  With the overwhelming popularity of Knowledge Graphs (KGs), researchers have
poured attention to link prediction to fill in missing facts for a long time.
However, they mainly focus on link prediction on binary relational data, where
facts are usually represented as triples in the form of (head entity, relation,
tail entity). In practice, n-ary relational facts are also ubiquitous. When
encountering such facts, existing studies usually decompose them into triples
by introducing a multitude of auxiliary virtual entities and additional
triples. These conversions result in the complexity of carrying out link
prediction on n-ary relational data. It has even proven that they may cause
loss of structure information. To overcome these problems, in this paper, we
represent each n-ary relational fact as a set of its role and role-value pairs.
We then propose a method called NaLP to conduct link prediction on n-ary
relational data, which explicitly models the relatedness of all the role and
role-value pairs in an n-ary relational fact. We further extend NaLP by
introducing type constraints of roles and role-values without any external
type-specific supervision, and proposing a more reasonable negative sampling
mechanism. Experimental results validate the effectiveness and merits of the
proposed methods.
