Traversing Knowledge Graphs in Vector Space
Table 2: Path query answering and knowledge base completion. We compare the performance of single-edge training (Single) vs compositional training (Comp). MQ: mean quantile, H@10: hits at 10, %red: percentage reduction in error.
['[BOLD] Path query task', '[BOLD] Path query task', '[BOLD] Bilinear Single', '[BOLD] Bilinear Comp', '[BOLD] Bilinear (%red)', '[BOLD] Bilinear-Diag Single', '[BOLD] Bilinear-Diag Comp', '[BOLD] Bilinear-Diag (%red)', '[BOLD] TransE Single', '[BOLD] TransE Comp', '[BOLD] TransE (%red)']
On WordNet, TransE benefits the most, with a 43.3% reduction in error. On Freebase, Bilinear benefits the most, with a 38.8% reduction in error. This is somewhat surprising, since Single is trained on a training set which distributionally matches the test set, whereas Comp is not. However, Comp’s better performance on path queries suggests that there must be another factor at play. At a high level, training on paths must be providing some form of structural regularization which reduces cascading errors. For example, consider the following Horn clause: parents(x,y)∧location(y,z)⇒place\_of\_birth(x,z), which states that if x has a parent with location z, then x has place of birth z. The body of the Horn clause expresses a path from x to z. If Comp models the path better, then it should be better able to use that knowledge to infer the head of the Horn clause.