/
02a-energy.tex
345 lines (288 loc) · 15.9 KB
/
02a-energy.tex
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% https://tex.stackexchange.com/questions/124269/energy-level-diagrams-with-tex
\tikzset{
level/.style = {
ultra thick,
},
connect/.style = {
dashed,
red
},
notice/.style = {
draw,
rectangle callout,
callout relative pointer={#1}
},
label/.style = {
text width=2cm
}
}
% EM ALGORITHM SLIDES
\begin{frame}
\centering
\hspace{-0.7cm}
\only<1|handout:0>{\begin{minipage}{.49\textwidth}
% EM Algorithm
\begin{tikzpicture}[scale=0.95]
% Draw all levels
\draw[draw=none] (0,8) -- node[above] {EM Algorithm} (5,8); % new top
\draw[level,colred] (0,6.5) -- node[above] {} node[below] {} (5,6.5); % top
\draw[level,colblu] (0,3.25) -- node[above] {} node[below] {} (2.5,3.25); % mid
\draw[level] (0,0) -- node[above] {} (5,0); % bottom
% Draw arrows
\draw[<->,very thick] (0.75,3.25) -- node[left] {$\KL(q\Vert p)$} (0.75,6.5);
\draw[<->,very thick] (1.75,0) -- node[left] {$\cL(q;\theta^{\text{old}})$} (1.75,3.25);
\draw[<->,very thick] (3.5,0) -- node[right] {$\log p(y;\theta^{\text{old}})$} (3.5,6.5);
\end{tikzpicture}
\end{minipage}
\begin{minipage}{.49\textwidth}
% Variational Inference
\begin{tikzpicture}[scale=0.95,opacity=0.25]
% Draw all levels
\draw[draw=none] (0,8) -- node[above] {Variational Inference} (5,8); % new top
\draw[level,colred] (0,6.5) -- node[above] {} node[below] {} (5,6.5); % top
\draw[level,colblu] (0,3.25) -- node[above] {} node[below] {} (2.5,3.25); % mid
\draw[level] (0,0) -- node[above] {} (5,0); % bottom
% Draw arrows
\draw[<->,very thick] (0.75,3.25) -- node[left] {$\KL(q\Vert p)$} (0.75,6.5);
\draw[<->,very thick] (1.75,0) -- node[left] {$\cL(q;\theta^{\text{old}})$} (1.75,3.25);
\draw[<->,very thick] (3.5,0) -- node[right] {$\log p(y;\theta^{\text{old}})$} (3.5,6.5);
\end{tikzpicture}
\end{minipage}}
\only<2|handout:0>{\begin{minipage}{.49\textwidth}
% EM Algorithm
\begin{tikzpicture}[scale=0.95]
% Draw all levels
\draw[draw=none] (0,8) -- node[above] {EM (E-step)} (5,8); % new top
\draw[level,colred] (0,6.5) -- node[above] {} node[below] {} (5,6.5); % top
\draw[level,colblu,dashed] (0,3.25) -- node[above] {} node[below] {} (2.5,3.25); % mid
\draw[level] (0,0) -- node[above] {} (5,0); % bottom
% Draw arrows
\draw[<->,very thick,opacity=0] (0.75,3.25) -- node[left] {$\KL(q\Vert p)$} (0.75,6.5);
\draw[<->,very thick] (3.5,0) -- node[right] {$\log p(y;\theta^{\text{old}})$} (3.5,6.5);
% E-step
\draw[level,colblu] (0,6.5) -- node[above] {$\color{black} \KL(\tilde q\Vert p) = 0$} (2.5,6.5); % top
\draw[->,very thick,colblu] (2,3.25) -- node[left] {} (2,6.5);
\draw[<->,very thick] (1.25,0) -- node[left,yshift=-33] {$\cL(\tilde q;\theta^{\text{old}})$} (1.25,6.5);
\end{tikzpicture}
\end{minipage}
\begin{minipage}{.49\textwidth}
% Variational Inference
\begin{tikzpicture}[scale=0.95,opacity=0.25]
