论文标题
核表示无限尺寸希尔伯特空间措施的核心Stein差异差异差异
A Fourier representation of kernel Stein discrepancy with application to Goodness-of-Fit tests for measures on infinite dimensional Hilbert spaces
论文作者
论文摘要
内核Stein差异（KSD）是一种基于内核的概率度量差异的量度。它通常在用户从候选概率度量中收集的样本集合的情况下使用，并希望将它们与指定目标概率度量进行比较。 KSD已用于一系列设置，包括拟合优点测试，参数推断，MCMC输出评估和生成建模。但是，到目前为止，该方法仅限于有限维数据。我们在可分离的希尔伯特空间（例如功能数据）中提供了KSD的首次分析。主要结果是通过将测量方程式理论与内核方法相结合，获得了KSD的新型傅立叶表示。这使我们可以证明KSD可以分开措施，因此在实践中使用有效。此外，我们的结果通过将内核和Stein操作员的效果解耦来提高KSD的可解释性。我们通过在许多合成数据实验中对各种高斯和非高斯功能模型进行拟合优度测试来证明所提出的方法的功效。
Kernel Stein discrepancy (KSD) is a widely used kernel-based measure of discrepancy between probability measures. It is often employed in the scenario where a user has a collection of samples from a candidate probability measure and wishes to compare them against a specified target probability measure. KSD has been employed in a range of settings including goodness-of-fit testing, parametric inference, MCMC output assessment and generative modelling. However, so far the method has been restricted to finite-dimensional data. We provide the first analysis of KSD in the generality of data lying in a separable Hilbert space, for example functional data. The main result is a novel Fourier representation of KSD obtained by combining the theory of measure equations with kernel methods. This allows us to prove that KSD can separate measures and thus is valid to use in practice. Additionally, our results improve the interpretability of KSD by decoupling the effect of the kernel and Stein operator. We demonstrate the efficacy of the proposed methodology by performing goodness-of-fit tests for various Gaussian and non-Gaussian functional models in a number of synthetic data experiments.
