counting.tex (690B)
1 \begin{frame}{Proof of Principle: Counting Paths} 2 \begin{block}{Proposition} 3 Given the \alert{path} \raisebox{-0.6em}{\input{mainmatter/graph/3-path.tex}} we expect \(\rndm{r}_1 \notindependent \rndm{r}_2 \notindependent \rndm{r}_3\). 4 \end{block} 5 \begin{block}{Goal} 6 Compute the mutual information \(\operatorname{I}(\rndm{r}_2; \rndm{r}_1, \rndm{r}_3)\) 7 \end{block} 8 \pause 9 \begin{block}{Path Counting Algorithm} 10 We can (slowly) sample \alert{walks} using power of the adjacency matrix. 11 12 \begin{enumerate} 13 \item Sample a walk by chaining neighbors 14 \item Reject non-path 15 \item Count the accepted paths weighted by importance 16 \end{enumerate} 17 \end{block} 18 \end{frame}