Inverse Ising inference with correlated samples

Abstract

Correlations between two variables of a high-dimensional system can be indicative of an underlying interaction, but can also result from indirect effects. Inverse Ising inference is a method to distinguish one from the other. Essentially, the parameters of the least constrained statistical model are learned from the observed correlations such that direct interactions can be separated from indirect correlations. Among many other applications, this approach has been helpful for protein structure prediction, because residues which interact in the 3D structure often show correlated substitutions in a multiple sequence alignment. In this context, samples used for inference are not independent but share an evolutionary history on a phylogenetic tree. Here, we discuss the effects of correlations between samples on global inference. Such correlations could arise due to phylogeny but also via other slow dynamical processes. We present a simple analytical model to address the resulting inference biases, and develop an exact method accounting for background correlations in alignment data by combining phylogenetic modeling with an adaptive cluster expansion algorithm. We find that popular reweighting schemes are only marginally effective at removing phylogenetic bias, suggest a rescaling strategy that yields better results, and provide evidence that our conclusions carry over to the frequently used mean-field approach to the inverse Ising problem.

18 pages, 6 figures; accepted at New J Phys

References in corpus (12)

• Weak pairwise correlations imply strongly correlated network states in a neural population
• Direct-coupling analysis of residue co-evolution captures native contacts across many protein families
• Identification of direct residue contacts in protein-protein interaction by message passing
• A Random Matrix Approach to Cross-Correlations in Financial Data
• Statistical mechanics for natural flocks of birds
• High-dimensional Ising model selection using ${\ell }_1$-regularized logistic regression
• Inverse Ising inference using all the data
• Adaptive Cluster Expansion for Inferring Boltzmann Machines with Noisy Data
• From principal component to direct coupling analysis of coevolution in proteins: Low-eigenvalue modes are needed for structure prediction
• Small-correlation expansions for the inverse Ising problem
• Monte Carlo study of the random-field Ising model
• Mean-field theory for the inverse Ising problem at low temperatures

Cited by in corpus (2)

• Optimal design of experiments by combining coarse and fine measurements
• Adaptive Cluster Expansion for Ising spin models