Crosslingual Document Embedding as Reduced-Rank Ridge Regression
Table 1. Precision at k on document retrieval. One row per language pair (l1, l2; codes resolved in Sec. 4.1); each pair evaluated in both directions (query in l1, candidates in l2, and vice versa) and using both similarity measures (cosine, CSLS; cf. Sec. 4.1).
['[EMPTY]', '[ITALIC] l1', '[ITALIC] l2', 'Query in  [ITALIC] l1 (cosine) P@1', 'Query in  [ITALIC] l1 (cosine) P@5', 'Query in  [ITALIC] l1 (cosine) P@10', 'Query in  [ITALIC] l2 (cosine) P@1', 'Query in  [ITALIC] l2 (cosine) P@5', 'Query in  [ITALIC] l2 (cosine) P@10', 'Query in  [ITALIC] l1 (CSLS) P@1', 'Query in  [ITALIC] l1 (CSLS) P@5', 'Query in  [ITALIC] l1 (CSLS) P@10', 'Query in  [ITALIC] l2 (CSLS) P@1', 'Query in  [ITALIC] l2 (CSLS) P@5', 'Query in  [ITALIC] l2 (CSLS) P@10', '# docs in intersection']
Sec. (Since CSLS is better everywhere for AdvRefine, and nearly everywhere for Cr5, we focus on this measure in our discussion.) First, we note that the performance of Cr5 is overall high in absolute terms: the smallest P@1 (P@10) is 35.9% (67.3%), i.e., for all pairs, the correct target document is ranked first for at least one third of all queries, and among the top 10 for at least two thirds of them. The gains are especially high for pairs involving low\hypresource languages, such as Danish and Vietnamese, where we increase P@1 from 8.1% to 36.4%. These outcomes are echoed visually by Fig.