Adaptive Thouless-Anderson-Palmer approach to inverse Ising problems with quenched random fields

Abstract

The adaptive Thouless-Anderson-Palmer equation is derived for inverse Ising problems in the presence of quenched random fields. We test the proposed scheme on Sherrington-Kirkpatrick, Hopfield, and random orthogonal models and find that the adaptive Thouless-Anderson-Palmer approach allows surprisingly accurate inference of quenched random fields whose distribution can be either Gaussian or bimodal, compared with other existing mean-field methods.

9 pages, 4 figures, extensively revised

References in corpus (5)

• Identification of direct residue contacts in protein-protein interaction by message passing
• The Ising Model for Neural Data: Model Quality and Approximate Methods for Extracting Functional Connectivity
• Small-correlation expansions for the inverse Ising problem
• Susceptibility Propagation by Using Diagonal Consistency
• A mean field method with correlations determined by linear response

Cited by in corpus (9)

• High-temperature Expansions and Message Passing Algorithms
• Large Pseudo-Counts and $L_2$-Norm Penalties Are Necessary for the Mean-Field Inference of Ising and Potts Models
• Mechanisms of dimensionality reduction and decorrelation in deep neural networks
• Solving the inverse Ising problem by mean-field methods in a clustered phase space with many states
• A mean field method with correlations determined by linear response
• Effects of hidden nodes on network structure inference
• Resummed mean-field inference for strongly coupled data
• Interpolating between boolean and extremely high noisy patterns through Minimal Dense Associative Memories
• Improving variational methods via pairwise linear response identities