.git

• Python >= 3.8
• PyTorch >= 1.8.0
• torchvision
• pyro-ppl
• Jax
• POT

Create environment:

conda create -n ex2mcmc python=3.8
conda activate ex2mcmc

Install poetry (if absent):

curl -sSL https://install.python-poetry.org | python3 -
poetry config virtualenvs.create false

Install the project:

poetry install --with dev
poetry add git+https://github.com/kwotsin/mimicry.git@a7fda06c4aff1e6af8dc4c4a35ed6636e434c766

CIFAR10 checkpoints:

MNIST checkpoints:

You also can run script to download checkpoints:

chmod +x get_ckpts.sh
./get_ckpts.sh

Download statistics for FID cimputation for CIFAR10 dataset:

mkdir -p stats & gdown 1jjgB_iuvmoVAXPRvVTI_hBfuIz7mQgOg -O stats/fid_stats_cifar10.npz

Demonstration on SNGAN:

FlEx²MCMC vs NUTS:

Experiment	Path	Colab
Toyish Gaussian	experiments/exp_synthetic/toyish_gaussian.ipynb	TBD
Ex2MCMC for Mixture of Gaussians	experiments/exp_synthetic/ex2mcmc_mog.ipynb
FlEx2MCMC for Mixture of Gaussians	experiments/exp_synthetic/flex_mog.ipynb
FlEx2MCMC for banana-shaped distribution	experiments/exp_synthetic/flex_banana.ipynb
FlEx2MCMC for Neal's funnel distribution	experiments/exp_synthetic/flex_funnel.ipynb

To reproduce the experimets on banana-shaped and funnel distributions:

python experiments/exp_synthetic/banana_funnel_metrics.py --distribution {banana,funnel} --device cuda:0

experiments/exp_mnist/JSGAN_samples.ipynb TBD

experiments/exp_mnist/WGAN_samples.ipynb

experiments/exp_cifar10_demo/DCGAN_samples.ipynb

experiments/exp_cifar10_demo/SNGAN_samples.ipynb

python experiments/exp_cifar10_fid/run.py configs/mcmc_configs/{ula,mala,isir,ex2mcmc,flex2mcmc}.yml configs/mmc_dcgan.yml

To run a full experiment:

chmod +x experiments/exp_cifar10_fid/run.sh & ./experiments/exp_cifar10_fid/run.sh

Projection of GAN samples onto the energy landsape when trained on MNIST dataset:

Generation trajectories for DCGAN.

• ULA:

• MALA:

• i-SIR:

• Ex²MCMC:

• FlEx²MCMC:

@article{samsonov2022local,
  title={Local-Global MCMC kernels: the best of both worlds},
  author={Samsonov, Sergey and Lagutin, Evgeny and Gabri{\'e}, Marylou and Durmus, Alain and Naumov, Alexey and Moulines, Eric},
  journal={Advances in Neural Information Processing Systems},
  volume={35},
  pages={5178--5193},
  year={2022}
}