用核化Stein差异实现单次观测下异质随机图的精准检验
A Pure Hypothesis Test for Inhomogeneous Random Graph Models Based on a Kernelised Stein Discrepancy
- 基于核化Stein差异设计单样本图检验方法
- 适用于任意规模网络，尤其擅长小样本场景
- 提供理论保证，无需渐近假设
复杂数据常以图形式表示，这类图可视为异质随机图模型（IRG）的实现。针对高维数据的快速拟合优度检验，核化Stein差异（KSD）是一种有力工具。本文提出一种适用于IRG模型的KSD型检验方法，仅需一次网络观测即可执行。该方法适用于任意规模的网络，尤其在小样本情形下具有优势，因传统渐近检验在此不适用。同时，本文提供了理论保障。
原文摘要 · Abstract (English)
Complex data are often represented as a graph, which in turn can often be viewed as a realisation of a random graph, such as an inhomogeneous random graph model (IRG). For general fast goodness-of-fit tests in high dimensions, kernelised Stein discrepancy (KSD) tests are a powerful tool. Here, we develop a KSD-type test for IRG models that can be carried out with a single observation of the network. The test applies to a network of any size, but is particularly interesting for small networks for which asymptotic tests are not warranted. We also provide theoretical guarantees.
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