Information-theoretical analysis of the statistical dependencies among three variables: Applications to written language
Table 5: Pairs of words with lowest irreducible interaction. The first column displays a tag that allows us to identify each triplet in Fig. 7. Top: OS. Bottom: AM. Values in bits.
['[EMPTY]', '[ITALIC] i', '[ITALIC] j', '[ITALIC] Iij', 'Δ [ITALIC] ij', '[ITALIC] kmed']
In these triplets, most of the interaction between words wi and wj is explained in terms of wk. Mediators tend to have a high semantic content, and to provide a context in which the other two words interact. In the right panels of Fig. When compared with the network of mutual informations (left panels), the irreducible network contains weaker bonds, as expected, since by definition, Δij cannot be larger than Iij. Such pairs appear with a significantly weaker bond in the right panel, as for example, bee-wax (mediator = cell, OS), and stimulus-accuracy, (mediator = response, AM). Moreover, one can also identify the pairs whose interaction is intrinsic (that is, not mediated by a third word) as those where the link on the right has approximately the same width as on the left. Notable examples are male-female (OS), and depend-upon.