# Ex2MCMC: Local-Global MCMC kernels: the bost of both worlds (NeurIPS 2022) [[Paper]](https://proceedings.neurips.cc/paper_files/paper/2022/hash/21c86d5b10cdc28664ccdadf0a29065a-Abstract-Conference.html)
[[ArXiv]](https://arxiv.org/abs/2111.02702)
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.*
>
<!-- This repository contains Python code to reproduce experiments from [**Local-Global MCMC kernels: the bost of both worlds**](https://proceedings.neurips.cc/paper_files/paper/2022/hash/21c86d5b10cdc28664ccdadf0a29065a-Abstract-Conference.html) (NeurIPS'22). -->
- [Ex2MCMC: Local-Global MCMC kernels: the bost of both worlds (NeurIPS 2022) \[Paper\]](#ex2mcmc-local-global-mcmc-kernels-the-bost-of-both-worlds-neurips-2022-paper)
- [Single chain mixing](#single-chain-mixing)
- [Sampling from GAN as Energy-Based Models with MCMC](#sampling-from-gan-as-energy-based-models-with-mcmc)
- [Algorithms](#algorithms)
- [Installation](#installation)
- [Usage](#usage)
- [Demonstration on SNGAN](#demonstration-on-sngan)
- [Experiments with synthetic distributions:](#experiments-with-synthetic-distributions)
- [Experiments with GANs on MNIST dataset](#experiments-with-gans-on-mnist-dataset)
- [Experiments with GANs on CIFAR10 dataset](#experiments-with-gans-on-cifar10-dataset)
- [Sampling and FID computation](#sampling-and-fid-computation)
- [Results](#results)
- [FID and Inception Score (CIFAR10)](#fid-and-inception-score-cifar10)
- [Sampling trajectories (CIFAR10)](#sampling-trajectories-cifar10)
- [Energy landscape approximation (MNIST)](#energy-landscape-approximation-mnist)
- [Citation](#citation)
## Single chain mixing
<img src="./imgs/gaussian_mixture.png" alt="i-SIR" width="900"/>
## Sampling from GAN as Energy-Based Models with MCMC
<img src="./imgs/fid_flex.png" alt="FID" width="385"/> <img src="./imgs/is_flex.png" alt="Inception Score" width="400"/>
<!-- <img src="./imgs/energy_flex.png" alt="Energy" width="270"/> -->
## Algorithms
<!-- **i-SIR:**
<img src="./algs/isir.png" alt="i-SIR" width="600"/> -->
**Ex<sup>2</sup>MCMC:**
<img src="./imgs/ex2.png" alt="Ex<sup>2</sup>MCMC" width="600"/>
**FlEx<sup>2</sup>MCMC:**
<img src="./imgs/flex.png" alt="FlEx<sup>2</sup>MCMC" width="600"/>
## Installation
Create environment:
```bash
conda create -n ex2mcmc python=3.8
conda activate ex2mcmc
```
Install poetry (if absent):
```bash
curl -sSL https://install.python-poetry.org | python3 -
poetry config virtualenvs.create false
```
Install the project:
```bash
poetry install
```
Download checkpoints:
CIFAR10:
| GAN | Steps | Path, G | Path, D |
|:----------|:-------------:|:------:|:------:|
| DCGAN NS | 100k | [netG_100000_steps.pth](https://drive.google.com/file/d/1gv8_qr_xa8hJzdJpBXiKr8v922EqcE-E/view?usp=share_link) | [netD_100000_steps.pth](https://drive.google.com/file/d/1u1sPUmlvyhcbNDX2DVsR-mGOzqQ6U8sh/view?usp=share_link) |
