The mighty force: statistical inference and high-dimensional statistics

Erik Aurell (1) , Jean Barbier (2) , Aurélien Decelle (3, 4, 5, 6) , Roberto Mulet (7)

1 Stockton - Stockton University
2 ICTP - Abdus Salam International Centre for Theoretical Physics [Trieste]
3 LRI - Laboratoire de Recherche en Informatique
4 LISN - Laboratoire Interdisciplinaire des Sciences du Numérique
5 TAU - TAckling the Underspecified
6 UCM - Universidad Complutense de Madrid = Complutense University of Madrid [Madrid]
7 UH - University of Havana (Universidad de la Habana)

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.

Domaines: Mécanique statistique [cond-mat.stat-mech]; Systèmes désordonnés et réseaux de neurones [cond-mat.dis-nn]

Erik Aurell, Jean Barbier, Aurélien Decelle, Roberto Mulet. The mighty force: statistical inference and high-dimensional statistics. Spin Glass Theory & Far Beyond - Replica Symmetry Breaking after 40 Years, World Scientific, In press, ⟨10.48550/arXiv.2205.00750⟩. ⟨hal-03795572⟩