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  1. UCI_N4/aol/summary.json +0 -0
  2. UCI_N4/jmlr_tables.tex +0 -469
  3. UCI_N4/ldlt-resnet/summary.json +0 -0
  4. UCI_N4/ldlt/summary.json +0 -0
  5. UCI_N4/ortho/summary.json +0 -0
  6. UCI_N4/sandwich/summary.json +0 -0
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UCI_N4/aol/summary.json DELETED
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UCI_N4/jmlr_tables.tex DELETED
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- % JMLR-ready tables for two-column papers
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- % Required packages (no siunitx):
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- % \usepackage{booktabs}
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- % \usepackage{threeparttable}
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- % \usepackage{threeparttablex} % for TableNotes + longtable
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- % \usepackage{longtable}
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- % Optional for landscape: \usepackage{pdflscape}
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-
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- \begin{table*}[t]
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- \centering
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- \begin{threeparttable}
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- \caption{Model dimension ranges (min--max across all datasets and folds). Input/Output dimensions follow dataset label spaces.}
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- \label{tab:model-ranges}
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- \begin{tabular}{l r r r r r r}
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- \toprule
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- Algorithm & Width & Depth & Parameters & Padding & Input dim & Output dim \\
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- \midrule
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- AOL & 32--512 & 4--4 & 282--694837 & 10--524 & 3--262 & 2--100 \\
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- Orthogonal & 32--512 & 4--4 & 285--694840 & 10--524 & 3--262 & 2--100 \\
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- Sandwich & 32--512 & 4--4 & 615--1520140 & 10--524 & 3--262 & 2--100 \\
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- SLL & 32--512 & 4--4 & 1558--1084073 & 10--524 & 3--262 & 2--100 \\
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- LDLT-L & 32--512 & 4--4 & 3366--929297 & 10--524 & 3--262 & 2--100 \\
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- LDLT-R & 32--512 & 4--4 & 3463--1063442 & 10--524 & 3--262 & 2--100 \\
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- \bottomrule
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- \end{tabular}
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- \end{threeparttable}
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- \end{table*}
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-
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- \begin{table*}[t]
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- \centering
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- \begin{threeparttable}
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- \caption{Sorted mean$\pm$std across $N$ datasets for each algorithm.}
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- \label{tab:metric_summary}
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- \begin{tabular}{l r lllll}
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- \toprule
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- & & & \multicolumn{4}{c}{Certified Accuracy} \\
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- \cmidrule(lr){4-7}
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- Algorithm & $N$ & Accuracy & 36/255 & 72/255 & 108/255 & 255/255 \\
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- \midrule
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- AOL & 121 & 0.6295\,\tiny$\pm$0.2278 & 0.3655\,\tiny$\pm$0.2921 & 0.2628\,\tiny$\pm$0.2971 & 0.2078\,\tiny$\pm$0.2826 & 0.0989\,\tiny$\pm$0.1874 \\
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- Orthogonal & 121 & 0.6969\,\tiny$\pm$0.1938 & 0.6072\,\tiny$\pm$0.2290 & 0.5114\,\tiny$\pm$0.2592 & 0.4332\,\tiny$\pm$0.2662 & 0.1957\,\tiny$\pm$0.2289 \\
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- Sandwich & 121 & 0.7215\,\tiny$\pm$0.1871 & \textbf{0.6393\,\tiny$\pm$0.2310} & \textbf{0.5626\,\tiny$\pm$0.2520} & \textbf{0.4870\,\tiny$\pm$0.2671} & \textbf{0.2466\,\tiny$\pm$0.2478} \\
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- SLL & 121 & 0.6978\,\tiny$\pm$0.1998 & 0.5929\,\tiny$\pm$0.2426 & 0.4964\,\tiny$\pm$0.2662 & 0.4126\,\tiny$\pm$0.2744 & 0.1858\,\tiny$\pm$0.2235 \\
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- \midrule
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- LDLT-L & 121 & \textbf{0.7223\,\tiny$\pm$0.1868} & 0.5299\,\tiny$\pm$0.2946 & 0.4279\,\tiny$\pm$0.3081 & 0.3505\,\tiny$\pm$0.3005 & 0.1620\,\tiny$\pm$0.2287 \\
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- LDLT-R & 121 & 0.7022\,\tiny$\pm$0.1944 & 0.6152\,\tiny$\pm$0.2312 & 0.5295\,\tiny$\pm$0.2548 & 0.4481\,\tiny$\pm$0.2674 & 0.2164\,\tiny$\pm$0.2322 \\
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- \bottomrule
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- \end{tabular}
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- \end{threeparttable}
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- \end{table*}
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-
