Emergence of functional information from multivariate correlations

TL;DR

This paper demonstrates that functional information can be derived from multivariate correlations within sequences, enabling prediction of observables in new sequences and revealing how information emerges from complex correlation hierarchies.

Contribution

It introduces a method to extract functional information from multivariate correlations, allowing predictions on out-of-sample sequences based on training data.

Findings

Multivariate correlation-based scores predict sequence observables.

Prediction accuracy scales with correlation complexity.

Functional information emerges from hierarchical correlations.

Abstract

The information content of symbolic sequences (such as nucleic- or amino acid sequences, but also neuronal firings or strings of letters) can be calculated from an ensemble of such sequences, but because information cannot be assigned to single sequences, we cannot correlate information to other observables attached to the sequence. Here we show that an information score obtained from multivariate (multiple-variable) correlations within sequences of a "training" ensemble can be used to predict observables of out-of-sample sequences with an accuracy that scales with the complexity of correlations, showing that functional information emerges from a hierarchy of multi-variable correlations.