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.

Predicting missing facts in a knowledge graph(KG) is a crucial task in knowledge base construction and reasoning, and it has been the subject of much research in recent works us-ing KG embeddings. While existing KG embedding approaches mainly learn and predict facts within a single KG, a more plausible solution would benefit from the knowledge in multiple language-specific KGs, considering that different KGs have their own strengths and limitations on data quality and coverage. This is quite challenging since the transfer of knowledge among multiple independently maintained KGs is often hindered by the insufficiency of alignment information and inconsistency of described facts. In this paper, we propose kens, a novel framework for embedding learning and ensemble knowledge transfer across a number of language-specific KGs.KEnS embeds all KGs in a shared embedding space, where the association of entities is captured based on self-learning. Then, KEnS performs ensemble inference to com-bine prediction results from multiple language-specific embeddings, for which multiple en-semble techniques are investigated. Experiments on the basis of five real-world language-specific KGs show that, by effectively identifying and leveraging complementary knowledge, KEnS consistently improves state-of-the-art methods on KG completion.