Differentiating Metropolis-Hastings to Optimize Intractable Densities
Abstract
We develop an algorithm for automatic differentiation of Metropolis-Hastings samplers, allowing us to differentiate through probabilistic inference, even if the model has discrete components within it. Our approach fuses recent advances in stochastic automatic differentiation with traditional Markov chain coupling schemes, providing an unbiased and low-variance gradient estimator. 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.
Cite
Text
Arya et al. "Differentiating Metropolis-Hastings to Optimize Intractable Densities." ICML 2023 Workshops: Differentiable_Almost_Everything, 2023.Markdown
[Arya et al. "Differentiating Metropolis-Hastings to Optimize Intractable Densities." ICML 2023 Workshops: Differentiable_Almost_Everything, 2023.](https://mlanthology.org/icmlw/2023/arya2023icmlw-differentiating/)BibTeX
@inproceedings{arya2023icmlw-differentiating,
title = {{Differentiating Metropolis-Hastings to Optimize Intractable Densities}},
author = {Arya, Gaurav and Seyer, Ruben and Schäfer, Frank and Chandra, Kartik and Lew, Alexander K. and Huot, Mathieu and Mansinghka, Vikash and Ragan-Kelley, Jonathan and Rackauckas, Christopher Vincent and Schauer, Moritz},
booktitle = {ICML 2023 Workshops: Differentiable_Almost_Everything},
year = {2023},
url = {https://mlanthology.org/icmlw/2023/arya2023icmlw-differentiating/}
}