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\samepage \begin{displaymath}CU(C_k)=P(C_k)\sum_i\sum_j\lbrack P(A_i=V_{ij}|C_k)^2 -
P(A_i=V_{ij})^2\rbrack,\end{displaymath}
}

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{\newpage
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\samepage \begin{figure}%
\vspace*{1.0in}

\label{tree-example}
\end{figure}
}

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\samepage \begin{figure}%
\vspace*{1.0in}

\label{up-tree-example}
\end{figure}
}

\stepcounter{subsection}
{\newpage
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\samepage \begin{table}\centering
\begin{tabbing}
Fu\=nction ORDER(Root)\\ 
\> If \= Root is a leaf Then Return(observations covered by Root)\\ 
\>\> Else \= Order \= children of Root from those covering the most\\ 
\>\>\>\>       observations to those covering the least.\\ 
\>\>\>      For each child, $C_k$, of Root (in order) Do $L_k$ $\leftarrow$ ORDER($C_k$)\\ 
\>\>\>      $L$ $\leftarrow$ MERGE(\{$L_k|$list of objects constructed by ORDER($C_k$)\})\\ 
\>\>\>      Return($L$)

\end{tabbing}
 
\label{order}
\end{table}
}

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{\newpage
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\samepage \begin{figure}%
\vspace*{1.0in}

\label{hier-opt}
\end{figure}
}

\stepcounter{subsection}
{\newpage
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\samepage \begin{table}\centering
\begin{tabular}{ll|l|l|}
\\ 
&                   &Random        &Similarity\\  \cline{2-4}\cline{2-4}
&sort               &1.53 (0.11) &1.08 (0.18) \\  \cline{3-4}
Soybean (small) &reorder/resort     &1.61 (0.02) &1.56 (0.08) \\  \cline{3-4}
(47 obs, 36 vars) &iter. redist.      &1.54 (0.10) &1.34 (0.20) \\  \cline{3-4}
&hier. redist.      &1.60 (0.05) &1.50 (0.08) \\  \cline{2-4}\cline{2-4}
&sort               &0.89 (0.08) &0.66 (0.14) \\  \cline{3-4}
Soybean (large) &reorder/resort     &0.97 (0.04) &0.96 (0.05) \\  \cline{3-4}
(307 obs, 36 vars) &iter. redist.      &0.92 (0.07) &0.84 (0.10) \\  \cline{3-4}
&hier. redist.      &1.06 (0.02) &1.06 (0.01) \\  \cline{2-4}\cline{2-4}
&sort               &1.22 (0.30) &0.83 (0.16) \\  \cline{3-4}
House &reorder/resort     &1.66 (0.09) &1.57 (0.18) \\  \cline{3-4}
(435 obs, 17 vars) &iter. redist.      &1.24 (0.28) &1.06 (0.19) \\  \cline{3-4}
&hier. redist.      &1.68 (0.00) &1.68 (0.00) \\  \cline{2-4}\cline{2-4}
&sort               &1.10 (0.13) &0.73 (0.22) \\  \cline{3-4}
Mushroom &reorder/resort     &1.10 (0.08) &1.16 (0.08) \\  \cline{3-4}
(1000 obs, 23 vars) &iter. redist.      &1.10 (0.12) &0.95 (0.19) \\  \cline{3-4}
&hier. redist.      &1.27 (0.00) &1.24 (0.10) \\  \cline{2-4}\cline{2-4}
\end{tabular}

\label{experiments}
\end{table}
}

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{\newpage
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\samepage \begin{table}\centering
\begin{tabular}{l|l|l||l|l|} 

&\multicolumn{2}{c}{Random} &\multicolumn{2}{c}{Similarity} \\  
                &height 2    &height 4     &height 2 &height 4 \\  \hline\hline
Soybean (small) &1.60 (0.05) &1.62 (0.00) &1.50 (0.08) &1.62 (0.00)\\  \hline 
Soybean (large) &1.06 (0.02) &1.07 (0.02) &1.06 (0.01) &1.07 (0.01)\\  \hline 
House           &1.68 (0.00) &1.68 ($0.0\overline{0}$) &1.68 (0.00) &1.68 ($0.0\overline{0}$) \\  \hline
Mushroom        &1.27 (0.00)   &1.27 (0.00) &1.24 (0.10) &1.27 (0.00)\\  \hline 
\end{tabular}

