Differentiating Metropolis-Hastings to Optimize Intractable Densities
Övrigt konferensbidrag, 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
Författare
Gaurav Arya
Massachusetts Institute of Technology (MIT)
Ruben Seyer
Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik
Göteborgs universitet
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
Göteborgs universitet
Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik
Differentiable Almost Everything Workshop of the 40th International Conference on Machine Learning
Honolulu, Hawaii, USA,
Honolulu, Hawaii, USA,
Ämneskategorier
Beräkningsmatematik
Transportteknik och logistik
Sannolikhetsteori och statistik
Fundament
Grundläggande vetenskaper