AI 中文总结
本研究提出将无条件核斯坦差异（KSD）推广到条件场景的框架，用于在无协变量分布信息时评估样本条件分布与目标的拟合优度，实验验证了该统计量在光滑流形和离散空间上测试的可行性。
AI 中文摘要
核斯坦差异（KSDs）是一种用于比较分布的通用工具，其主要应用之一是量化数据生成分布与指定目标分布之间的拟合优度（GoF）。本研究探讨相关的条件拟合优度量化问题：仅给定（可能未归一化的）条件目标模型，而无其协变量分布的信息，以及联合分布的样本，目标是评估样本的条件分布与目标的匹配程度。为解决该场景，我们提出一个框架，通过协变量空间上的算子值核将无条件KSD推广到条件场景，超越了已知的欧氏情况。我们证明，当且仅当条件模型与真实条件分布对几乎所有协变量都一致时，我们提出的统计量为零，并将其用于测试光滑流形和离散空间上的条件拟合优度。我们在水平、功效和运行时间方面的实验表明，使用所提出的统计量在这些领域进行测试是可行的。
英文摘要
Kernel Stein discrepancies (KSDs) provide a versatile tool for comparing distributions. One of their main applications is in quantifying the goodness-of-fit (GoF) between a data-generating distribution and a prescribed target distribution. In this work, we study the related problem of conditional GoF quantification: given only a (possibly non-normalized) conditional target model, without information on the distribution of its covariates, and samples from a joint distribution, the goal is to assess how well the conditional distribution of the samples matches the target. To tackle this setting, we present a framework that allows lifting unconditional KSDs to the conditional setting through an operator-valued kernel on the covariate space, going beyond the known Euclidean case. We establish that our suggested statistic vanishes if and only if the conditional model and the true conditional distribution agree for almost all covariates and deploy it to test conditional GoF on smooth manifolds and on discrete spaces. Our experiments on level, power, and runtime demonstrate the viability of testing on these domains using the proposed statistic.