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- \begin{table}[t]
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- \centering
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- \begin{threeparttable}
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- {\small
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- \caption{Overall comparison on Mean Accuracy: average rank (lower is better) with Iman--Davenport $F=44.33$ (df=5,600), $p=1.11e-16$; Nemenyi CD$=0.969$. Counts are significant wins/losses after Holm within-metric at $\alpha=0.05$.}
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- \label{tab:overall:mean_test_acc}
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- \setlength{\tabcolsep}{4pt}
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- \begin{tabular}{@{}l r r r r r r@{}}
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- \toprule
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- Algorithm & \shortstack{Avg \\ rank} $\downarrow$ & \shortstack{sig \\ wins} & \shortstack{sig \\ losses} & \shortstack{net \\ wins} & \shortstack{win \\ share} & mean $r$ \\
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- \midrule
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- LDLT-L & 2.434 & 4 & 0 & 4 & 0.800 & 0.577 \\
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- Sandwich & 2.566 & 4 & 0 & 4 & 0.800 & 0.517 \\
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- LDLT-R & 3.438 & 1 & 2 & -1 & 0.200 & 0.629 \\
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- SLL & 3.624 & 1 & 2 & -1 & 0.200 & 0.678 \\
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- Orthogonal & 3.831 & 1 & 2 & -1 & 0.200 & 0.639 \\
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- AOL & 5.107 & 0 & 5 & -5 & 0.000 & 0.000 \\
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- \bottomrule
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- \end{tabular}
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- }
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- \end{threeparttable}
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- \end{table}
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-
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- \begin{table}[t]
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- \centering
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- \begin{threeparttable}
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- {\small
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- \caption{Overall comparison on Mean Certified Accuracy (36/255): average rank (lower is better) with Iman--Davenport $F=82.25$ (df=5,600), $p=1.11e-16$; Nemenyi CD$=0.969$. Counts are significant wins/losses after Holm within-metric at $\alpha=0.05$.}
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- \label{tab:overall:mean_cert_acc_36}
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- \setlength{\tabcolsep}{4pt}
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- \begin{tabular}{@{}l r r r r r r@{}}
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- \toprule
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- Algorithm & \shortstack{Avg \\ rank} $\downarrow$ & \shortstack{sig \\ wins} & \shortstack{sig \\ losses} & \shortstack{net \\ wins} & \shortstack{win \\ share} & mean $r$ \\
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- \midrule
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- Sandwich & 2.223 & 5 & 0 & 5 & 1.000 & 0.564 \\
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- LDLT-R & 2.715 & 4 & 1 & 3 & 0.800 & 0.478 \\
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- SLL & 3.248 & 2 & 2 & 0 & 0.400 & 0.624 \\
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- Orthogonal & 3.380 & 2 & 2 & 0 & 0.400 & 0.627 \\
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- LDLT-L & 3.760 & 1 & 4 & -3 & 0.200 & 0.737 \\
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- AOL & 5.674 & 0 & 5 & -5 & 0.000 & 0.000 \\
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- \bottomrule
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- \end{tabular}
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- }
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- \end{threeparttable}
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- \end{table}
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-
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- \begin{table}[t]
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- \centering
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- \begin{threeparttable}
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- {\small
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- \caption{Overall comparison on Mean Certified Accuracy (72/255): average rank (lower is better) with Iman--Davenport $F=102.13$ (df=5,600), $p=1.11e-16$; Nemenyi CD$=0.969$. Counts are significant wins/losses after Holm within-metric at $\alpha=0.05$.}
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- \label{tab:overall:mean_cert_acc_72}
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- \setlength{\tabcolsep}{4pt}
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- \begin{tabular}{@{}l r r r r r r@{}}
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- \toprule
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- Algorithm & \shortstack{Avg \\ rank} $\downarrow$ & \shortstack{sig \\ wins} & \shortstack{sig \\ losses} & \shortstack{net \\ wins} & \shortstack{win \\ share} & mean $r$ \\
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- \midrule
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- Sandwich & 1.979 & 5 & 0 & 5 & 1.000 & 0.662 \\
