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 KSD-based goodness-of-fit testing procedures.
翻译:我们根据Kernel Stein Discency (KSD) 调查了基于“Kernel Stein Dismission” (KSD) 的 " 最佳测试 " 的特性。 我们引入了一项设计试验的战略,称为 " KSDAgg " (KSDAgg),该试验用不同的内核集成多个测试。 KSDAgg避免将数据分解以进行内核选择(这导致测试力丧失),而是将内核集合的测试力最大化。 我们为KSDAgg的力量提供了理论保障:我们显示它达到了收藏中最小的统一分离率,直到一个对数术语。 KSDADgg可以精确地在实际中进行计算,因为它依靠一个参数式靴子陷阱或野生靴来估计孔值和水平校正。 特别是对于一个固定内核的关键选择带带,它避免诉诸任意的超导(如中位或标准偏差)或数据分解。 我们从合成和真实世界数据中发现, KSDgg(SDgg) 超越了其他最先进的适应性KSD-SD基础的“良好” 测试程序。