  By representing words with probability densities rather than point vectors,
probabilistic word embeddings can capture rich and interpretable semantic
information and uncertainty. The uncertainty information can be particularly
meaningful in capturing entailment relationships -- whereby general words such
as "entity" correspond to broad distributions that encompass more specific
words such as "animal" or "instrument". We introduce density order embeddings,
which learn hierarchical representations through encapsulation of probability
densities. In particular, we propose simple yet effective loss functions and
distance metrics, as well as graph-based schemes to select negative samples to
better learn hierarchical density representations. Our approach provides
state-of-the-art performance on the WordNet hypernym relationship prediction
task and the challenging HyperLex lexical entailment dataset -- while retaining
a rich and interpretable density representation.