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- LDLT-R & 2.628 & 4 & 1 & 3 & 0.800 & 0.542 \\
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- SLL & 3.306 & 2 & 2 & 0 & 0.400 & 0.647 \\
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- Orthogonal & 3.417 & 2 & 2 & 0 & 0.400 & 0.632 \\
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- LDLT-L & 4.008 & 1 & 4 & -3 & 0.200 & 0.754 \\
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- AOL & 5.661 & 0 & 5 & -5 & 0.000 & 0.000 \\
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- \bottomrule
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- \end{tabular}
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- }
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- \end{threeparttable}
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- \end{table}
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-
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- \begin{table}[t]
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- \centering
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- \begin{threeparttable}
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- {\small
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- \caption{Overall comparison on Mean Certified Accuracy (108/255): average rank (lower is better) with Iman--Davenport $F=128.94$ (df=5,600), $p=1.11e-16$; Nemenyi CD$=0.969$. Counts are significant wins/losses after Holm within-metric at $\alpha=0.05$.}
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- \label{tab:overall:mean_cert_acc_108}
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- \setlength{\tabcolsep}{4pt}
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- \begin{tabular}{@{}l r r r r r r@{}}
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- \toprule
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- Algorithm & \shortstack{Avg \\ rank} $\downarrow$ & \shortstack{sig \\ wins} & \shortstack{sig \\ losses} & \shortstack{net \\ wins} & \shortstack{win \\ share} & mean $r$ \\
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- \midrule
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- Sandwich & 1.876 & 5 & 0 & 5 & 1.000 & 0.680 \\
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- LDLT-R & 2.525 & 4 & 1 & 3 & 0.800 & 0.548 \\
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- SLL & 3.318 & 2 & 2 & 0 & 0.400 & 0.662 \\
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- Orthogonal & 3.364 & 2 & 2 & 0 & 0.400 & 0.677 \\
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- LDLT-L & 4.194 & 1 & 4 & -3 & 0.200 & 0.824 \\
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- AOL & 5.723 & 0 & 5 & -5 & 0.000 & 0.000 \\
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- \bottomrule
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- \end{tabular}
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- }
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- \end{threeparttable}
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- \end{table}
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-
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- \begin{table}[t]
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- \centering
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- \begin{threeparttable}
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- {\small
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- \caption{Overall comparison on Mean Certified Accuracy (255/255): average rank (lower is better) with Iman--Davenport $F=89.04$ (df=5,600), $p=1.11e-16$; Nemenyi CD$=0.969$. Counts are significant wins/losses after Holm within-metric at $\alpha=0.05$.}
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- \label{tab:overall:mean_cert_acc_255}
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- \setlength{\tabcolsep}{4pt}
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- \begin{tabular}{@{}l r r r r r r@{}}
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- \toprule
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- Algorithm & \shortstack{Avg \\ rank} $\downarrow$ & \shortstack{sig \\ wins} & \shortstack{sig \\ losses} & \shortstack{net \\ wins} & \shortstack{win \\ share} & mean $r$ \\
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- \midrule
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- Sandwich & 2.029 & 5 & 0 & 5 & 1.000 & 0.663 \\
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- LDLT-R & 2.517 & 4 & 1 & 3 & 0.800 & 0.584 \\
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- Orthogonal & 3.409 & 2 & 2 & 0 & 0.400 & 0.600 \\
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- SLL & 3.409 & 2 & 2 & 0 & 0.400 & 0.643 \\
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- LDLT-L & 4.174 & 1 & 4 & -3 & 0.200 & 0.808 \\
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- AOL & 5.463 & 0 & 5 & -5 & 0.000 & 0.000 \\
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- \bottomrule
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- \end{tabular}
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- }
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- \end{threeparttable}
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- \end{table}
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-
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- \begin{table}[t]
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- \centering
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- \begin{threeparttable}
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- {
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- \caption{Pairwise Wilcoxon outcomes for Mean Accuracy (Holm within-metric at $\alpha=0.05$): row vs. column (\textcolor{green}{$\blacktriangle$} win, \textcolor{red}{$\blacktriangledown$} loss, $\cdot$ none).}
