Differentiating Metropolis-Hastings to Optimize Intractable Densities
This addresses the challenge of gradient-based optimization in probabilistic models with intractable densities, which is incremental as it builds on existing stochastic differentiation and coupling methods.
The paper tackles the problem of optimizing objectives expressed as expectations over intractable densities by developing an algorithm for automatic differentiation of Metropolis-Hastings samplers, enabling gradient-based optimization even with discrete components, and demonstrates it by finding ambiguous observations in a Gaussian mixture model and maximizing specific heat in an Ising model.
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.