Knowledge Graph Completion

MEI introduces the multi-partition embedding interaction technique with block term tensor format to systematically address the efficiency--expressiveness trade-off in knowledge graph embedding. It divides the embedding vector into multiple partitions and learns the local interaction patterns from data instead of using fixed special patterns as in ComplEx or SimplE models. This enables MEI to achieve optimal efficiency--expressiveness trade-off, not just being fully expressive. Previous methods such as TuckER, RESCAL, DistMult, ComplEx, and SimplE are suboptimal restricted special cases of MEI.

To avoid the problem caused by low-frequent entity-relation pairs, our MBS uses the estimated probabilities from a trained model $\mathbf{\theta}'$ to calculate frequencies for each triplet and query. By using $\mathbf{\theta}'$, the NS loss in KGE with MBS is represented as follows: \begin{align} &\ell_{mbs}(\mathbf{\theta};\mathbf{\theta}') \nonumber \ =&-\frac{1}{|D|}\sum_{(x,y) \in D} \Bigl[A_{mbs}(\mathbf{\theta}')\log(\sigma(s_{\mathbf{\theta}}(x,y)+\gamma))\nonumber\ &+\frac{1}{\nu}sum_{y_{i}\sim p_n(y_{i}|x)}^{\nu}B_{mbs}(\mathbf{\theta}')\log(\sigma(-s_{\mathbf{\theta}}(x,y_i)-\gamma))\Bigr], \end{align}

Graph Path Feature Learning is a probabilistic rule learner optimized to mine instantiated first-order logic rules from knowledge graphs. Instantiated rules contain constants extracted from KGs. Compared to abstract rules that contain no constants, instantiated rules are capable of explaining and expressing concepts in more detail. GPFL utilizes a novel two-stage rule generation mechanism that first generalizes extracted paths into templates that are acyclic abstract rules until a certain degree of template saturation is achieved, then specializes the generated templates into instantiated rules.

CP with N3 Regularizer and Relation Prediction

ComplEx model trained with a nuclear norm regularizer; A relation prediction objective is added on top of the commonly used 1vsAll objective.

RESCAL model trained with a relation prediction objective on top of the 1vsAll loss

TuckER model trained with a relation prediction objective on top of the 1vsAll loss