Anomalies and Non-exchangeable: Statistical Analysis of Network Data

This lecture covers the statistical analysis of network data, focusing on anomaly detection. Anomalies are data portions that deviate from the dataset's patterns, often caused by fraudulent behavior. The lecture explores detecting anomalous nodes, edges, and communities using structure-based and community-based patterns. It delves into ego-nets, summary statistics, triangle counts, and subgraph values to identify anomalies. Additionally, the lecture discusses exchangeability extensions in network analysis, including finite and infinite exchangeable arrays, graphons, and point processes. It explains edge exchangeable networks, higher-order extensions using d-dimensional simplices, and the adjacency tensor to study network interactions.