\label{dep4}
\end{table}
}

{\newpage
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\samepage \begin{table}\centering
\begin{tabular}{ll|l|l|}
\\ 
&                   &Random        &Similarity\\  \cline{2-4}\cline{2-4}
&sort               &6.98 (1.43) &7.21 (1.31) \\  \cline{3-4}
Soybean (small) &reorder/resort     &14.82 (2.60) &18.27 (6.00) \\  \cline{3-4}
(47 obs, 36 vars) &iter. redist.      &9.00 (5.94) &15.51 (7.72) \\  \cline{3-4}
&hier. redist.      &6.99 (1.28) &8.87 (3.58) \\  \cline{2-4}\cline{2-4}
&sort               &50.62 (6.11) &54.09 (13.25) \\  \cline{3-4}
Soybean (large) &reorder/resort     &141.36 (46.99) &153.22 (43.59) \\  \cline{3-4}
(307 obs, 36 vars) &iter. redist.   &166.53 (55.53) &307.59 (160.66) \\  \cline{3-4}
&hier. redist.      &79.00 (19.23) &87.27 (19.64) \\  \cline{2-4}\cline{2-4}
&sort               &34.99 (7.55) &39.15 (7.60) \\  \cline{3-4}
House &reorder/resort     &87.78 (23.94) &97.63 (29.54) \\  \cline{3-4}
(435 obs, 17 vars) &iter. redist. &177.75 (94.53) &320.43 (124.78) \\  \cline{3-4}
&hier. redist.      &55.90 (11.92) &73.54 (10.05) \\  \cline{2-4}\cline{2-4}
&sort               &111.47 (19.19) &119.33 (25.86) \\  \cline{3-4}
Mushroom &reorder/resort     &301.34 (100.56) &391.80 (211.54) \\  \cline{3-4}
(1000 obs, 23 vars) &iter. redist.      &162.58 (85.20) &390.11 (191.62) \\  \cline{3-4}
&hier. redist.      &91.87 (29.50) &151.45 (48.89) \\  \cline{2-4}\cline{2-4}
\end{tabular}

\label{time-experiments}
\end{table}
}

\stepcounter{subsection}
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\samepage \begin{table}\centering
\begin{tabular}{ll|l|l||l|l|}
\\ 
&&\multicolumn{2}{c}{Random} &\multicolumn{2}{c}{Similarity} \\  
                &&height 2  &height 4  &height 2 &height 4 \\  \hline\hline
Soy (small) &sort  &6.98 (1.4) &18 (2) &7.21 (1.3) &21 (2)\\  
                &hier. redist. &6.99 (1.3) &94 (28) &8.87
(3.6) &133 (28) \\  \hline
Soy (large) &sort   &50.62 (6.1) &142 (10)  &54.09 (13.3) &152 (11) \\  
                &hier. redist. &79.00 (19.2) &436 (139) &87.27
(19.6) &576 (260) \\  \hline
House       &sort       &34.99 (7.6) &104 (9) &39.15 (7.6) &120 (12) \\  
            &hier. redist. &55.90 (11.9) &355 (71) &73.54
(10.1) &425 (105) \\  \hline
Mushroom    &sort    &111.47 (19.2) &407 (64) &119.33 (25.9) &443 (65) \\  
            &hier. redist. &91.87 (29.5) &1288 (458) &151.45
(48.9) &1368 (335) \\  \hline
\end{tabular}

\label{time-dep4}
\end{table}
}

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\label{frontiers}
\end{figure}
}

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\samepage \begin{table}\centering
\begin{tabular}{l|l|l|}