| SNGAN, Hinge | 100k | [netG.pth](https://drive.google.com/file/d/118zC_iEkN27jGLVNmDuQpMeyw7BKOUra/view?usp=share_link) | [netD.pth](https://drive.google.com/file/d/1xU5FV59TLhAlkFubJGmJVS87HnZZ2xHT/view?usp=share_link) |
MNIST:
| GAN | Path |
|:----------|:-------------:|
| Vanilla | [vanilla_gan.pth](https://drive.google.com/file/d/1xa1v4hPQQdU2RkhjMn5sFZCITxTJ5Dhj/view?usp=share_link) |
| WGAN CP | [wgan.pth](https://drive.google.com/file/d/17nQJnfs2_T6kyahnkW3fu8AVY54kmRmw/view?usp=share_link) |
You also can run script to download checkpoints:
```bash
chmod +x get_ckpts.sh
./get_ckpts.sh
```
Download statistics for FID cimputation for CIFAR10 dataset:
```bash
mkdir -p stats & gdown 1jjgB_iuvmoVAXPRvVTI_hBfuIz7mQgOg -O stats/fid_stats_cifar10.npz
```
<!-- | WGAN GP | -- | [TBD]() | [TBD]() | -->
## Usage
### Demonstration on SNGAN
Try with colab: [](https://colab.research.google.com/drive/1EQQ_OdwCLn5MsOzlG-GS7yNcjTBU-KMp?usp=sharing)
### Experiments with synthetic distributions:
FlEx<sup>2</sup>MCMC vs NUTS:
<img src="./imgs/flex_mog.png" alt="FlEx<sup>2</sup>MCMC" width="600"/> <img src="./imgs/nuts_mog.png" alt="NUTS" width="425"/>
| Experiment | Path | Colab |
|:----------|:-------|:-----:|
| Toyish Gaussian | ```experiments/exp_synthetic/toyish_gaussian.ipynb``` | [TBD]() |
| Gaussian mixture | ```experiments/exp_synthetic/gaussian_mixture.ipynb``` | [](https://colab.research.google.com/drive/1xmBOZr1YhN8E7Y8GuwjgdM7hqaCgE6ik?usp=sharing) |
| FlEx for banana-shaped distribution | ```experiments/exp_synthetic/flex_banana.ipynb``` | []() |
| FlEx for Neal's funnel distribution | ```experiments/exp_synthetic/flex_funnel.ipynb``` | []() |
To reproduce the experimets on banana-shaped and funnel distributions:
```bash
python experiments/exp_synthetic/banana_funnel_metrics.py --distribution {banana,funnel} --device cuda:0
```
### Experiments with GANs on MNIST dataset
```experiments/exp_mnist/JSGAN_samples.ipynb``` []()
```experiments/exp_mnist/WGAN_samples.ipynb``` []()
### Experiments with GANs on CIFAR10 dataset
```experiments/exp_cifar10_demo/DCGAN_samples.ipynb```
<!-- []() -->
```experiments/exp_cifar10_demo/SNGAN_samples.ipynb```
<!-- []() -->
### Sampling and FID computation
```bash
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:
```bash
chmod +x experiments/exp_cifar10_fid/run.sh & ./experiments/exp_cifar10_fid/run.sh
```
## Results
### FID and Inception Score (CIFAR10)
| GAN | MCMC | Steps | Inception Score | FID |
|:----|:-----|:------:|:---------------:|:----:|
|DCGAN| none | 0 | 6.3 | 28.4 |
|DCGAN| i-SIR | 1k | 6.96 | 22.7 |
|DCGAN| MALA | 1k | 6.95 | 23.4 |
|DCGAN| Ex<sup>2</sup>MCMC (our) | 1k | <ins>7.56<ins> | <ins>19.0<ins> |
|DCGAN| FlEx<sup>2</sup>MCMC (our) | 1k | **7.92** | 19.2 |
|DCGAN| FlEx<sup>2</sup>MCMC (our) | 180 | 7.62 | **17.1** |
### Sampling trajectories (CIFAR10)
Generation trajectories for DCGAN.
