https://github.com/gaurav-arya/differentiable_mh

Code for paper https://arxiv.org/abs/2306.07961
https://github.com/gaurav-arya/differentiable_mh

Last synced: 27 days ago
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Code for paper https://arxiv.org/abs/2306.07961

• Host: GitHub
• URL: https://github.com/gaurav-arya/differentiable_mh
• Owner: gaurav-arya
• Created: 2023-06-13T02:24:03.000Z (about 1 year ago)
• Default Branch: main
• Last Pushed: 2023-11-14T20:07:10.000Z (8 months ago)
• Last Synced: 2024-02-18T21:39:43.679Z (4 months ago)
• Language: Julia
• Homepage:
• Size: 1.01 MB
• Stars: 43
• Watchers: 6
• Forks: 1
• Open Issues: 1
• Metadata Files:
  • Readme: README.md

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README

        
![](plots/gaussian_plot_alts_bare.png)

[![arXiv article](https://img.shields.io/badge/article-arXiv%3A10.48550-B31B1B)](https://arxiv.org/abs/2306.07961)

# Differentiable Metropolis-Hastings 

This repository contains the code to reproduce the experiments in our working paper [Differentiating Metropolis-Hastings to Optimize Intractable Densities](https://arxiv.org/abs/2306.07961).

## Abstract

When performing inference on probabilistic models, target densities often become intractable, necessitating the use of Monte Carlo samplers. We develop a methodology for unbiased differentiation of the Metropolis-Hastings sampler, allowing us to differentiate through probabilistic inference. By fusing recent advances in stochastic differentiation with Markov chain coupling schemes, the procedure can be made unbiased, low-variance, and automatic. This allows us to apply gradient-based optimization to objectives expressed as expectations over intractable target densities. We demonstrate our approach by finding an ambiguous observation in a Gaussian mixture model and by maximizing the specific heat in an Ising model.

## Citation

```

@inproceedings{arya2023differentiating,

    title={Differentiating Metropolis-Hastings to Optimize Intractable Densities},

    author={Gaurav Arya and Ruben Seyer and Frank Sch{\"a}fer and Kartik Chandra and Alexander K. Lew and Mathieu Huot and Vikash Mansinghka and Jonathan Ragan-Kelley and Christopher Vincent Rackauckas and Moritz Schauer},

    booktitle={ICML 2023 Workshop on Differentiable Almost Everything: Differentiable Relaxations, Algorithms, Operators, and Simulators},

    year={2023},

    url={https://openreview.net/forum?id=2jag4Yatsz}

}

```

## Reproducing plots

To reproduce the plots in the `plots` folder:

* Enter the `scripts` folder.

* Run `julia _setup_env.jl` to setup your environment.

* Run `julia {script name}.jl` for each of the four scripts to produce the plots.