&Unvalidated &Validated \\  \hline\hline
Soybean (small)&&\\  \hline
Leaves   &18.00 (0.00) &13.10 (1.59)\\  \cline{2-3}
Accuracy &0.85 (0.01)&0.85 (0.01)\\  \cline{2-3}
Ave. Frontier Size &18.00 (0.00) &2.75 (1.17) \\  \hline\hline
Soybean (large) &&\\  \hline
Leaves &122.00 (0.00) &79.10 (5.80) \\  \cline{2-3}
Accuracy &0.83 (0.02) &0.83 (0.02)\\  \cline{2-3}
Ave. Frontier Size &122.00 (0.00) &17.01 (4.75) \\  \hline\hline
House&&\\  \hline
Leaves  &174.00 (0.00) &49.10 (7.18) \\  \cline{2-3}
Accuracy &0.76 (0.02) &0.81 (0.01)\\  \cline{2-3}
Ave. Frontier Size &174.00 (0.00) &9.90 (5.16) \\  \hline\hline 
Mushroom &&\\  \hline
Leaves &400.00 (0.00) &96.30 (11.79) \\  \cline{2-3}
Accuracy &0.80 (0.01) &0.82 (0.01)\\  \cline{2-3}
Ave. Frontier Size &400.00 (0.00) &11.07 (4.28) \\  \hline\hline 
\end{tabular}

\label{opt-prediction}
\end{table}
}

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\samepage \begin{table}\centering
\begin{tabular}{l|l|l||l|l|}

&\multicolumn{2}{c}{Unoptimized} &\multicolumn{2}{c}{Optimized} \\ 
&Unvalidated &Validated &Unvalidated &Validated \\  \hline\hline
Soybean (small)&&&&\\  \hline
Leaves   &18.00 (0.00) &15.35 (1.81) &18.00 (0.00) &13.10 (1.59)\\  \cline{2-5}
Accuracy &0.84 (0.18)  &0.85 (0.01) &0.85 (0.01)&0.85 (0.01)\\  \cline{2-5}
Ave. Frontier Size &18.00 (0.00) &3.97 (1.62) &18.00 (0.00) &2.75 (1.17) \\  \hline\hline
Soybean (large) &&&&\\  \hline
Leaves &122.00 (0.00) &88.55 (4.46) &122.00 (0.00) &79.10 (5.80) \\  \cline{2-5}
Accuracy &0.82 (0.02) &0.82 (0.02) &0.83 (0.02) &0.83 (0.02)\\  \cline{2-5}
Ave. Frontier Size &122.00 (0.00) &24.74 (7.52) &122.00 (0.00) &17.01 (4.75) \\  \hline\hline
House&&&&\\  \hline
Leaves  &174.00 (0.00) &68.95 (8.15) &174.00 (0.00) &49.10 (7.18) \\  \cline{2-5}
Accuracy &0.76 (0.02) &0.81 (0.02) &0.76 (0.02) &0.81 (0.01) \\  \cline{2-5}
Ave. Frontier Size &174.00 (0.00) &17.72 (7.81) &174.00 (0.00) &9.90 (5.16) \\  \hline\hline 
Mushroom &&&&\\  \hline
Leaves &400.00 (0.00) &145.50 (20.64) &400.00 (0.00) &96.30 (11.79) \\  \cline{2-5}
Accuracy &0.80 (0.01) &0.82 (0.01) &0.80 (0.01) &0.82 (0.01)\\  \cline{2-5}
Ave. Frontier Size &400.00 (0.00) &22.85 (8.75) &400.00 (0.00) &11.07 (4.28) \\  \hline\hline 
\end{tabular}

\label{prediction}
\end{table}
}

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\samepage \begin{table}\centering
\begin{tabular}{l|l|l||l|l|}

