The scarcity of crossing dependencies: a direct outcome of a specific constraint?
Table 2: Summary of results for each treebank: number of distinct sentence lengths, average Δ0, and average, median and standard deviation of the average values of Δ2 over the groups of sentences with the same length. Languages are sorted decreasingly by average Ctrue according to Stanford dependencies as in Table 1.
['Treebank', '[ITALIC] Stanford annotation #Lengths', '[ITALIC] Stanford annotation Δ0 (avg.)', 'Δ2 (avg.)', 'Δ2 (median)', 'Δ2 (st. dev.)', '[ITALIC] Prague annotation #Lengths', '[ITALIC] Prague annotation Δ0 (avg.)', 'Δ2 (avg.)', 'Δ2 (median)', 'Δ2 (st. dev.)']
To control for sentence length, sentences were grouped by length and the average Δ2 was computed for the sentences within each group. Interestingly, the average over group averages of Δ2 decreases with respect to the previous analysis: it does not exceed 4.3%. Thus, the average Δ2 is at least 7 times smaller than the baseline error, again Δ0≈33%. The minimum size of a group is one sentence; the qualitative results are very similar if the minimum size is set to 2. If we instead look at the table obtained by grouping by sentence lengths As a representative example, if we focus on Stanford dependencies, the best prediction (average Δ2=0.014) is obtained for Arabic: an Afro-Asiatic, non-agglutinating language whose treebank contains long sentences with a relatively high number of crossings; while the third best (average Δ2=0.021) corresponds to Japanese: a Japonic, agglutinating language with short sentences and little observed crossings. The situation is very similar with Prague annotations, with Japanese exhibiting the best prediction, and Arabic the second best. These simple and partial linguistic analyses are just reported to illustrate the potential of future linguistic research that explores in more depth the relationship between language traits and annotation criteria on the one hand, and crossings and predictions on the other.