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.

中文翻译：

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从多元相关性中出现功能信息

符号序列（例如核酸或氨基酸序列，以及神经元放电或字母串）的信息内容可以从这些序列的集合中计算出来，但由于信息不能分配给单个序列，我们不能将信息与附加到序列的其他 observables。在这里，我们展示了从“训练”集合序列内的多变量（多变量）相关性中获得的信息分数可用于预测样本外序列的可观察量，其准确性随相关性的复杂性而变化，表明功能信息来自多变量相关性的层次结构。