Paper总结 - KB2E: Learning to represent knowledge graphs with Gaussian embedding

$$\mathcal{P}_{h} \sim \mathcal{N}\left(\boldsymbol{\mu}_{h}, \boldsymbol{\Sigma}_{h}\right)$$

$$\mathcal{P}_{r} \sim \mathcal{N}\left(\boldsymbol{\mu}_{r}, \boldsymbol{\Sigma}_{r}\right)$$

$$\mathcal{P}_{t} \sim \mathcal{N}\left(\boldsymbol{\mu}_{t}, \boldsymbol{\Sigma}_{t}\right)$$

$$P_{e} \sim N\left(u_{n}-u_{t}, \Sigma_{n}+\Sigma_{r}\right) \quad P_{r} \sim N\left(u_{r}, \Sigma_{r}\right)$$

Then, they use two method to model the similarity of $$P_e$$ and $$P_r$$.

Loss function：

$$\mathcal{L}=\sum_{(h, r, t) \in \Gamma} \sum_{\left(h^{\prime}, r^{\prime}, t^{\prime}\right) \in \Gamma_{(h, r, t)}^{\prime}}\left[\mathcal{E}(h, r, t)+\gamma-\mathcal{E}\left(h^{\prime}, r^{\prime}, t^{\prime}\right)\right]_{+}$$