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- \label{tab:signif:mean_test_acc}
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- \setlength{\tabcolsep}{3pt}
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- \begin{tabular}{@{}l c c c c c c @{}}
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- \toprule
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- & AOL & LDLT-L & LDLT-R & Orthogonal & Sandwich & SLL \\
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- \midrule
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- AOL & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} \\
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- LDLT-L & \textcolor{green}{$\blacktriangle$} & $\cdot$ & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & $\cdot$ & \textcolor{green}{$\blacktriangle$} \\
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- LDLT-R & \textcolor{green}{$\blacktriangle$} & \textcolor{red}{$\blacktriangledown$} & $\cdot$ & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & $\cdot$ \\
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- Orthogonal & \textcolor{green}{$\blacktriangle$} & \textcolor{red}{$\blacktriangledown$} & $\cdot$ & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & $\cdot$ \\
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- Sandwich & \textcolor{green}{$\blacktriangle$} & $\cdot$ & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & $\cdot$ & \textcolor{green}{$\blacktriangle$} \\
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- SLL & \textcolor{green}{$\blacktriangle$} & \textcolor{red}{$\blacktriangledown$} & $\cdot$ & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & $\cdot$ \\
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- \bottomrule
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- \end{tabular}
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- }
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- \end{threeparttable}
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- \end{table}
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-
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- \begin{table}[t]
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- \centering
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- \begin{threeparttable}
193
- {
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- \caption{Pairwise Wilcoxon outcomes for Mean Certified Accuracy (36/255) (Holm within-metric at $\alpha=0.05$): row vs. column (\textcolor{green}{$\blacktriangle$} win, \textcolor{red}{$\blacktriangledown$} loss, $\cdot$ none).}
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- \label{tab:signif:mean_cert_acc_36}
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- \setlength{\tabcolsep}{3pt}
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- \begin{tabular}{@{}l c c c c c c @{}}
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- \toprule
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- & AOL & LDLT-L & LDLT-R & Orthogonal & Sandwich & SLL \\
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- \midrule
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- AOL & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} \\
202
- LDLT-L & \textcolor{green}{$\blacktriangle$} & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} \\
203
- LDLT-R & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & $\cdot$ & \textcolor{green}{$\blacktriangle$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{green}{$\blacktriangle$} \\
204
- Orthogonal & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & \textcolor{red}{$\blacktriangledown$} & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & $\cdot$ \\
205
- Sandwich & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & $\cdot$ & \textcolor{green}{$\blacktriangle$} \\
206
- SLL & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & \textcolor{red}{$\blacktriangledown$} & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & $\cdot$ \\
207
- \bottomrule
208
- \end{tabular}
209
- }
210
- \end{threeparttable}
211
- \end{table}
212
-
213
- \begin{table}[t]
214
- \centering
215
- \begin{threeparttable}
216
- {
217
- \caption{Pairwise Wilcoxon outcomes for Mean Certified Accuracy (72/255) (Holm within-metric at $\alpha=0.05$): row vs. column (\textcolor{green}{$\blacktriangle$} win, \textcolor{red}{$\blacktriangledown$} loss, $\cdot$ none).}
218
- \label{tab:signif:mean_cert_acc_72}
219
- \setlength{\tabcolsep}{3pt}
220
- \begin{tabular}{@{}l c c c c c c @{}}
221
- \toprule
222
- & AOL & LDLT-L & LDLT-R & Orthogonal & Sandwich & SLL \\
223
- \midrule
224
- AOL & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} \\
225
- LDLT-L & \textcolor{green}{$\blacktriangle$} & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} \\
226
- LDLT-R & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & $\cdot$ & \textcolor{green}{$\blacktriangle$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{green}{$\blacktriangle$} \\
227
- Orthogonal & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & \textcolor{red}{$\blacktriangledown$} & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & $\cdot$ \\
228
- Sandwich & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & $\cdot$ & \textcolor{green}{$\blacktriangle$} \\
229
- SLL & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & \textcolor{red}{$\blacktriangledown$} & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & $\cdot$ \\
230
- \bottomrule
231
- \end{tabular}
232
- }
233
- \end{threeparttable}
234
- \end{table}
235
-
236
- \begin{table}[t]
237
