Inverse Ising inference with correlated samples

TL;DR

This paper investigates how correlations between samples, such as those caused by phylogeny, affect inverse Ising inference and proposes methods to correct for these biases, improving the accuracy of inferred interactions.

Contribution

It introduces an analytical model and an exact method combining phylogenetic modeling with adaptive cluster expansion to address sample correlations in inverse Ising inference.

Findings

Popular reweighting schemes are only marginally effective

A rescaling strategy improves inference results

Conclusions extend to mean-field approaches

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.