&\multicolumn{2}{c}{Unoptimized} &\multicolumn{2}{c}{Optimized} \\ 
&Unvalidated &Validated &Unvalidated &Validated \\  \hline\hline
Soybean (small)&&&&\\  \hline
Leaves   &18.00 (0.00) &15.35 (1.81) &18.00 (0.00) &13.10 (1.59)\\  \cline{2-5}
EPL      &40.90 (3.64)  &31.90 (6.94) &54.20 (4.74)&34.50 (6.49)\\  \cline{2-5}
Depth$^*$ &2.27       &2.08         &3.01         &2.63 \\  \cline{2-5}
Breadth$^*$ &3.57     &3.72         &2.61         &2.66 \\  \cline{2-5}
Cost$^*$    &8.10     &7.74         &7.86         &7.00 \\  \hline\hline
Soybean (large) &&&&\\  \hline
Leaves &122.00 (0.00) &88.55 (4.46) &122.00 (0.00) &79.10 (5.80) \\  \cline{2-5}
EPL    &437.20 (34.74) &280.40 (28.07) &657.65 (28.38) &380.65 (43.63)\\  \cline{2-5}
Depth$^*$ &3.58       &3.17         &5.39         &4.81 \\  \cline{2-5}
Breadth$^*$ &3.82     &4.11         &2.44         &2.48 \\  \cline{2-5}
Cost$^*$   &13.68     &13.03        &13.15        &11.93 \\  \hline\hline
House&&&&\\  \hline
Leaves  &174.00 (0.00) &68.95 (8.15) &174.00 (0.00) &49.10 (7.18) \\  \cline{2-5}
EPL &664.65 (41.16) &196.20 (35.32) &1005.10 (27.42) &217.25 (39.75) \\  \cline{2-5}
Depth$^*$ &3.82   &2.85            &5.78           &4.42 \\  \cline{2-5}
Breadth$^*$ &3.86 &4.42            &2.44           &2.41 \\  \cline{2-5}
Cost$^*$   &14.75  &12.60          &14.10          &10.65 \\   \hline\hline 
Mushroom &&&&\\  \hline
Leaves &400.00 (0.00) &145.50 (20.64) &400.00 (0.00) &96.30 (11.79) \\  \cline{2-5}
EPL &2238.20 (123.63) &660.90 (117.86) &2608.85 (56.01) &503.40 (72.22)\\  \cline{2-5}
Depth$^*$  &5.60     &4.54           &6.52           &5.23 \\  \cline{2-5}
Breadth$^*$ &2.92    &3.00           &2.51           &2.39 \\  \cline{2-5}
Cost$^*$    &16.35   &13.62          &16.37          &12.50 \\  \hline\hline 
\end{tabular}

\label{cost-prediction}
\end{table}
}

\stepcounter{subsection}
{\newpage
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\samepage \begin{displaymath}P(C_k)\sum_i\sum_j\lbrack P(A_i=V_{ij}|C_k)\log_2P(A_i=V_{ij}|C_k) 
- P(A_i=V_{ij})\log_2P(A_i=V_{ij})\rbrack.\end{displaymath}
}

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\samepage \setbox\sizebox=\hbox{${\sum_jP(A_i=V_{ij})\sum_k\lbrack P(C_k|A_i=V_{ij})\log_2P(C_k|A_i=V_{ij}) 
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\samepage \setbox\sizebox=\hbox{${\sum_jP(A_i=V_{ij})\sum_k\lbrack P(C_k|A_i=V_{ij})\log_2P(C_k|A_i=V_{ij}) 
- P(C_k)\log_2P(C_k)\rbrack}\over{-\sum_j\sum_k
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{\newpage
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\samepage \setbox\sizebox=\hbox{$\sum_i{{\sum_k P(C_k)\sum_j\lbrack P(A_i=V_{ij}|C_k)\log_2P(A_i=V_{ij}|C_k) 
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{\newpage
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\samepage \setbox\sizebox=\hbox{$\sum_i {{\sum_k P(C_k)\sum_j\lbrack P(A_i=V_{ij}|C_k)\log_2P(A_i=V_{ij}|C_k) 
               - P(A_i=V_{ij})\log_2P(A_i=V_{ij})\rbrack}\over{-\sum_k\sum_j 
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{\newpage
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\samepage \setbox\sizebox=\hbox{$P(H|D) \propto P(D|H)P(H)$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline1525: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
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\end{document}
