Gradient-based Adaptive Markov Chain Monte Carlo
This work addresses a bottleneck in MCMC sampling for Bayesian inference and statistical modeling by improving adaptation efficiency, though it appears incremental as it builds on existing adaptive MCMC methods.
The paper tackles the problem of adapting Markov chain Monte Carlo (MCMC) proposal distributions to intractable targets by introducing a gradient-based learning method with a maximum entropy regularized objective, enabling adaptation even when candidate states are rejected. The result shows that this method can outperform other MCMC algorithms, including Hamiltonian Monte Carlo schemes, in empirical tests.
We introduce a gradient-based learning method to automatically adapt Markov chain Monte Carlo (MCMC) proposal distributions to intractable targets. We define a maximum entropy regularised objective function, referred to as generalised speed measure, which can be robustly optimised over the parameters of the proposal distribution by applying stochastic gradient optimisation. An advantage of our method compared to traditional adaptive MCMC methods is that the adaptation occurs even when candidate state values are rejected. This is a highly desirable property of any adaptation strategy because the adaptation starts in early iterations even if the initial proposal distribution is far from optimum. We apply the framework for learning multivariate random walk Metropolis and Metropolis-adjusted Langevin proposals with full covariance matrices, and provide empirical evidence that our method can outperform other MCMC algorithms, including Hamiltonian Monte Carlo schemes.