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diff --git a/aied2018/presentation/rules.tex b/aied2018/presentation/rules.tex index f2a31c7..b974530 100644 --- a/aied2018/presentation/rules.tex +++ b/aied2018/presentation/rules.tex @@ -1,8 +1,14 @@ \textbf{The dataset} \begin{columns} +\begin{column}{0.50\textwidth} + \begin{itemize} + \item $S_i$: submitted programs + \item $P_i$: patterns (binary features) + \item each submission is classified either as $correct$ or $incorrect$ based on test cases + \end{itemize} +\end{column} \begin{column}{0.40\textwidth} - \begin{tabular}{l|rrrr|l} & $P_1$ & $P_2$ & $P_3$ & $\ldots$ & class \\ \hline @@ -12,98 +18,121 @@ $S_3$ & 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{2cm} +\vspace{1cm} + +\textbf{Characterizing errors and solutions} +\vspace{0.5cm} +Induce rules to predict whether a program is correct (\emph{p-rules}) or not (\emph{n-rules}) based on patterns that appear in it. + +\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: Greatest Absolutist} - \begin{itemize} - \item 155 submissions (57 correct, 98 incorrect) - \item 8298 patterns, 15 n-rules and 6 p-rules - \end{itemize} - \underline{\smash{A solution:}} - \begin{Verbatim} + \begin{column}{0.42\textwidth} + \textbf{\emph{n-rules}} describe errors: \\IF $P_1 \land \ldots \land P_k$ THEN $incorrect$ + \end{column} + \begin{column}{0.50\textwidth} + \textbf{\emph{p-rules}} describe alternative solutions: \\IF $P_1 \land \ldots \land P_k$ THEN $correct$ + \end{column} +\end{columns} + +\vspace{1.5cm} + +\begin{columns}[T] + \begin{column}{0.58\textwidth} +\textbf{Example: Greatest Absolutist} + +\vspace{0.5cm} +Find element with the largest absolue value. + +\vspace{0.5cm} +\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} - \underline{\smash{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} - \vspace{0.5cm} - \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{0.5cm} - \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{1.5cm} -\underline{\smash{Vizualizations of rules / patterns}} +\end{Verbatim} + +\vspace{0.5cm} +We collected 155 submissions for this problem. Using extracted patterns our approach induced 15~n-rules and 6~p-rules. + +\vspace{1cm} +\underline{\smash{Example n-rules}} + +\vspace{0.5cm} \begin{itemize} - \item \textsf{P64} (blue left) matches functions returning variable compared in the \textsf{if} clause. - \item \textsf{P2} (red right) matches functions that return the variable used in an assignment statement within a for-if block; \textsf{P70} (blue) matches the call to \textsf{abs} in an assignment statement nested within a for loop and an if clause. + \item \textsf{\green{$P_G$} ⇒ incorrect } (covers 22) + \item \textsf{$\red{P_R} ∧ \blue{P_B}$ ⇒ incorrect} (covers 17) \end{itemize} + +\end{column} + +\begin{column}{0.35\textwidth} + \textbf{Results} + + \vspace{0.5cm} + + \fbox{ + \begin{minipage}[t]{0.99\textwidth} + \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{2cm} +\underline{\smash{Vizualizing rules / patterns}} + +\begin{columns} +\begin{column}{0.4\textwidth} \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} +\textbf{def} max_abs(l): + vmax = 0 + \textbf{for} i \textbf{in} range(len(l)): + \textbf{if} \textbf{\green{vmax}} < abs(l[i]): + vmax = l[i] + \textbf{return} \textbf{\green{vmax}} \end{Verbatim} +\end{column} +\begin{column}{0.55\textwidth} +\begin{Verbatim} +\textbf{def} max_abs(l): + vmax = None + \textbf{for} v \textbf{in} l: + \textbf{if} vmax==None \textbf{or} vmax<v: + \textbf{\red{vmax}} = \textbf{\blue{abs}}(v) + \textbf{return} \textbf{\red{vmax}} +\end{Verbatim} +\end{column} +\end{columns} + +\vspace{1.5cm} +\textbf{Evaluation.} +We evaluated this approach on exercises covering introduction to Python, loops and functions, +by comparing the classification accuracy of a random-forest classifier based on patterns to the majority classifier. %\begin{Verbatim} %\textbf{def} max_abs(l): \textbf{def} max_abs(l): |