80 lines
3.1 KiB
TeX
80 lines
3.1 KiB
TeX
\section{Algorithm}
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\begin{itemize}
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\item[] // notation
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\item $n$ features ${\cal{X}} = \{X_1, \dots, X_n\}$ and the class $Y$
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\item $m$ instances.
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\item $D = \{ (x_1^i, \dots, x_n^i, y^i) \}_{i=1}^{m}$
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\item $W$ a weights vector. $W_0$ are the initial weights.
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\item $D[W]$ dataset with weights $W$ for the instances.
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\end{itemize}
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\bigskip
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\begin{enumerate}
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\item[] // initialization
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\item $W_0 \leftarrow (w_1, \dots, w_m) \leftarrow 1/m$
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\item $W \leftarrow W_0$
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\item $Vars \leftarrow {\cal{X}}$
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\item $\delta \leftarrow 10^{-4}$
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\item $convergence \leftarrow True$ // hyperparameter
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\item $maxTolerancia \leftarrow 3$ // hyperparameter
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\item $bisection \leftarrow False$ // hyperparameter
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\item $finished \leftarrow False$
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\item $AODE \leftarrow \emptyset$ \hspace*{2cm} // the ensemble
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\item $tolerance \leftarrow 0$
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\item $numModelsInPack \leftarrow 0$
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\item $maxAccuracy \leftarrow -1$
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\item[]
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\newpage
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\item[] // main loop
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\item While $(\lnot finished)$
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\begin{enumerate}
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\item $\pi \leftarrow SortFeatures(Vars, criterio, D[W])$
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\item $k \leftarrow 2^{tolerance}$
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\item if ($tolerance == 0$) $numItemsPack \leftarrow0$
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\item $P \leftarrow Head(\pi,k)$ \hspace*{2cm} // first k features in order
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\item $spodes \leftarrow \emptyset$
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\item $i \leftarrow 0$
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\item While ($ i < size(P)$)
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\begin{enumerate}
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\item $X \leftarrow P[i]$
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\item $i \leftarrow i + 1$
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\item $numItemsPack \leftarrow numItemsPack + 1$
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\item $Vars.remove(X)$
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\item $spode \leftarrow BuildSpode(X, {\cal{X}}, D[W])$
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\item $\hat{y}[] \leftarrow spode.Predict(D)$
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\item $\epsilon \leftarrow error(\hat{y}[], y[])$
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\item $\alpha \leftarrow \frac{1}{2} ln \left ( \frac{1-\epsilon}{\epsilon} \right )$
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\item if ($\epsilon > 0.5$)
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\begin{enumerate}
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\item $finished \leftarrow True$
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\item break
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\end{enumerate}
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\item $spodes.add( (spode,\alpha_t) )$
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\item $W \leftarrow UpdateWeights(W,\alpha,y[],\hat{y}[])$
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\end{enumerate}
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\item $AODE.add( spodes )$
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\item if ($convergence \land \lnot finished$)
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\begin{enumerate}
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\item $\hat{y}[] \leftarrow AODE.Predict(D)$
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\item $actualAccuracy \leftarrow accuracy(\hat{y}[], y[])$
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\item $if (maxAccuracy == -1)\; maxAccuracy \leftarrow actualAccuracy$
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\item if $((accuracy - maxAccuracy) < \delta)$\hspace*{2cm} // result doesn't improve enough
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\begin{enumerate}
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\item $tolerance \leftarrow tolerance + 1$
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\end{enumerate}
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\item else
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\begin{enumerate}
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\item $tolerance \leftarrow 0$
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\item $numItemsPack \leftarrow 0$
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\end{enumerate}
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\end{enumerate}
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\item If $(Vars == \emptyset \lor tolerance>maxTolerance) \; finished \leftarrow True$
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\item $lastAccuracy \leftarrow max(lastAccuracy, actualAccuracy)$
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\end{enumerate}
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\item if ($tolerance > maxTolerance$) \hspace*{1cm} // algorithm finished because of lack of convergence
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\begin{enumerate}
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\item $removeModels(AODE, numItemsPack)$
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\end{enumerate}
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\item Return $AODE$
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\end{enumerate} |