Algebraic statistics, tables, and networks: The Fienberg advantage

TL;DR

This paper discusses Stephen Fienberg's influential approach to hypothesis testing in network models using algebraic statistics, emphasizing contingency tables and exponential families, with extensions to complex graph structures.

Contribution

It highlights Fienberg's innovative perspective on algebraic statistics applied to network models and extends his ideas to multigraphs and hypergraphs.

Findings

Fienberg's approach provides a new framework for hypothesis testing in network models.

Extensions to multigraphs and hypergraphs broaden the applicability of algebraic statistical methods.

The paper underscores the impact of Fienberg's vision on modern statistical network analysis.

Abstract

Stephen Fienberg's affinity for contingency table problems and reinterpreting models with a fresh look gave rise to a new approach for hypothesis testing of network models that are linear exponential families. We outline his vision and influence in this fundamental problem, as well as generalizations to multigraphs and hypergraphs.