106 lines
3.1 KiB
TeX
106 lines
3.1 KiB
TeX
\tikzset{
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observed/.style={circle, draw},
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partly observed/.style 2 args={draw, fill=#2, path picture={
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\fill[#1, sharp corners] (path picture bounding box.south west) -|
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(path picture bounding box.north east) -- cycle;},
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circle},
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unobserved/.style={draw, circle, fill=gray!40},
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residual/.style={draw, rectangle}
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}
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\begin{figure}[htbp!]
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\centering
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\begin{subfigure}[t]{0.48\textwidth}
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\centering
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\begin{tikzpicture}
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\node[observed] (y) {$Y$};
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\node[unobserved, above=of y] (x) {$X$};
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\node[observed, left=of x] (w) {$W$};
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\node[observed,right=of x] (z) {$Z$};
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\draw[-] (z) to (y);
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\draw[-] (z) -- (x);
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\draw[-] (x) -- (y);
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\draw[-] (x) -- (w);
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\end{tikzpicture}
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\caption{In \emph{Simulation 1a}, classifications $W$ are conditionally independent of $Y$ so a model using $W$ as a proxy for $X$ has non-differential error. \label{fig:simulation.1a}}
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\end{subfigure}
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\hfill
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\begin{subfigure}[t]{0.48\textwidth}
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\centering
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\begin{tikzpicture}
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\node[observed] (y) {$Y$};
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\node[unobserved, above=of y] (x) {$X$};
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\node[observed, left=of x] (w) {$W$};
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\node[observed,right=of x] (z) {$Z$};
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\draw[-] (z) to (y);
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\draw[-] (z) -- (x);
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\draw[-] (x) -- (y);
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\draw[-] (x) -- (w);
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\draw[-] (x) to (y);
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\draw[-] (w) -- (y);
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\end{tikzpicture}
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\caption{In \emph{Simulation 1b}, the edge from $W$ to $Y$ signifies that the automatic classifications $W$ are not conditionally independent of $Y$ given $X$, indicating differential error.
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\label{fig:simulation.1b}
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}
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\end{subfigure}
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\\
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\hfill
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\begin{subfigure}[t]{0.48\textwidth}
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\centering
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\begin{tikzpicture}
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\node[unobserved] (y) {$Y$};
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\node[observed, above=of y] (x) {$X$};
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\node[observed, right=of y] (w) {$W$};
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\node[observed,right=of x] (z) {$Z$};
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\draw[-] (z) to (y);
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\draw[-] (x) -- (y);
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\draw[-] (y) -- (w);
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\draw[-] (x) -- (z);
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\end{tikzpicture}
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\caption{In \emph{Simulation 2a}, an unbiased classifier measures the outcome. \label{fig:simulation.2a}}
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\end{subfigure} \hfill
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\begin{subfigure}[t]{0.48\textwidth}
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\centering
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\begin{tikzpicture}
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\node[unobserved] (y) {$Y$};
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\node[observed={white}{gray!40}, above=of y] (x) {$X$};
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\node[observed, right=of y] (w) {$W$};
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\node[observed,right=of x] (z) {$Z$};
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\draw[-] (x) -- (y);
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\draw[-] (z) -- (w);
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\draw[-] (y) -- (w);
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\draw[-] (x) -- (z);
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\draw[-] (z) -- (y);
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\end{tikzpicture}
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\caption{In \emph{Simulation 2b}, the edge connecting $W$ and $Z$ signifies that the predictions $W$ are not conditionally independent of $Z$ given $Y$, indicating systematic misclassification. \label{fig:simulation.2b}}
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\end{subfigure}
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\vspace{1em}
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\begin{subfigure}[t]{0.2\textwidth}
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\centering
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\begin{tikzpicture}
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\matrix [draw, below, font=\small, align=center, column sep=2\pgflinewidth, inner sep=0.4em, outer sep=0em, nodes={align=center, anchor=center}] at (current bounding box.south){
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\node[observed,label=right:observed] {}; \\
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\node[unobserved,label=right:automatically classified]{}; \\
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};
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\end{tikzpicture}
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\end{subfigure}
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\caption{
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Bayesnet networks representing the conditional independence structure of our simulations. \label{bayesnets}
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}
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\end{figure}
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