The latent space model is one of the well-known methods for statistical inference of network data. While the model has been much studied for a single network, it has not attracted much attention to analyze collectively when multiple networks and their latent embeddings are present. We adopt a topology-based representation of latent space embeddings to learn over a population of network model fits, which allows us to compare networks of potentially varying sizes in an invariant manner to label permutation and rigid motion. This approach enables us to propose algorithms for clustering and multi-sample hypothesis tests by adopting well-established theories for Hilbert space-valued analysis. After the proposed method is validated via simulated examples, we apply the framework to analyze educational survey data from Korean innovative school reform.
翻译:潜伏空间模型是众所周知的网络数据统计推论方法之一。虽然该模型已经为单一网络进行了大量研究,但并没有引起多大的注意来集体分析存在多个网络及其潜在嵌入点的情况。我们采用了基于地形的潜在空间嵌入层代表,以在网络模型群中学习,从而使我们能够以变化不定的方式比较可能不同大小的网络,以标签变异和僵硬运动。这种方法使我们能够通过采用Hilbert空间价值分析的既定理论,提出集群和多样本假设测试的算法。在通过模拟实例验证了拟议方法之后,我们运用了框架来分析韩国创新学校改革产生的教育调查数据。