The mighty force: statistical inference and high-dimensional statistics

TL;DR

This review highlights key graph-based models and methods from the spin glass community that have significantly advanced high-dimensional statistics, focusing on graph inference, community detection, and the dynamic cavity method for causal inference.

Contribution

It synthesizes contributions from the spin glass community on three influential models and methodologies impacting high-dimensional statistical inference.

Findings

Insights into graph inference techniques like direct coupling analysis

Advancements in community detection algorithms

Application of the dynamic cavity method for causal inference

Abstract

This is a review to appear as a contribution to the edited volume "Spin Glass Theory & Far Beyond - Replica Symmetry Breaking after 40 Years", World Scientific. It showcases a selection of contributions from the spin glass community at large to high-dimensional statistics, by focusing on three important graph-based models and methodologies having deeply impacted the field: inference of graphs (a.k.a. direct coupling analysis), inference from graphs (the community detection problem), and the dynamic cavity method, which in particular allows for inference from graphs encoding causal relations.