- \centering
238
- \begin{threeparttable}
239
- {
240
- \caption{Pairwise Wilcoxon outcomes for Mean Certified Accuracy (108/255) (Holm within-metric at $\alpha=0.05$): row vs. column (\textcolor{green}{$\blacktriangle$} win, \textcolor{red}{$\blacktriangledown$} loss, $\cdot$ none).}
241
- \label{tab:signif:mean_cert_acc_108}
242
- \setlength{\tabcolsep}{3pt}
243
- \begin{tabular}{@{}l c c c c c c @{}}
244
- \toprule
245
- & AOL & LDLT-L & LDLT-R & Orthogonal & Sandwich & SLL \\
246
- \midrule
247
- AOL & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} \\
248
- LDLT-L & \textcolor{green}{$\blacktriangle$} & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} \\
249
- LDLT-R & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & $\cdot$ & \textcolor{green}{$\blacktriangle$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{green}{$\blacktriangle$} \\
250
- Orthogonal & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & \textcolor{red}{$\blacktriangledown$} & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & $\cdot$ \\
251
- Sandwich & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & $\cdot$ & \textcolor{green}{$\blacktriangle$} \\
252
- SLL & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & \textcolor{red}{$\blacktriangledown$} & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & $\cdot$ \\
253
- \bottomrule
254
- \end{tabular}
255
- }
256
- \end{threeparttable}
257
- \end{table}
258
-
259
- \begin{table}[t]
260
- \centering
261
- \begin{threeparttable}
262
- {
263
- \caption{Pairwise Wilcoxon outcomes for Mean Certified Accuracy (255/255) (Holm within-metric at $\alpha=0.05$): row vs. column (\textcolor{green}{$\blacktriangle$} win, \textcolor{red}{$\blacktriangledown$} loss, $\cdot$ none).}
264
- \label{tab:signif:mean_cert_acc_255}
265
- \setlength{\tabcolsep}{3pt}
266
- \begin{tabular}{@{}l c c c c c c @{}}
267
- \toprule
268
- & AOL & LDLT-L & LDLT-R & Orthogonal & Sandwich & SLL \\
269
- \midrule
270
- AOL & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} \\
271
- LDLT-L & \textcolor{green}{$\blacktriangle$} & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} \\
272
- LDLT-R & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & $\cdot$ & \textcolor{green}{$\blacktriangle$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{green}{$\blacktriangle$} \\
273
- Orthogonal & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & \textcolor{red}{$\blacktriangledown$} & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & $\cdot$ \\
274
- Sandwich & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & $\cdot$ & \textcolor{green}{$\blacktriangle$} \\
275
- SLL & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & \textcolor{red}{$\blacktriangledown$} & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & $\cdot$ \\
276
- \bottomrule
277
- \end{tabular}
278
- }
279
- \end{threeparttable}
280
- \end{table}
281
-
282
-
283
- \begin{table*}[t]
284
- \centering
285
- \begin{threeparttable}
286
- \caption[Mean Accuracy]{Wilcoxon signed-rank tests (two-sided) for Mean Accuracy; $p$-values with Holm FWER corrections within-metric and global.}
287
- \label{tab:wilcoxon:mean_test_acc}
288
- \begingroup
289
- \setlength{\tabcolsep}{4pt}
290
- \begin{tabular}{ll r r r r r r r r r r r}
291
- \toprule
292
- \multicolumn{2}{c}{Algorithms} & \multicolumn{6}{c}{Run Statistics} & \multicolumn{5}{c}{Wilcoxon pairwise Statistics} \\\cmidrule(lr){1-2} \cmidrule(lr){3-8} \cmidrule(lr){9-13}
293
- Alg A & Alg B & $n$ & wins$_A$ & wins$_B$ & ties & WinRate A & \shortstack{Median \\ $\Delta$ (A--B)} & $W$ & $p$ & $p_{\text{Holm,within}}$ & $p_{\text{Holm,global}}$ & $r$ \\
294
- \midrule
295
- AOL & LDLT-L & 121 & 16 & 105 & 0 & 0.1322 & -0.0568 & 412 & $2.3e-17^{***}$ & $3.4e-16^{***}$ & $0^{***}$ & 0.7708 \\
296
- AOL & Sandwich & 121 & 18 & 103 & 0 & 0.1488 & -0.0595 & 518 & $2.3e-16^{***}$ & $0^{***}$ & $0^{***}$ & 0.7459 \\
297
- AOL & SLL & 121 & 22 & 99 & 0 & 0.1818 & -0.0351 & 806 & $0^{***}$ & $0^{***}$ & $0^{***}$ & 0.6782 \\
298
- AOL & Orthogonal & 121 & 27 & 94 & 0 & 0.2231 & -0.0265 & 971 & $0^{***}$ & $0^{***}$ & $1.0e-10^{***}$ & 0.6394 \\
299
- AOL & LDLT-R & 121 & 25 & 96 & 0 & 0.2066 & -0.0313 & 1013 & $0^{***}$ & $0^{***}$ & $2.0e-10^{***}$ & 0.6295 \\
300
- Orthogonal & Sandwich & 121 & 31 & 89 & 1 & 0.2603 & -0.0126 & 1269 & $6.0e-10^{***}$ & $6.3e-09^{***}$ & $2.3e-08^{***}$ & 0.5643 \\
301
- LDLT-L & Orthogonal & 121 & 94 & 27 & 0 & 0.7769 & 0.0139 & 1309 & $7.0e-10^{***}$ & $6.6e-09^{***}$ & $2.6e-08^{***}$ & 0.5599 \\
302
- LDLT-L & SLL & 121 & 86 & 35 & 0 & 0.7107 & 0.0111 & 1503 & $1.5e-08^{***}$ & $1.2e-07^{***}$ & $5.1e-07^{***}$ & 0.5143 \\
303
- LDLT-L & LDLT-R & 121 & 87 & 33 & 1 & 0.7231 & 0.0108 & 1689 & $3.7e-07^{***}$ & $2.6e-06^{***}$ & $1.1e-05^{***}$ & 0.4639 \\
304
- Sandwich & SLL & 121 & 83 & 38 & 0 & 0.6860 & 0.0090 & 1789 & $8.8e-07^{***}$ & $5.3e-06^{***}$ & $2.4e-05^{***}$ & 0.4470 \\
305
- LDLT-R & Sandwich & 121 & 43 & 78 & 0 & 0.3554 & -0.0068 & 2364 & $6.0e-04^{***}$ & $3.0e-03^{**}$ & $9.1e-03^{**}$ & 0.3118 \\
306
- LDLT-R & SLL & 121 & 66 & 54 & 1 & 0.5496 & 0.0019 & 3070 & $1.4e-01$ & $5.7e-01$ & $8.6e-01$ & 0.1338 \\
307
- LDLT-R & Orthogonal & 121 & 71 & 50 & 0 & 0.5868 & 0.0025 & 3138 & $1.5e-01$ & $5.7e-01$ & $8.6e-01$ & 0.1298 \\
308
- Orthogonal & SLL & 121 & 60 & 61 & 0 & 0.4959 & -0.0004 & 3623 & $8.6e-01$ & $1.0e+00$ & $1.0e+00$ & 0.0158 \\
309
- LDLT-L & Sandwich & 121 & 59 & 62 & 0 & 0.4876 & -0.0002 & 3624 & $8.6e-01$ & $1.0e+00$ & $1.0e+00$ & 0.0155 \\
310
- \bottomrule
311
- \end{tabular}
312
- \begin{tablenotes}
313
- \item Stars mark significance ($^*\,p\!\le\!0.05$, $^{**}\,p\!\le\!0.01$, $^{***}\,p\!\le\!0.001$).
