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Paper · 2202.00824 · 2022

KSD Aggregated Goodness-of-fit Test

arXiv · PDF · Open in the Atlas

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We lifted 6 functions out of this paper's own repositories and ran 4 of them in a sandbox. "Ran" means the function executed on a synthesized input and returned a value. It is not a reproduction of the paper's results.

RepositoryRoleRan
antoninschrab/ksdagg-paper canonical 1 of 2
antoninschrab/ksdagg canonical 1 of 1
copy not recorded — 2 of 3
FunctionStatusWhere it lives
create_weights Ran this paper's copy was not recorded; identical code first harvested from antoninschrab/ksdagg
pointer only · get_code("35e8a1dce671edd0")
create_weights Ran antoninschrab/ksdagg/ksdagg/np.py
code served (permissive licence) · get_code("297f50cd6da36f51")
jax_distances Ran this paper's copy was not recorded; identical code first harvested from antoninschrab/ksdagg
pointer only · get_code("f3d6af9cdda0f3d5")
ksdagg Ran antoninschrab/ksdagg-paper/ksdagg/np.py
code served (permissive licence) · get_code("312c1dced4120601")
ksdagg Not yet run this paper's copy was not recorded; identical code first harvested from antoninschrab/ksdagg
pointer only · get_code("c07fb17178973f65")
ksdagg Not yet run antoninschrab/ksdagg-paper/ksdagg/jax.py
code served (permissive licence) · get_code("c7d475d23ef062c8")

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Abstract

We investigate properties of goodness-of-fit tests based on the Kernel Stein Discrepancy (KSD). We introduce a strategy to construct a test, called KSDAgg, which aggregates multiple tests with different kernels. KSDAgg avoids splitting the data to perform kernel selection (which leads to a loss in test power), and rather maximises the test power over a collection of kernels. We provide non-asymptotic guarantees on the power of KSDAgg: we show it achieves the smallest uniform separation rate of the collection, up to a logarithmic term. For compactly supported densities with bounded model score function, we derive the rate for KSDAgg over restricted Sobolev balls; this rate corresponds to the minimax optimal rate over unrestricted Sobolev balls, up to an iterated logarithmic term. KSDAgg can be computed exactly in practice as it relies either on a parametric bootstrap or on a wild bootstrap to estimate the quantiles and the level corrections. In particular, for the crucial choice of bandwidth of a fixed kernel, it avoids resorting to arbitrary heuristics (such as median or standard deviation) or to data splitting. We find on both synthetic and real-world data that KSDAgg outperforms other state-of-the-art quadratic-time adaptive KSD-based goodness-of-fit testing procedures.

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