<!-- , top to bottom: ULA, MALA, i-SIR, Ex<sup>2</sup>MCMC, FlEx<sup>2</sup>MCMC: -->
<!-- <img src="./imgs/cifar10_dcgan_gen.png" alt="CIFAR10 generations" width="600"/> -->
* ULA:
<img src="./imgs/mmc_dcgan_ula.png" alt="CIFAR10 generations with ULA" width="600"/>
* MALA:
<img src="./imgs/mmc_dcgan_mala.png" alt="CIFAR10 generations with MALA" width="600"/>
* i-SIR:
<img src="./imgs/mmc_dcgan_isir.png" alt="CIFAR10 generations with i-SIR" width="600"/>
* Ex<sup>2</sup>MCMC:
<img src="./imgs/mmc_dcgan_ex2mcmc.png" alt="CIFAR10 generations with Ex2MCMC" width="600"/>
* FlEx<sup>2</sup>MCMC:
<img src="./imgs/mmc_dcgan_flex2mcmc.png" alt="CIFAR10 generations with FlEx2MCMC" width="600"/>
### Energy landscape approximation (MNIST)
Projection of GAN samples onto the energy landsape when trained on MNIST dataset:
<img src="./imgs/energy_landscape.png" alt="energy landscape" width="600"/>
## Citation
```bibtex
@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}
}
```
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"description": "# Ex2MCMC: Local-Global MCMC kernels: the bost of both worlds (NeurIPS 2022) [[Paper]](https://proceedings.neurips.cc/paper_files/paper/2022/hash/21c86d5b10cdc28664ccdadf0a29065a-Abstract-Conference.html)\n\n[[ArXiv]](https://arxiv.org/abs/2111.02702)\n\nAuthors: Sergey Samsonov, Evgeny Lagutin, Marylou Gabri\u00e9, Alain Durmus, Alexey Naumov, Eric Moulines.\n\n> **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.*\n> \n<!-- This repository contains Python code to reproduce experiments from [**Local-Global MCMC kernels: the bost of both worlds**](https://proceedings.neurips.cc/paper_files/paper/2022/hash/21c86d5b10cdc28664ccdadf0a29065a-Abstract-Conference.html) (NeurIPS'22). -->\n\n\n- [Ex2MCMC: Local-Global MCMC kernels: the bost of both worlds (NeurIPS 2022) \\[Paper\\]](#ex2mcmc-local-global-mcmc-kernels-the-bost-of-both-worlds-neurips-2022-paper)\n - [Single chain mixing](#single-chain-mixing)\n - [Sampling from GAN as Energy-Based Models with MCMC](#sampling-from-gan-as-energy-based-models-with-mcmc)\n - [Algorithms](#algorithms)\n - [Installation](#installation)\n - [Usage](#usage)\n - [Demonstration on SNGAN](#demonstration-on-sngan)\n - [Experiments with synthetic distributions:](#experiments-with-synthetic-distributions)\n - [Experiments with GANs on MNIST dataset](#experiments-with-gans-on-mnist-dataset)\n - [Experiments with GANs on CIFAR10 dataset](#experiments-with-gans-on-cifar10-dataset)\n - [Sampling and FID computation](#sampling-and-fid-computation)\n - [Results](#results)\n - [FID and Inception Score (CIFAR10)](#fid-and-inception-score-cifar10)\n - [Sampling trajectories (CIFAR10)](#sampling-trajectories-cifar10)\n - [Energy landscape approximation (MNIST)](#energy-landscape-approximation-mnist)\n - [Citation](#citation)\n\n## Single chain mixing\n\n<img src=\"./imgs/gaussian_mixture.png\" alt=\"i-SIR\" width=\"900\"/>\n\n## Sampling from GAN as Energy-Based Models with MCMC\n\n\n<img src=\"./imgs/fid_flex.png\" alt=\"FID\" width=\"385\"/> <img src=\"./imgs/is_flex.png\" alt=\"Inception Score\" width=\"400\"/> \n<!