论文标题
部分可观测时空混沌系统的无模型预测
Comparing multiple latent space embeddings using topological analysis
论文作者
论文摘要
潜在空间模型是网络数据统计推断的知名方法之一。尽管该模型已经对单个网络进行了大量研究，但是当存在多个网络及其潜在嵌入时，它并没有引起太多关注。我们采用基于拓扑的潜在空间嵌入的表示，以学习网络模型拟合的群体，这使我们能够以不变的方式比较潜在变化大小的网络，以标记置换和僵化的运动。这种方法使我们能够通过采用公认的希尔伯特空间值分析的理论来提出用于聚类和多样本假设检验的算法。在通过模拟示例验证了提出的方法之后，我们将框架应用框架来分析韩国创新学校改革的教育调查数据。
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.