% Draw all levels
\draw[draw=none] (0,8) -- node[above] {VI (E-step)} (5,8); % new top
\draw[level,colred] (0,6.5) -- node[above] {} node[below] {} (5,6.5); % top
\draw[level,colblu,dashed] (0,3.25) -- node[above] {} node[below] {} (2.5,3.25); % mid
\draw[level] (0,0) -- node[above] {} (5,0); % bottom
% Draw arrows
\draw[<->,very thick] (0.75,5.25) -- node[left] {$\KL(\tilde q \Vert p)$} (0.75,6.5);
\draw[<->,very thick] (3.5,0) -- node[right] {$\log p(y;\theta^{\text{old}})$} (3.5,6.5);
% E-step
\draw[level,colblu] (0,5.25) -- node[above] {} (2.5,5.25); % new KL level
\draw[->,very thick,colblu] (2,3.25) -- node[left] {} (2,5.25); % increase in L
\draw[<->,very thick] (1.25,0) -- node[left,yshift=-33] {$\cL(\tilde q;\theta^{\text{old}})$} (1.25,5.25);
\end{tikzpicture}
\end{minipage}}
\only<3>{\begin{minipage}{.49\textwidth}
% EM Algorithm
\begin{tikzpicture}[scale=0.95]
% Draw all levels
\draw[level,colred] (0,8) -- node[above] {\color{black} EM (M-step)} (5,8); % new top
\draw[level,colblu,dashed] (0,6.5) -- node[above] {} node[below] {} (2.5,6.5); % mid
\draw[level,colred,dashed] (2.5,6.5) -- node[above] {} node[below] {} (5,6.5); % mid
\draw[level] (0,0) -- node[above] {} (5,0); % bottom
\draw[level,colblu] (0,7.25) -- node[above] {} node[below] {} (2.5,7.25); % mid
% Draw arrows
\draw[<->,very thick] (0.75,7.25) -- node[left] {$\KL(\tilde q\Vert p)$} (0.75,8);
\draw[<->,very thick] (1.25,0) -- node[left] {$\cL(\tilde q;\theta^*)$} (1.25,7.25);
\draw[<->,very thick] (3.5,0) -- node[right] {$\log p(y;\theta^*)$} (3.5,8);
\draw[->,very thick,colblu] (2,6.5) -- node[left] {} (2,7.25);
\draw[->,very thick,colred] (4.5,6.5) -- node[left] {} (4.5,8);
\end{tikzpicture}
\end{minipage}
\begin{minipage}{.49\textwidth}
% Variational Inference
\begin{tikzpicture}[scale=0.95,opacity=0.25]
% Draw all levels
\draw[level,colred] (0,8) -- node[above] {\color{black} VI (M-step)} (5,8); % new top
\draw[level,colred,dashed] (2.5,6.5) -- node[above] {} node[below] {} (5,6.5); % top
\draw[level,colblu] (0,6.5) -- node[above] {} node[below] {} (2.5,6.5); % top
\draw[level] (0,0) -- node[above] {} (5,0); % bottom
\draw[level,colblu,dashed] (0,5.25) -- node[above] {} (2.5,5.25); % new KL level
% Draw arrows
\draw[<->,very thick] (0.75,6.5) -- node[left] {$\KL(\tilde q\Vert p)$} (0.75,8);
\draw[<->,very thick] (1.25,0) -- node[left] {$\cL(\tilde q;\theta^*)$} (1.25,6.5);
\draw[<->,very thick] (3.5,0) -- node[right] {$\log p(y;\theta^*)$} (3.5,8);
\draw[->,very thick,colblu] (2,5.25) -- node[left] {} (2,6.5);
\draw[->,very thick,colred] (4.5,6.5) -- node[left] {} (4.5,8);
\end{tikzpicture}
\end{minipage}}
\end{frame}
% VARIATIONAL INFERENCE SLIDES
\begin{frame}
\centering
\hspace{-0.7cm}
\only<1|handout:0>{\begin{minipage}{.49\textwidth}
% EM Algorithm
\begin{tikzpicture}[scale=0.95,opacity=0.25]
% Draw all levels
