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About this paper
Florian Kalinke, Zoltán Szabó, Bharath K. Sriperumbudur
The authors accelerate kernel Stein discrepancy goodness-of-fit testing by using a Nyström subspace built from a smaller set of observed points for both the test statistic and its wild-bootstrap threshold. They prove asymptotic level and local consistency under stated spectral and alternative-class conditions. Experiments on spherical and functional data report similar level and power with lower runtime than quadratic-time KSD.
Key insights
- Nyström acceleration successfully reduces the computational complexity of KSD estimation and its bootstrap, making goodness-of-fit tests feasible for large datasets.
- The Nyström-accelerated KSD tests maintain critical statistical guarantees, including asymptotic level and local consistency, achieving the same optimal separation rate as their quadratic-time counterparts.
- The Nyström-accelerated wild bootstrap consistently approximates the intractable null distribution, enabling valid and efficient hypothesis testing in general separable metric spaces.
Summary by alphaXiv.
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