  Kernelized Stein discrepancy (KSD), though being extensively used in
goodness-of-fit tests and model learning, suffers from the
curse-of-dimensionality. We address this issue by proposing the sliced Stein
discrepancy and its scalable and kernelized variants, which employ kernel-based
test functions defined on the optimal one-dimensional projections. When applied
to goodness-of-fit tests, extensive experiments show the proposed discrepancy
significantly outperforms KSD and various baselines in high dimensions. For
model learning, we show its advantages over existing Stein discrepancy
baselines by training independent component analysis models with different
discrepancies. We further propose a novel particle inference method called
sliced Stein variational gradient descent (S-SVGD) which alleviates the
mode-collapse issue of SVGD in training variational autoencoders.
