Work

Differentiating Metropolis-Hastings to Optimize Intractable Densities

Year: 2023

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2306.07961

Authors: Arya, Gaurav, Seyer, Ruben, Schäfer, Frank, Chandra, Kartik, Lew, Alexander K., Huot, Mathieu, Mansinghka, Vikash K., Ragan-Kelley, Jonathan, Rackauckas, Christopher, Schauer, Moritz

Institutions: Massachusetts Institute of Technology, Chalmers University of Technology, University of Gothenburg, University of Oxford

Language: English

Topic: Markov Chains and Monte Carlo Methods

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4380715589

Cites:

Cited by: 4

Related to: 10