Inferring couplings in networks across order-disorder phase transitions

TL;DR

This paper investigates how the effectiveness of direct coupling analysis (DCA) varies across different data regimes in ferromagnetic Ising models, revealing that DCA's performance depends on temperature and data quality, with limitations at high temperatures and limited data.

Contribution

The study provides a detailed analysis of DCA's performance across phase transitions in Ising models, highlighting conditions where it outperforms or underperforms compared to simpler methods.

Findings

DCA performs best at intermediate temperatures with minimal macroscopic order.

DCA outperforms local methods at low temperatures but not when data is limited.

Inference quality is strongly influenced by the data's underlying phase and temperature.

Abstract

Statistical inference is central to many scientific endeavors, yet how it works remains unresolved. Answering this requires a quantitative understanding of the intrinsic interplay between statistical models, inference methods and data structure. To this end, we characterize the efficacy of direct coupling analysis (DCA)--a highly successful method for analyzing amino acid sequence data--in inferring pairwise interactions from samples of ferromagnetic Ising models on random graphs. Our approach allows for physically motivated exploration of qualitatively distinct data regimes separated by phase transitions. We show that inference quality depends strongly on the nature of generative models: optimal accuracy occurs at an intermediate temperature where the detrimental effects from macroscopic order and thermal noise are minimal. Importantly our results indicate that DCA does not always outperform its local-statistics-based predecessors; while DCA excels at low temperatures, it becomes inferior to simple correlation thresholding at virtually all temperatures when data are limited. Our findings offer new insights into the regime in which DCA operates so successfully and more broadly how inference interacts with data structure.