Differentiating Metropolis-Hastings to Optimize Intractable Densities
Other conference contribution, 2023
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.
Metropolis-Hastings
Markov chain coupling
automatic differentiation
Author
Gaurav Arya
Massachusetts Institute of Technology (MIT)
Ruben Seyer
Chalmers, Mathematical Sciences, Applied Mathematics and Statistics
University of Gothenburg
Frank Schäfer
Massachusetts Institute of Technology (MIT)
Kartik Chandra
Massachusetts Institute of Technology (MIT)
Alexander Lew
Massachusetts Institute of Technology (MIT)
Mathieu Huot
University of Oxford
Vikash Mansinghka
Massachusetts Institute of Technology (MIT)
Jonathan Ragan-Kelley
Massachusetts Institute of Technology (MIT)
Christopher Vincent Rackauckas
Massachusetts Institute of Technology (MIT)
JuliaHub, Inc.
Pumas-AI Inc.
Moritz Schauer
University of Gothenburg
Chalmers, Mathematical Sciences, Applied Mathematics and Statistics
Differentiable Almost Everything Workshop of the 40th International Conference on Machine Learning
Honolulu, Hawaii, USA,
Honolulu, Hawaii, USA,
Subject Categories
Computational Mathematics
Transport Systems and Logistics
Probability Theory and Statistics
Roots
Basic sciences