Stein Variational Inference for Discrete Distributions

Gradient-based approximate inference methods, such as Stein variational gradient descent (SVGD) \cite{liu2016stein}, provide simple and general-purpose inference engines for differentiable continuous distributions. However, existing forms of SVGD can not be directly applied to discrete distributions. In this work, we fill this gap by proposing a simple general-purpose framework that transforms discrete distributions to equivalent piecewise continuous distribution, on which we apply gradient-free Stein variational gradient descent to perform efficient approximate inference. Our empirical results show that our method outperforms traditional algorithms such as Gibbs sampling and discontinuous Hamiltonian Monte Carlo on various challenging benchmarks of discrete graphical models. We demonstrate that our method provides a promising tool for learning ensembles of binarized neural network (BNN), outperforming other widely used ensemble methods on learning binarized AlexNet on CIFAR-10. In addition, such transform can be straightforwardly employed in gradient-free kernelized Stein discrepancy to perform goodness-of-fit (GOF) test on discrete distributions. Our proposed method outperforms existing GOF test methods for intractable discrete distributions.