Stochastic Stein Discrepancies
This work addresses a computational bottleneck for researchers and practitioners in machine learning using approximate inference methods, offering a significant speed-up while maintaining performance.
The paper tackles the computational expense of Stein discrepancies (SDs) in approximate inference by introducing stochastic Stein discrepancies (SSDs) based on subsampled approximations, which inherit convergence control properties and reduce likelihood evaluations by orders of magnitude in experiments.
Stein discrepancies (SDs) monitor convergence and non-convergence in approximate inference when exact integration and sampling are intractable. However, the computation of a Stein discrepancy can be prohibitive if the Stein operator - often a sum over likelihood terms or potentials - is expensive to evaluate. To address this deficiency, we show that stochastic Stein discrepancies (SSDs) based on subsampled approximations of the Stein operator inherit the convergence control properties of standard SDs with probability 1. Along the way, we establish the convergence of Stein variational gradient descent (SVGD) on unbounded domains, resolving an open question of Liu (2017). In our experiments with biased Markov chain Monte Carlo (MCMC) hyperparameter tuning, approximate MCMC sampler selection, and stochastic SVGD, SSDs deliver comparable inferences to standard SDs with orders of magnitude fewer likelihood evaluations.