# Algebraic Statistics in Practice: Applications to Networks

## TL;DR

This survey explores how algebraic statistics employs algebraic, geometric, and combinatorial tools to address complex problems in network models, causal discovery, and phylogenetics, highlighting recent advances and practical applications.

## Contribution

It provides an overview of recent algebraic statistical methods applied to network-related problems, emphasizing their statistical and practical significance.

## Key findings

- Enhanced understanding of network models through algebraic methods
- Improved causal structure discovery techniques
- Applications to phylogenetics demonstrating practical relevance

## Abstract

Algebraic statistics uses tools from algebra (especially from multilinear algebra, commutative algebra and computational algebra), geometry and combinatorics to provide insight into knotty problems in mathematical statistics. In this survey we illustrate this on three problems related to networks, namely network models for relational data, causal structure discovery and phylogenetics. For each problem we give an overview of recent results in algebraic statistics with emphasis on the statistical achievements made possible by these tools and their practical relevance for applications to other scientific disciplines.