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 seque
nces, 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.
How information is encoded in bio-molecular sequences is difficult to quantify since such an analysis usually requires sampling an exponentially large genetic space. Here we show how information theory reveals both robust and compressed encodings in
the largest complete genotype-phenotype map (over 5 trillion sequences) obtained to date.
