Solving the inverse Ising problem by mean-field methods in a clustered phase space with many states

Abstract

In this work we explain how to properly use mean-field methods to solve the inverse Ising problem when the phase space is clustered, that is many states are present. The clustering of the phase space can occur for many reasons, e.g. when a system undergoes a phase transition. Mean-field methods for the inverse Ising problem are typically used without taking into account the eventual clustered structure of the input configurations and may led to very bad inference (for instance in the low temperature phase of the Curie-Weiss model). In the present work we explain how to modify mean-field approaches when the phase space is clustered and we illustrate the effectiveness of the new method on different clustered structures (low temperature phases of Curie-Weiss and Hopfield models).

6 pages, 5 figures

References in corpus (4)

• Improved contact prediction in proteins: Using pseudolikelihoods to infer Potts models
• High-dimensional Ising model selection using ${\ell }_1$-regularized logistic regression
• The Ising Model for Neural Data: Model Quality and Approximate Methods for Extracting Functional Connectivity
• Mean-field theory for the inverse Ising problem at low temperatures

Cited by in corpus (11)

• Estimation of effective temperatures in quantum annealers for sampling applications: A case study with possible applications in deep learning
• Neural activity in quarks language: Lattice Field Theory for a network of real neurons
• Hopfield model with planted patterns: a teacher-student self-supervised learning model
• Learning phase transitions from regression uncertainty: A new regression-based machine learning approach for automated detection of phases of matter
• Inverse problem for multi-species mean field models in the low temperature phase
• Inverse problem for the mean-field monomer-dimer model with attractive interaction
• Ising distribution as a latent variable model
• The inverse problem beyond two-body interaction: the cubic mean-field Ising model
• Worldwide bilateral geopolitical interactions network inferred from national disciplinary profiles
• Leading Tree in DPCLUS and Its Impact on Building Hierarchies
• On the role of non-linear latent features in bipartite generative neural networks