314
- \end{tablenotes}
315
- \endgroup
316
- \end{threeparttable}
317
- \end{table*}
318
-
319
-
320
-
321
- \begin{table*}[t]
322
- \centering
323
- \begin{threeparttable}
324
- \caption[Mean Certified Accuracy (36/255)]{Wilcoxon signed-rank tests (two-sided) for Mean Certified Accuracy (36/255); $p$-values with Holm FWER corrections within-metric and global.}
325
- \label{tab:wilcoxon:mean_cert_acc_36}
326
- \begingroup
327
- \setlength{\tabcolsep}{4pt}
328
- \begin{tabular}{ll r r r r r r r r r r r}
329
- \toprule
330
- \multicolumn{2}{c}{Algorithms} & \multicolumn{6}{c}{Run Statistics} & \multicolumn{5}{c}{Wilcoxon pairwise Statistics} \\\cmidrule(lr){1-2} \cmidrule(lr){3-8} \cmidrule(lr){9-13}
331
- Alg A & Alg B & $n$ & wins$_A$ & wins$_B$ & ties & WinRate A & \shortstack{Median \\ $\Delta$ (A--B)} & $W$ & $p$ & $p_{\text{Holm,within}}$ & $p_{\text{Holm,global}}$ & $r$ \\
332
- \midrule
333
- AOL & SLL & 121 & 4 & 117 & 0 & 0.0331 & -0.1998 & 27 & $2.7e-21^{***}$ & $4.0e-20^{***}$ & $2.0e-19^{***}$ & 0.8613 \\
334
- AOL & Sandwich & 121 & 6 & 114 & 1 & 0.0537 & -0.2626 & 32 & $4.5e-21^{***}$ & $6.1e-20^{***}$ & $3.2e-19^{***}$ & 0.8601 \\
335
- AOL & LDLT-R & 121 & 4 & 117 & 0 & 0.0331 & -0.2302 & 47 & $4.4e-21^{***}$ & $6.1e-20^{***}$ & $3.2e-19^{***}$ & 0.8566 \\
336
- AOL & Orthogonal & 121 & 8 & 113 & 0 & 0.0661 & -0.2204 & 87 & $1.2e-20^{***}$ & $1.4e-19^{***}$ & $7.9e-19^{***}$ & 0.8472 \\
337
- AOL & LDLT-L & 121 & 17 & 104 & 0 & 0.1405 & -0.1415 & 554 & $5.0e-16^{***}$ & $0^{***}$ & $0^{***}$ & 0.7374 \\
338
- LDLT-L & Sandwich & 121 & 31 & 89 & 1 & 0.2603 & -0.0387 & 998 & $0^{***}$ & $1.0e-10^{***}$ & $2.0e-10^{***}$ & 0.6291 \\
339
- LDLT-L & LDLT-R & 121 & 40 & 81 & 0 & 0.3306 & -0.0297 & 1410 & $3.7e-09^{***}$ & $3.3e-08^{***}$ & $1.3e-07^{***}$ & 0.5361 \\
340
- Orthogonal & Sandwich & 121 & 28 & 93 & 0 & 0.2314 & -0.0238 & 1424 & $4.6e-09^{***}$ & $3.7e-08^{***}$ & $1.6e-07^{***}$ & 0.5327 \\
341
- Sandwich & SLL & 121 & 83 & 38 & 0 & 0.6860 & 0.0207 & 1530 & $2.3e-08^{***}$ & $1.6e-07^{***}$ & $7.4e-07^{***}$ & 0.5079 \\
342
- LDLT-L & Orthogonal & 121 & 48 & 73 & 0 & 0.3967 & -0.0200 & 1957 & $7.4e-06^{***}$ & $4.4e-05^{***}$ & $1.8e-04^{***}$ & 0.4075 \\
343
- LDLT-L & SLL & 121 & 47 & 73 & 1 & 0.3926 & -0.0085 & 2014 & $2.3e-05^{***}$ & $1.2e-04^{***}$ & $4.4e-04^{***}$ & 0.3862 \\
344
- LDLT-R & SLL & 121 & 76 & 43 & 2 & 0.6364 & 0.0095 & 2285 & $6.6e-04^{***}$ & $2.6e-03^{**}$ & $9.2e-03^{**}$ & 0.3123 \\
345
- LDLT-R & Sandwich & 121 & 44 & 77 & 0 & 0.3636 & -0.0089 & 2466 & $1.5e-03^{**}$ & $4.6e-03^{**}$ & $1.7e-02^{*}$ & 0.2878 \\
346
- LDLT-R & Orthogonal & 121 & 78 & 42 & 1 & 0.6488 & 0.0084 & 2756 & $2.2e-02^{*}$ & $4.4e-02^{*}$ & $2.0e-01$ & 0.2088 \\
347
- Orthogonal & SLL & 121 & 60 & 60 & 1 & 0.5000 & 0.0000 & 2916 & $6.2e-02$ & $6.2e-02$ & $4.9e-01$ & 0.1705 \\
348
- \bottomrule
349
- \end{tabular}
350
- \begin{tablenotes}
351
- \item Stars mark significance ($^*\,p\!\le\!0.05$, $^{**}\,p\!\le\!0.01$, $^{***}\,p\!\le\!0.001$).