-- <img src=\"./imgs/energy_flex.png\" alt=\"Energy\" width=\"270\"/> -->\n\n\n## Algorithms \n<!-- **i-SIR:**\n\n<img src=\"./algs/isir.png\" alt=\"i-SIR\" width=\"600\"/> -->\n\n**Ex<sup>2</sup>MCMC:**\n\n<img src=\"./imgs/ex2.png\" alt=\"Ex<sup>2</sup>MCMC\" width=\"600\"/>\n\n**FlEx<sup>2</sup>MCMC:**\n\n<img src=\"./imgs/flex.png\" alt=\"FlEx<sup>2</sup>MCMC\" width=\"600\"/>\n\n## Installation\n\nCreate environment:\n\n```bash\nconda create -n ex2mcmc python=3.8\nconda activate ex2mcmc\n```\n\nInstall poetry (if absent):\n```bash\ncurl -sSL https://install.python-poetry.org | python3 -\npoetry config virtualenvs.create false\n```\n\nInstall the project:\n```bash\npoetry install\n```\n\nDownload checkpoints:\n\nCIFAR10:\n\n| GAN | Steps | Path, G | Path, D |\n|:----------|:-------------:|:------:|:------:|\n| DCGAN NS | 100k | [netG_100000_steps.pth](https://drive.google.com/file/d/1gv8_qr_xa8hJzdJpBXiKr8v922EqcE-E/view?usp=share_link) | [netD_100000_steps.pth](https://drive.google.com/file/d/1u1sPUmlvyhcbNDX2DVsR-mGOzqQ6U8sh/view?usp=share_link) |\n| SNGAN, Hinge | 100k | [netG.pth](https://drive.google.com/file/d/118zC_iEkN27jGLVNmDuQpMeyw7BKOUra/view?usp=share_link) | [netD.pth](https://drive.google.com/file/d/1xU5FV59TLhAlkFubJGmJVS87HnZZ2xHT/view?usp=share_link) |\n\nMNIST:\n\n| GAN | Path |\n|:----------|:-------------:|\n| Vanilla | [vanilla_gan.pth](https://drive.google.com/file/d/1xa1v4hPQQdU2RkhjMn5sFZCITxTJ5Dhj/view?usp=share_link) |\n| WGAN CP | [wgan.pth](https://drive.google.com/file/d/17nQJnfs2_T6kyahnkW3fu8AVY54kmRmw/view?usp=share_link) |\n\nYou also can run script to download checkpoints:\n\n```bash\nchmod +x get_ckpts.sh\n./get_ckpts.sh\n```\n\nDownload statistics for FID cimputation for CIFAR10 dataset:\n\n```bash\nmkdir -p stats & gdown 1jjgB_iuvmoVAXPRvVTI_hBfuIz7mQgOg -O stats/fid_stats_cifar10.npz\n```\n\n<!-- | WGAN GP | -- | [TBD]() | [TBD]() | -->\n\n## Usage\n\n### Demonstration on SNGAN\n\nTry with colab: [](https://colab.research.google.com/drive/1EQQ_OdwCLn5MsOzlG-GS7yNcjTBU-KMp?usp=sharing)\n\n ### Experiments with synthetic distributions:\n\nFlEx<sup>2</sup>MCMC vs NUTS:\n\n<img src=\"./imgs/flex_mog.png\" alt=\"FlEx<sup>2</sup>MCMC\" width=\"600\"/> <img src=\"./imgs/nuts_mog.png\" alt=\"NUTS\" width=\"425\"/>\n\n \n| Experiment | Path | Colab |\n|:----------|:-------|:-----:|\n| Toyish Gaussian | ```experiments/exp_synthetic/toyish_gaussian.ipynb``` | [TBD]() |\n| Gaussian mixture | ```experiments/exp_synthetic/gaussian_mixture.ipynb``` | [](https://colab.research.google.com/drive/1xmBOZr1YhN8E7Y8GuwjgdM7hqaCgE6ik?usp=sharing) |\n| FlEx for banana-shaped distribution | ```experiments/exp_synthetic/flex_banana.ipynb``` | []() |\n| FlEx