\draw[draw=none] (0,8) -- node[above] {EM Algorithm} (5,8); % new top
\draw[level,colred] (0,6.5) -- node[above] {} node[below] {} (5,6.5); % top
\draw[level,colblu] (0,3.25) -- node[above] {} node[below] {} (2.5,3.25); % mid
\draw[level] (0,0) -- node[above] {} (5,0); % bottom
% Draw arrows
\draw[<->,very thick] (0.75,3.25) -- node[left] {$\KL(q\Vert p)$} (0.75,6.5);
\draw[<->,very thick] (1.75,0) -- node[left] {$\cL(q;\theta^{\text{old}})$} (1.75,3.25);
\draw[<->,very thick] (3.5,0) -- node[right] {$\log p(y;\theta^{\text{old}})$} (3.5,6.5);
\end{tikzpicture}
\end{minipage}
\begin{minipage}{.49\textwidth}
% Variational Inference
\begin{tikzpicture}[scale=0.95]
% Draw all levels
\draw[draw=none] (0,8) -- node[above] {Variational Inference} (5,8); % new top
\draw[level,colred] (0,6.5) -- node[above] {} node[below] {} (5,6.5); % top
\draw[level,colblu] (0,3.25) -- node[above] {} node[below] {} (2.5,3.25); % mid
\draw[level] (0,0) -- node[above] {} (5,0); % bottom
% Draw arrows
\draw[<->,very thick] (0.75,3.25) -- node[left] {$\KL(q\Vert p)$} (0.75,6.5);
\draw[<->,very thick] (1.75,0) -- node[left] {$\cL(q;\theta^{\text{old}})$} (1.75,3.25);
\draw[<->,very thick] (3.5,0) -- node[right] {$\log p(y;\theta^{\text{old}})$} (3.5,6.5);
\end{tikzpicture}
\end{minipage}}
\only<2|handout:0>{\begin{minipage}{.49\textwidth}
% EM Algorithm
\begin{tikzpicture}[scale=0.95,opacity=0.25]
% Draw all levels
\draw[draw=none] (0,8) -- node[above] {EM (E-step)} (5,8); % new top
\draw[level,colred] (0,6.5) -- node[above] {} node[below] {} (5,6.5); % top
\draw[level,colblu,dashed] (0,3.25) -- node[above] {} node[below] {} (2.5,3.25); % mid
\draw[level] (0,0) -- node[above] {} (5,0); % bottom
% Draw arrows
\draw[<->,very thick,opacity=0] (0.75,3.25) -- node[left] {$\KL(q\Vert p)$} (0.75,6.5);
\draw[<->,very thick] (3.5,0) -- node[right] {$\log p(y;\theta^{\text{old}})$} (3.5,6.5);
% E-step
\draw[level,colblu] (0,6.5) -- node[above] {$\color{black} \KL(\tilde q\Vert p) = 0$} (2.5,6.5); % top
\draw[->,very thick,colblu] (2,3.25) -- node[left] {} (2,6.5);
\draw[<->,very thick] (1.25,0) -- node[left,yshift=-33] {$\cL(\tilde q;\theta^{\text{old}})$} (1.25,6.5);
\end{tikzpicture}
\end{minipage}
\begin{minipage}{.49\textwidth}
% Variational Inference
\begin{tikzpicture}[scale=0.95]
% Draw all levels
\draw[draw=none] (0,8) -- node[above] {VI (E-step)} (5,8); % new top
\draw[level,colred] (0,6.5) -- node[above] {} node[below] {} (5,6.5); % top
\draw[level,colblu,dashed] (0,3.25) -- node[above] {} node[below] {} (2.5,3.25); % mid
\draw[level] (0,0) -- node[above] {} (5,0); % bottom
% Draw arrows
\draw[<->,very thick] (0.75,5.25) -- node[left] {$\KL(\tilde q \Vert p)$} (0.75,6.5);
\draw[<->,very thick] (3.5,0) -- node[right] {$\log p(y;\theta^{\text{old}})$} (3.5,6.5);
% E-step
\draw[level,colblu] (0,5.25) -- node[above] {} (2.5,5.25); % new KL level
