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Pré-Publication, Document De Travail Année : 2022

KSD Aggregated Goodness-of-fit Test

Résumé

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 theoretical guarantees on the power of KSDAGG: we show it achieves the smallest uniform separation rate of the collection, up to a 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 adaptive KSDbased goodness-of-fit testing procedures.
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Dates et versions

hal-03554423 , version 1 (03-02-2022)

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Antonin Schrab, Benjamin Guedj, Arthur Gretton. KSD Aggregated Goodness-of-fit Test. 2022. ⟨hal-03554423⟩
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