Differentiating Metropolis-Hastings to Optimize Intractable Densities

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

Keywords: probabilistic programming, bayesian inference, automatic differentiation, gradient estimation

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.

Submission Number: 23