\draw[->,very thick,colblu] (2,3.25) -- node[left] {} (2,5.25); % increase in L
\draw[<->,very thick] (1.25,0) -- node[left,yshift=-33] {$\cL(\tilde q;\theta^{\text{old}})$} (1.25,5.25);
\end{tikzpicture}
\end{minipage}}
\only<3|handout:0>{\begin{minipage}{.49\textwidth}
% EM Algorithm
\begin{tikzpicture}[scale=0.95,opacity=0.25]
% Draw all levels
\draw[level,colred] (0,8) -- node[above] {\color{black} EM (M-step)} (5,8); % new top
\draw[level,colblu,dashed] (0,6.5) -- node[above] {} node[below] {} (2.5,6.5); % mid
\draw[level,colred,dashed] (2.5,6.5) -- node[above] {} node[below] {} (5,6.5); % mid
\draw[level] (0,0) -- node[above] {} (5,0); % bottom
\draw[level,colblu] (0,7.25) -- node[above] {} node[below] {} (2.5,7.25); % mid
% Draw arrows
\draw[<->,very thick] (0.75,7.25) -- node[left] {$\KL(\tilde q\Vert p)$} (0.75,8);
\draw[<->,very thick] (1.25,0) -- node[left] {$\cL(\tilde q;\theta^*)$} (1.25,7.25);
\draw[<->,very thick] (3.5,0) -- node[right] {$\log p(y;\theta^*)$} (3.5,8);
\draw[->,very thick,colblu] (2,6.5) -- node[left] {} (2,7.25);
\draw[->,very thick,colred] (4.5,6.5) -- node[left] {} (4.5,8);
\end{tikzpicture}
\end{minipage}
\begin{minipage}{.49\textwidth}
% Variational Inference
\begin{tikzpicture}[scale=0.95]
% Draw all levels
\draw[level,colred] (0,8) -- node[above] {\color{black} VI (M-step)} (5,8); % new top
\draw[level,colred,dashed] (2.5,6.5) -- node[above] {} node[below] {} (5,6.5); % top
\draw[level,colblu] (0,6.5) -- node[above] {} node[below] {} (2.5,6.5); % top
\draw[level] (0,0) -- node[above] {} (5,0); % bottom
\draw[level,colblu,dashed] (0,5.25) -- node[above] {} (2.5,5.25); % new KL level
% Draw arrows
\draw[<->,very thick] (0.75,6.5) -- node[left] {$\KL(\tilde q\Vert p)$} (0.75,8);
\draw[<->,very thick] (1.25,0) -- node[left] {$\cL(\tilde q;\theta^*)$} (1.25,6.5);
\draw[<->,very thick] (3.5,0) -- node[right] {$\log p(y;\theta^*)$} (3.5,8);
\draw[->,very thick,colblu] (2,5.25) -- node[left] {} (2,6.5);
\draw[->,very thick,colred] (4.5,6.5) -- node[left] {} (4.5,8);
\end{tikzpicture}
\end{minipage}}
\only<4|handout:0>{\begin{minipage}{.49\textwidth}
% EM Algorithm
\begin{tikzpicture}[scale=0.95,opacity=0.25]
% Draw all levels
\draw[level,colred] (0,8) -- node[above] {\color{black} EM (M-step)} (5,8); % new top
\draw[level,colblu,dashed] (0,6.5) -- node[above] {} node[below] {} (2.5,6.5); % mid
\draw[level,colred,dashed] (2.5,6.5) -- node[above] {} node[below] {} (5,6.5); % mid
\draw[level] (0,0) -- node[above] {} (5,0); % bottom
\draw[level,colblu] (0,7.25) -- node[above] {} node[below] {} (2.5,7.25); % mid
% Draw arrows
\draw[<->,very thick] (0.75,7.25) -- node[left] {$\KL(\tilde q\Vert p)$} (0.75,8);
\draw[<->,very thick] (1.25,0) -- node[left] {$\cL(\tilde q;\theta^*)$} (1.25,7.25);
\draw[<->,very thick] (3.5,0) -- node[right] {$\log p(y;\theta^*)$} (3.5,8);
\draw[->,very thick,colblu] (2,6.5) -- node[left] {} (2,7.25);