352
- \end{tablenotes}
353
- \endgroup
354
- \end{threeparttable}
355
- \end{table*}
356
-
357
-
358
-
359
- \begin{table*}[t]
360
- \centering
361
- \begin{threeparttable}
362
- \caption[Mean Certified Accuracy (72/255)]{Wilcoxon signed-rank tests (two-sided) for Mean Certified Accuracy (72/255); $p$-values with Holm FWER corrections within-metric and global.}
363
- \label{tab:wilcoxon:mean_cert_acc_72}
364
- \begingroup
365
- \setlength{\tabcolsep}{4pt}
366
- \begin{tabular}{ll r r r r r r r r r r r}
367
- \toprule
368
- \multicolumn{2}{c}{Algorithms} & \multicolumn{6}{c}{Run Statistics} & \multicolumn{5}{c}{Wilcoxon pairwise Statistics} \\\cmidrule(lr){1-2} \cmidrule(lr){3-8} \cmidrule(lr){9-13}
369
- Alg A & Alg B & $n$ & wins$_A$ & wins$_B$ & ties & WinRate A & \shortstack{Median \\ $\Delta$ (A--B)} & $W$ & $p$ & $p_{\text{Holm,within}}$ & $p_{\text{Holm,global}}$ & $r$ \\
370
- \midrule
371
- AOL & Sandwich & 121 & 6 & 114 & 1 & 0.0537 & -0.2723 & 58 & $8.5e-21^{***}$ & $1.3e-19^{***}$ & $5.9e-19^{***}$ & 0.8538 \\
372
- AOL & SLL & 121 & 3 & 116 & 2 & 0.0331 & -0.1967 & 59 & $1.3e-20^{***}$ & $1.8e-19^{***}$ & $8.6e-19^{***}$ & 0.8534 \\
373
- AOL & LDLT-R & 121 & 5 & 116 & 0 & 0.0413 & -0.2325 & 103 & $1.7e-20^{***}$ & $2.2e-19^{***}$ & $1.1e-18^{***}$ & 0.8435 \\
374
- AOL & Orthogonal & 121 & 8 & 113 & 0 & 0.0661 & -0.2085 & 149 & $5.2e-20^{***}$ & $6.3e-19^{***}$ & $3.3e-18^{***}$ & 0.8327 \\
375
- AOL & LDLT-L & 121 & 16 & 102 & 3 & 0.1446 & -0.1155 & 460 & $2.6e-16^{***}$ & $0^{***}$ & $0^{***}$ & 0.7539 \\
376
- LDLT-L & Sandwich & 121 & 21 & 100 & 0 & 0.1736 & -0.0748 & 670 & $0^{***}$ & $0^{***}$ & $0^{***}$ & 0.7101 \\
377
- Orthogonal & Sandwich & 121 & 18 & 103 & 0 & 0.1488 & -0.0370 & 698 & $0^{***}$ & $0^{***}$ & $0^{***}$ & 0.7037 \\
378
- Sandwich & SLL & 121 & 91 & 28 & 2 & 0.7603 & 0.0396 & 823 & $0^{***}$ & $0^{***}$ & $0^{***}$ & 0.6676 \\
379
- LDLT-L & LDLT-R & 121 & 30 & 90 & 1 & 0.2521 & -0.0625 & 988 & $0^{***}$ & $0^{***}$ & $2.0e-10^{***}$ & 0.6315 \\
380
- LDLT-L & SLL & 121 & 42 & 79 & 0 & 0.3471 & -0.0231 & 1813 & $1.2e-06^{***}$ & $7.2e-06^{***}$ & $3.1e-05^{***}$ & 0.4414 \\
381
- LDLT-L & Orthogonal & 121 & 44 & 77 & 0 & 0.3636 & -0.0192 & 1857 & $2.1e-06^{***}$ & $1.1e-05^{***}$ & $5.3e-05^{***}$ & 0.4310 \\
382
- LDLT-R & SLL & 121 & 79 & 41 & 1 & 0.6570 & 0.0156 & 1982 & $1.6e-05^{***}$ & $6.4e-05^{***}$ & $3.5e-04^{***}$ & 0.3937 \\
