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\textbf{The dataset}
\begin{columns}
\begin{column}{0.40\textwidth}
\begin{tabular}{l|rrrr|l}
& $P_1$ & $P_2$ & $P_3$ & $\ldots$ & class \\
\hline
$S_1$ & 0 & 1 & 1 & $\ldots$ & $correct$ \\
$S_2$ & 1 & 0 & 0 & $\ldots$ & $correct$ \\
$S_3$ & 1 & 1 & 0 & $\ldots$ & $incorrect$ \\
$\vdotswithin{S_4}$ & & $\vdotswithin{1}$ & & & $\vdotswithin{correct}$ \\
\end{tabular}
\end{column}
\begin{column}{0.60\textwidth}
\begin{itemize}
\item Each submission ($S_1, S_2, S_3, \ldots$) becomes a learning instance.
\item Each constructed pattern ($P_1, P_2, P_3, \ldots$) is a binary feature.
\item Based on test results each submission is classified either as $correct$ or $incorrect$
\end{itemize}
\end{column}
\end{columns}
\vspace{1cm}
\begin{columns}
\begin{column}{0.01\textwidth}
\end{column}
\begin{column}{0.59\textwidth}
\textbf{Characterizing typical approaches and errors with rule learning}
\begin{itemize}
\item \emph{n-rules} describe buggy patterns: \\IF $condition$ THEN $incorrect$.
\item \emph{p-rules} describe necessary patterns for programs to be correct: \\IF $condition$ THEN $correct$.
\end{itemize}
\vspace{0.5cm}
\textbf{Example:} Implement a function that returns the element with the largest absolute value.
\begin{itemize}
\item 155 submissions (57 correct, 98 incorrect)
\item 8298 patterns, 15 n-rules and 6 p-rules.
\end{itemize}
\textbf{Correct solution:}
\begin{Verbatim}
\textbf{def} max_abs(l):
vmax = l[0]
\textbf{for} v \textbf{in} l:
\textbf{if} abs(v) > abs(vmax):
vmax = v
\textbf{return} vmax
\end{Verbatim}
\vspace{0.5cm}
\textbf{Two sample learned n-rules:}
\begin{itemize}
\item \textsf{P64 ⇒ incorrect } (covers 22)
\item \textsf{P2 ∧ P70 ⇒ incorrect} (covers 17)
\end{itemize}
\end{column}
\begin{column}{0.40\textwidth}
\fbox{
\begin{minipage}[t]{0.94\textwidth}
\textbf{How useful are patterns?}
\begin{itemize}
\item Compare accuracies of Random Forest and Majority Classifier.
\item Three types of exercises (basic, loops, functions)
\end{itemize}
\vspace{1cm}
\begin{center}
\begin{tabular}{l|rr}
\textbf{Problem} & Maj & RF \\
\hline
\textsf{F2C}& 0.579 & 0.933 \\
\textsf{ballistics}& 0.761 & 0.802 \\
\textsf{average}& 0.614 & 0.830 \\
\hline
\textsf{buy\_five}& 0.613 & 0.828 \\
\textsf{competition}& 0.703 & 0.847 \\
\textsf{top\_shop}& 0.721 & 0.758 \\
\textsf{minimax}& 0.650 & 0.644 \\
\textsf{ch\_account}& 0.521 & 0.744 \\
\textsf{con\_anon}& 0.688 & 0.800 \\
\hline
\textsf{greatest}& 0.585 & 0.859 \\
\textsf{greatest\_abs}& 0.632 & 0.845 \\
\textsf{greatest\_neg}& 0.636 & 0.815 \\
\hline
Average & 0.642 & 0.809 \\
\end{tabular}
\end{center}
\end{minipage}}
\end{column}
\end{columns}
\vspace{1.0cm}
\textbf{Vizualizations of patterns}; left program contains pattern \textsf{P64}, right program contains pattern \textsf{P2} (red) and \textsf{P70} (blue) that matches the call to \textsf{abs} in an assignment statement nested within a for loop and an if clause.
\begin{Verbatim}
\textbf{def} max_abs(l): \textbf{def} max_abs(l):
vmax = 0 vmax = None
\textbf{for} i \textbf{in} range(len(l)): \textbf{for} v \textbf{in} l:
\textbf{if} \blue{vmax} < abs(l[i]): \textbf{if} vmax==None or vmax<v:
vmax = l[i] \red{vmax} = \blue{abs}(v)
\textbf{return} \blue{vmax} \textbf{return} \red{vmax}
\end{Verbatim}
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