  Knowledge bases often consist of facts which are harvested from a variety of
sources, many of which are noisy and some of which conflict, resulting in a
level of uncertainty for each triple. Knowledge bases are also often
incomplete, prompting the use of embedding methods to generalize from known
facts, however, existing embedding methods only model triple-level uncertainty,
and reasoning results lack global consistency. To address these shortcomings,
we propose BEUrRE, a novel uncertain knowledge graph embedding method with
calibrated probabilistic semantics. BEUrRE models each entity as a box (i.e.
axis-aligned hyperrectangle) and relations between two entities as affine
transforms on the head and tail entity boxes. The geometry of the boxes allows
for efficient calculation of intersections and volumes, endowing the model with
calibrated probabilistic semantics and facilitating the incorporation of
relational constraints. Extensive experiments on two benchmark datasets show
that BEUrRE consistently outperforms baselines on confidence prediction and
fact ranking due to its probabilistic calibration and ability to capture
high-order dependencies among facts.
