statistics.tex (2176B)
1 \begin{frame}{Proof of Principle: Path Statistics} 2 \begin{block}{Path Frequency} 3 \footnotesize% 4 \vspace*{2mm}% 5 \begin{center}% 6 \begin{tabular}{@{}r c c@{}} 7 \toprule 8 Frequency & Relation Surface forms & Relation Identifiers \\ 9 \midrule 10 31.696‰ & \(\textsl{country} \relationComposition \textsl{diplomatic relation} \relationComposition \widebreve{\textsl{citizen of}}\) & \(\wdrel{17} \relationComposition \wdrel{530} \relationComposition \Pwidebreve{\wdrel{27}}\) \\ 11 \bottomrule 12 \end{tabular}% 13 \end{center}% 14 Example of path:\\ 15 \begin{tikzpicture} 16 \matrix[matrix of nodes, column sep=2.6cm, ampersand replacement=\&]{ 17 \node (vat phou) {Vat Phou}; \& 18 \node (laos) {Laos}; \& 19 \node (japan) {Japan}; \& 20 \node (souseki) {Natsume Sōseki}; \\ 21 }; 22 23 \draw[arrow] (vat phou) -- (laos) node[midway, above] {\tiny\strut\uhead{Vat Phou} is a ruined Khmer…}; 24 \draw[arrow] (laos) -- (japan) node[midway, above] {\tiny\strut …\vphantom{\uhead{x}}the historical relationship between…}; 25 \draw[arrow] (souseki) -- (japan) node[midway, above] {\tiny\strut\uhead{Sōseki} was a \utail{Japanese} novelist}; 26 % country 27 % diplomatic relation 28 % REV(citizen of) 29 \end{tikzpicture}% 30 \end{block} 31 \pause 32 \begin{block}{Summary Statistics} 33 \unskipdisplay 34 \begin{equation*} 35 \tikzmarknode{statistics-m1}{\operatorname{I}(\rndm{r}_2; \rndm{r}_1, \rndm{r}_3)} 36 = 37 \tikzmarknode{statistics-m2}{\expectation_{r_1, r_3}[\entropy_{P(\rndm{r}_2)}(\rndm{r}_2\mid r_1, r_3)]} 38 - 39 \tikzmarknode{statistics-m3}{\entropy(\rndm{r}_2\mid\rndm{r}_1,\rndm{r}_3)} 40 \end{equation*} 41 \begin{tikzpicture}[remember picture, overlay] 42 \node[below=1mm of statistics-m1] (statistics-e1) {\rotatebox{90}{\(\approx\)}}; 43 \node (statistics-e2) at (statistics-e1-|statistics-m2) {\rotatebox{90}{\(\approx\)}}; 44 \node (statistics-e3) at (statistics-e1-|statistics-m3) {\rotatebox{90}{\(\approx\)}}; 45 46 \node[below=-1mm of statistics-e1] {6.95 bits}; 47 \node[below=-1mm of statistics-e2] {8.01 bits}; 48 \node[below=-1mm of statistics-e3] {1.06 bits}; 49 \end{tikzpicture} 50 \vspace*{7mm} 51 \end{block} 52 \end{frame}