Sliced Kernelized Stein Discrepancy
This addresses scalability issues in high-dimensional statistical inference for researchers and practitioners, though it is incremental as it builds on existing Stein discrepancy methods.
The paper tackles the curse-of-dimensionality in Kernelized Stein Discrepancy (KSD) by proposing sliced Stein discrepancy and its variants, which use optimal one-dimensional projections, resulting in significant performance improvements in high-dimensional goodness-of-fit tests and advantages in model learning tasks like training independent component analysis models.
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.