\draw[->,very thick,colred] (4.5,6.5) -- node[left] {} (4.5,8);
\end{tikzpicture}
\end{minipage}
\begin{minipage}{.49\textwidth}
% Variational Inference
\begin{tikzpicture}[scale=0.95]
% Draw all levels
\draw[draw=none] (0,8) -- node[above] {\color{black} VI (M-step)} (5,8); % new top
\draw[level,colred] (0,7.25) -- node[above] {} (5,7.25); % new top
\draw[level,colred,dashed] (0,6.5) -- node[above] {} node[below] {} (5,6.5); % top
\draw[level,colblu] (0,6) -- node[above] {} node[below] {} (2.5,6); % top
\draw[level] (0,0) -- node[above] {} (5,0); % bottom
\draw[level,colblu,dashed] (0,5.25) -- node[above] {} (2.5,5.25); % new KL level
% Draw arrows
\draw[<->,very thick] (0.75,6) -- node[left,yshift=6.5] {$\KL(\tilde q\Vert p)$} (0.75,7.25);
\draw[<->,very thick] (1.25,0) -- node[left] {$\cL(\tilde q;\theta^*)$} (1.25,6);
\draw[<->,very thick] (3.5,0) -- node[right] {$\log p(y;\theta^*)$} (3.5,7.25);
\draw[->,very thick,colblu] (2,5.25) -- node[left] {} (2,6);
\draw[->,very thick,colred] (4.5,6.5) -- node[left] {} (4.5,7.25);
\end{tikzpicture}
\end{minipage}}
\only<5>{\begin{minipage}{.49\textwidth}
% EM Algorithm
\begin{tikzpicture}[scale=0.95,opacity=0.25]
% Draw all levels
\draw[level,colred] (0,8) -- node[above] {\color{black} EM (M-step)} (5,8); % new top
\draw[level,colblu,dashed] (0,6.5) -- node[above] {} node[below] {} (2.5,6.5); % mid
\draw[level,colred,dashed] (2.5,6.5) -- node[above] {} node[below] {} (5,6.5); % mid
\draw[level] (0,0) -- node[above] {} (5,0); % bottom
\draw[level,colblu] (0,7.25) -- node[above] {} node[below] {} (2.5,7.25); % mid
% Draw arrows
\draw[<->,very thick] (0.75,7.25) -- node[left] {$\KL(\tilde q\Vert p)$} (0.75,8);
\draw[<->,very thick] (1.25,0) -- node[left] {$\cL(\tilde q;\theta^*)$} (1.25,7.25);
\draw[<->,very thick] (3.5,0) -- node[right] {$\log p(y;\theta^*)$} (3.5,8);
\draw[->,very thick,colblu] (2,6.5) -- node[left] {} (2,7.25);
\draw[->,very thick,colred] (4.5,6.5) -- node[left] {} (4.5,8);
\end{tikzpicture}
\end{minipage}
\begin{minipage}{.49\textwidth}
% Variational Inference
\begin{tikzpicture}[scale=0.95]
% Draw all levels
\draw[draw=none] (0,8) -- node[above] {\color{black} VI (M-step)} (5,8); % new top
\draw[level,colred] (0,6.5) -- node[above] {} node[below] {} (5,6.5); % top
\draw[level,colblu] (0,5.8) -- node[above] {} node[below] {} (2.5,5.8); % top
\draw[level] (0,0) -- node[above] {} (5,0); % bottom
\draw[level,colblu,dashed] (0,5.25) -- node[above] {} (2.5,5.25); % new KL level
% Draw arrows
\draw[<->,very thick] (0.75,5.8) -- node[left] {$\KL(\tilde q\Vert p)$} (0.75,6.5);
\draw[<->,very thick] (1.25,0) -- node[left] {$\cL(\tilde q;\theta^*)$} (1.25,5.8);
\draw[<->,very thick] (3.5,0) -- node[right] {$\log p(y;\theta^*)$} (3.5,6.5);
\draw[->,very thick,colblu] (2,5.25) -- node[left] {} (2,5.8);
\end{tikzpicture}
\end{minipage}}
\end{frame}