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diff --git a/aied2018/presentation/rules.tex b/aied2018/presentation/rules.tex index fd53f9b..040ad72 100644 --- a/aied2018/presentation/rules.tex +++ b/aied2018/presentation/rules.tex @@ -1,34 +1,103 @@ +\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 n-rules:} \begin{itemize} - \item classification accuracy of each rule must exceed 90\%, because we deem a 10\% false-positive error as acceptable; - \item each term in the condition of a rule must be significant according to the likelihood test, meaning that each pattern in the condition part is indeed relevant (we set the significance threshold to p=0.05); - \item a condition can have at most 3 patterns; and - \item each rule must cover at least 5 distinct programs -- to avoid learning redundant rules representing the same error. - \end{itemize} + \item \textsf{P64 ⇒ incorrect } (covers 22) + \item \textsf{P2 ∧ P70 ⇒ incorrect} (covers 17) + \end{itemize} -\begin{table}[t] - \caption{Solving statistics, classification accuracy, and coverage of rules for several introductory Python problems. The second column shows the number of users attempting the problem. Columns 3 and 4 show the number of all / correct submissions. The next two columns show the classification accuracy for the majority and random-forest classifiers. The last three columns show percentages of covered examples: columns $n_p$ and $n$ give covered incorrect programs (n-rules with presence of patterns and all n-rules), and column $p$ gives the percentage of correct programs covered by p-rules.} - \centering - \begin{tabular}{l|c|cc|cc|ccc} - & & \multicolumn{2}{c|}{\textbf{Submissions}} & \multicolumn{2}{c|}{\textbf{CA}} & \multicolumn{3}{c}{\textbf{Coverage}} \\ - \textbf{Problem} & \textbf{Users} & Total & Correct & Maj & RF & $n_p$ & $n$ & $p$ \\ + \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{fahrenheit\_to\_celsius}& 521 & 1177 & 495 & 0.579 & 0.933 & 0.708 & 0.935 & 0.867 \\ - %\textsf{pythagorean\_theorem}& 349 & 669 & 317 & 0.499 & 0.809 \\ - \textsf{ballistics}& 248 & 873 & 209 & 0.761 & 0.802 & 0.551 & 0.666 & 0.478 \\ - \textsf{average}& 209 & 482 & 186 & 0.614 & 0.830 & 0.230 & 0.338 & 0.618 \\ + \textsf{F2C}& 0.579 & 0.933 \\ + \textsf{ballistics}& 0.761 & 0.802 \\ + \textsf{average}& 0.614 & 0.830 \\ \hline - \textsf{buy\_five}& 294 & 476 & 292 & 0.613 & 0.828 & 0.234 & 0.489 & 0.719 \\ - \textsf{competition}& 227 & 327 & 230 & 0.703 & 0.847 & 0.361 & 0.515 & 0.896 \\ - \textsf{top\_shop}& 142 & 476 & 133 & 0.721 & 0.758 & 0.399 & 0.802 & 0.444 \\ - \textsf{minimax}& 74 & 163 & 57 & 0.650 & 0.644 & 0.462 & 0.745 & 0.298 \\ - \textsf{checking\_account}& 132 & 234 & 112 & 0.521 & 0.744 & 0.143 & 0.491 & 0.115\\ - \textsf{consumers\_anon}& 65 & 170 & 53 & 0.688 & 0.800 & 0.376 & 0.880 & 0.623 \\ + \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}& 70 & 142 & 83 & 0.585 & 0.859 & 0.492 & 0.746 & 0.880\\ - \textsf{greatest\_abs}& 58 & 155 & 57 & 0.632 & 0.845 & 0.612 & 0.878 & 0.789 \\ - \textsf{greatest\_neg}& 62 & 195 & 71 & 0.636 & 0.815 & 0.621 & 0.960 & 0.718 \\ + \textsf{greatest}& 0.585 & 0.859 \\ + \textsf{greatest\_abs}& 0.632 & 0.845 \\ + \textsf{greatest\_neg}& 0.636 & 0.815 \\ \hline - Total / average & 2102 & 4811 & 1978 & 0.642 & 0.809 & 0.432 & 0.704 & 0.620 \\ - \end{tabular} - \label{tab:stats} -\end{table}
\ No newline at end of file + 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} + + |