for Neal's funnel distribution | ```experiments/exp_synthetic/flex_funnel.ipynb``` | []() |\n\nTo reproduce the experimets on banana-shaped and funnel distributions:\n\n```bash\npython experiments/exp_synthetic/banana_funnel_metrics.py --distribution {banana,funnel} --device cuda:0\n```\n\n ### Experiments with GANs on MNIST dataset\n \n ```experiments/exp_mnist/JSGAN_samples.ipynb``` []()\n\n ```experiments/exp_mnist/WGAN_samples.ipynb``` []()\n\n ### Experiments with GANs on CIFAR10 dataset\n\n```experiments/exp_cifar10_demo/DCGAN_samples.ipynb``` \n\n<!-- []() -->\n\n```experiments/exp_cifar10_demo/SNGAN_samples.ipynb``` \n\n<!-- []() -->\n\n### Sampling and FID computation\n\n```bash\npython experiments/exp_cifar10_fid/run.py configs/mcmc_configs/{ula,mala,isir,ex2mcmc,flex2mcmc}.yml configs/mmc_dcgan.yml\n```\n\nTo run a full experiment:\n\n```bash\nchmod +x experiments/exp_cifar10_fid/run.sh & ./experiments/exp_cifar10_fid/run.sh\n```\n\n## Results\n\n### FID and Inception Score (CIFAR10)\n| GAN | MCMC | Steps | Inception Score | FID |\n|:----|:-----|:------:|:---------------:|:----:|\n|DCGAN| none | 0 | 6.3 | 28.4 |\n|DCGAN| i-SIR | 1k | 6.96 | 22.7 |\n|DCGAN| MALA | 1k | 6.95 | 23.4 |\n|DCGAN| Ex<sup>2</sup>MCMC (our) | 1k | <ins>7.56<ins> | <ins>19.0<ins> |\n|DCGAN| FlEx<sup>2</sup>MCMC (our) | 1k | **7.92** | 19.2 |\n|DCGAN| FlEx<sup>2</sup>MCMC (our) | 180 | 7.62 | **17.1** |\n\n\n### Sampling trajectories (CIFAR10)\nGeneration trajectories for DCGAN.\n\n<!-- , top to bottom: ULA, MALA, i-SIR, Ex<sup>2</sup>MCMC, FlEx<sup>2</sup>MCMC: -->\n\n<!-- <img src=\"./imgs/cifar10_dcgan_gen.png\" alt=\"CIFAR10 generations\" width=\"600\"/> -->\n\n* ULA:\n\n<img src=\"./imgs/mmc_dcgan_ula.png\" alt=\"CIFAR10 generations with ULA\" width=\"600\"/> \n\n* MALA:\n\n<img src=\"./imgs/mmc_dcgan_mala.png\" alt=\"CIFAR10 generations with MALA\" width=\"600\"/> \n\n* i-SIR:\n\n<img src=\"./imgs/mmc_dcgan_isir.png\" alt=\"CIFAR10 generations with i-SIR\" width=\"600\"/> \n\n* Ex<sup>2</sup>MCMC:\n\n<img src=\"./imgs/mmc_dcgan_ex2mcmc.png\" alt=\"CIFAR10 generations with Ex2MCMC\" width=\"600\"/> \n\n* FlEx<sup>2</sup>MCMC:\n\n<img src=\"./imgs/mmc_dcgan_flex2mcmc.png\" alt=\"CIFAR10 generations with FlEx2MCMC\" width=\"600\"/> \n\n### Energy landscape approximation (MNIST)\n\nProjection of GAN samples onto the energy landsape when trained on MNIST dataset:\n\n<img src=\"./imgs/energy_landscape.png\" alt=\"energy landscape\" width=\"600\"/> \n\n## Citation\n\n```bibtex\n@article{samsonov2022local,\n title={Local-Global MCMC kernels: the best of both worlds},\n author={Samsonov, Sergey and Lagutin, Evgeny and Gabri{\\'e}, Marylou and Durmus, Alain and Naumov, Alexey and Moulines, Eric},\n journal={Advances in Neural Information Processing Systems},\n volume={35},\n pages={5178--5193},\n year={2022}\n}\n```\n\n\n\n\n",
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