entity predictor.tex (1461B)
1 \begin{frame}{Entity Predictors}% 2 \begin{block}{Hybrid \parencite{vae_re}}% 3 \(\psi(e_1, r, e_2) = \psi_\text{SP}(e_1, r, e_2) + \psi_\text{RESCAL}(e_1, r, e_2)\) 4 5 \bigskip 6 7 \(P(e_1 \mid r, e_2) = \displaystyle \frac{\exp \psi(e_1, r, e_2)}{\sum_{e'\in\entitySet} \exp \psi(e', r, e_2)} \) 8 \end{block}% 9 \begin{columns}[T]% 10 \begin{column}{6.5cm}% 11 \begin{block}{Selectional Preferences}% 12 \(\psi_\text{SP}(e_1, r, e_2) = \vctr{u}_{e_1}\transpose \vctr{a}_r + \vctr{u}_{e_2}\transpose \vctr{b}_r\) 13 14 \medskip 15 16 \(\mtrx{U}\in\symbb{R}^{\entitySet\times d}\) entity embeddings\\ 17 \(\mtrx{A}, \mtrx{B}\in\symbb{R}^{\relationSet\times d}\) relation embeddings 18 \end{block}% 19 \end{column}% 20 \begin{column}{6.5cm}% 21 \begin{block}{RESCAL}% 22 \(\psi_\text{RESCAL}(e_1, r, e_2) = \vctr{u}_{e_1}\transpose \mtrx{C}_r \vctr{u}_{e_2}\) 23 24 \medskip 25 26 \(\mtrx{U}\in\symbb{R}^{\entitySet\times d}\) entity embeddings\\ 27 \(\tnsr{C}\in\symbb{R}^{\relationSet\times d\times d}\) relation embeddings 28 \end{block}% 29 \end{column}% 30 \end{columns}% 31 \vspace*{1cm} 32 \begin{tikzpicture}[remember picture, overlay] 33 \node[anchor=south east, xshift=-1cm] at (current page.south east) {\(\displaystyle 34 \overbrace{P(e_{-i} \mid s, e_i)}^{\text{fill-in-the-blank}} 35 = \sum_{r\in\relationSet} \overbrace{P(r\mid s)}^{\text{classifier}} 36 \alert{\overbrace{P(e_{-i} \mid r, e_i)}^{\text{entity predictor}}} 37 \)}; 38 \end{tikzpicture} 39 \end{frame}