Differentiating Metropolis-Hastings to Optimize Intractable Densities
Machine Learning
2023-07-04 v3 Machine Learning
Computation
Methodology
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.
Keywords
Cite
@article{arxiv.2306.07961,
title = {Differentiating Metropolis-Hastings to Optimize Intractable Densities},
author = {Gaurav Arya and Ruben Seyer and Frank Schäfer and Kartik Chandra and Alexander K. Lew and Mathieu Huot and Vikash K. Mansinghka and Jonathan Ragan-Kelley and Christopher Rackauckas and Moritz Schauer},
journal= {arXiv preprint arXiv:2306.07961},
year = {2023}
}
Comments
6 pages, 6 figures; accepted at Differentiable Almost Everything Workshop of ICML 2023