A Density Consistency approach to the inverse Ising problem

Abstract

We propose a novel approach to the inverse Ising problem which employs the recently introduced Density Consistency approximation (DC) to determine the model parameters (couplings and external fields) maximizing the likelihood of given empirical data. This method allows for closed-form expressions of the inferred parameters as a function of the first and second empirical moments. Such expressions have a similar structure to the small-correlation expansion derived by Sessak and Monasson, of which they provide an improvement in the case of non-zero magnetization at low temperatures, as well as in presence of random external fields. The present work provides an extensive comparison with most common inference methods used to reconstruct the model parameters in several regimes, i.e. by varying both the network topology and the distribution of fields and couplings. The comparison shows that no method is uniformly better than every other one, but DC appears nevertheless as one of the most accurate and reliable approaches to infer couplings and fields from first and second moments in a significant range of parameters.

arXiv comment15 pages, 4 figures

References in corpus (17)

• Emergence of scaling in random networks
• Expectation Propagation for approximate Bayesian inference
• Inverse statistical problems: from the inverse Ising problem to data science
• Inverse Statistical Physics of Protein Sequences: A Key Issues Review
• The Ising Model for Neural Data: Model Quality and Approximate Methods for Extracting Functional Connectivity
• Inverse Ising inference using all the data
• Adaptive Cluster Expansion for Inferring Boltzmann Machines with Noisy Data
• Statistical physics of pairwise probability models
• Small-correlation expansions for the inverse Ising problem
• Adaptive cluster expansion for the inverse Ising problem: convergence, algorithm and tests
• The Bethe approximation for solving the inverse Ising problem: a comparison with other inference methods
• The Effect of Nonstationarity on Models Inferred from Neural Data
• Market structure explained by pairwise interactions
• Bethe-Peierls approximation and the inverse Ising model
• Large Pseudo-Counts and $L_2$-Norm Penalties Are Necessary for the Mean-Field Inference of Ising and Potts Models
• U.S. stock market interaction network as learned by the Boltzmann Machine
• Loop corrections in spin models through density consistency

Cited by in corpus (1)

• Inferring effective couplings with Restricted Boltzmann Machines