Active Slices for Sliced Stein Discrepancy

TL;DR

This paper introduces a theoretically justified and computationally efficient method for selecting slicing directions in Sliced Stein Discrepancy, significantly improving performance and speed in high-dimensional goodness-of-fit tests and model learning.

Contribution

It provides theoretical validation for using random slicing directions and proposes a fast spectral algorithm for optimal slicing direction search.

Findings

Achieves 14-80x speed-up in goodness-of-fit tests.

Improves test performance and convergence speed.

Validates the use of finite random slices in kernelized SSD.

Abstract

Sliced Stein discrepancy (SSD) and its kernelized variants have demonstrated promising successes in goodness-of-fit tests and model learning in high dimensions. Despite their theoretical elegance, their empirical performance depends crucially on the search of optimal slicing directions to discriminate between two distributions. Unfortunately, previous gradient-based optimisation approaches for this task return sub-optimal results: they are computationally expensive, sensitive to initialization, and they lack theoretical guarantees for convergence. We address these issues in two steps. First, we provide theoretical results stating that the requirement of using optimal slicing directions in the kernelized version of SSD can be relaxed, validating the resulting discrepancy with finite random slicing directions. Second, given that good slicing directions are crucial for practical performance, we propose a fast algorithm for finding such slicing directions based on ideas of active sub-space construction and spectral decomposition. Experiments on goodness-of-fit tests and model learning show that our approach achieves both improved performance and faster convergence. Especially, we demonstrate a 14-80x speed-up in goodness-of-fit tests when comparing with gradient-based alternatives.