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Sliced Stein discrepancy (SSD) and its kernelized variants have demonstratedpromising successes in goodness-of-fit tests and model learning in highdimensions. Despite their theoretical elegance, their empirical performancedepends crucially on the search of optimal slicing directions to discriminatebetween two distributions. Unfortunately, previous gradient-based optimisationapproaches for this task return sub-optimal results: they are computationallyexpensive, sensitive to initialization, and they lack theoretical guaranteesfor convergence. We address these issues in two steps. First, we providetheoretical results stating that the requirement of using optimal slicingdirections in the kernelized version of SSD can be relaxed, validating theresulting discrepancy with finite random slicing directions. Second, given thatgood slicing directions are crucial for practical performance, we propose afast algorithm for finding such slicing directions based on ideas of activesub-space construction and spectral decomposition. Experiments ongoodness-of-fit tests and model learning show that our approach achieves bothimproved performance and faster convergence. Especially, we demonstrate a14-80x speed-up in goodness-of-fit tests when comparing with gradient-basedalternatives.

Active Slices for Sliced Stein Discrepancy