383
- LDLT-R & Sandwich & 121 & 44 & 77 & 0 & 0.3636 & -0.0238 & 2090 & $3.5e-05^{***}$ & $1.1e-04^{***}$ & $6.3e-04^{***}$ & 0.3761 \\
384
- LDLT-R & Orthogonal & 121 & 77 & 42 & 2 & 0.6446 & 0.0106 & 2346 & $1.2e-03^{**}$ & $2.4e-03^{**}$ & $1.5e-02^{*}$ & 0.2974 \\
385
- Orthogonal & SLL & 121 & 61 & 59 & 1 & 0.5083 & 0.0002 & 3188 & $2.5e-01$ & $2.5e-01$ & $9.9e-01$ & 0.1055 \\
386
- \bottomrule
387
- \end{tabular}
388
- \begin{tablenotes}
389
- \item Stars mark significance ($^*\,p\!\le\!0.05$, $^{**}\,p\!\le\!0.01$, $^{***}\,p\!\le\!0.001$).
390
- \end{tablenotes}
391
- \endgroup
392
- \end{threeparttable}
393
- \end{table*}
394
-
395
-
396
-
397
- \begin{table*}[t]
398
- \centering
399
- \begin{threeparttable}
400
- \caption[Mean Certified Accuracy (108/255)]{Wilcoxon signed-rank tests (two-sided) for Mean Certified Accuracy (108/255); $p$-values with Holm FWER corrections within-metric and global.}
401
- \label{tab:wilcoxon:mean_cert_acc_108}
402
- \begingroup
403
- \setlength{\tabcolsep}{4pt}
404
- \begin{tabular}{ll r r r r r r r r r r r}
405
- \toprule
406
- \multicolumn{2}{c}{Algorithms} & \multicolumn{6}{c}{Run Statistics} & \multicolumn{5}{c}{Wilcoxon pairwise Statistics} \\\cmidrule(lr){1-2} \cmidrule(lr){3-8} \cmidrule(lr){9-13}
407
- Alg A & Alg B & $n$ & wins$_A$ & wins$_B$ & ties & WinRate A & \shortstack{Median \\ $\Delta$ (A--B)} & $W$ & $p$ & $p_{\text{Holm,within}}$ & $p_{\text{Holm,global}}$ & $r$ \\
408
- \midrule
409
- AOL & LDLT-R & 121 & 1 & 119 & 1 & 0.0124 & -0.2179 & 1 & $2.0e-21^{***}$ & $3.1e-20^{***}$ & $1.5e-19^{***}$ & 0.8675 \\
410
- AOL & SLL & 121 & 2 & 116 & 3 & 0.0289 & -0.1595 & 12 & $5.8e-21^{***}$ & $7.5e-20^{***}$ & $4.1e-19^{***}$ & 0.8648 \\
411
- AOL & Sandwich & 121 & 4 & 116 & 1 & 0.0372 & -0.2402 & 32 & $4.5e-21^{***}$ & $6.2e-20^{***}$ & $3.2e-19^{***}$ & 0.8601 \\
412
- AOL & Orthogonal & 121 & 6 & 113 & 2 & 0.0579 & -0.1817 & 72 & $1.8e-20^{***}$ & $2.1e-19^{***}$ & $1.2e-18^{***}$ & 0.8502 \\
413
- AOL & LDLT-L & 121 & 12 & 99 & 10 & 0.1405 & -0.0785 & 158 & $4.0e-18^{***}$ & $4.4e-17^{***}$ & $2.5e-16^{***}$ & 0.8237 \\
414
- LDLT-L & Sandwich & 121 & 17 & 104 & 0 & 0.1405 & -0.0905 & 492 & $1.3e-16^{***}$ & $0^{***}$ & $0^{***}$ & 0.7520 \\
415
- Orthogonal & Sandwich & 121 & 16 & 105 & 0 & 0.1322 & -0.0475 & 700 & $0^{***}$ & $0^{***}$ & $0^{***}$ & 0.7030 \\
416
- Sandwich & SLL & 121 & 93 & 26 & 2 & 0.7769 & 0.0480 & 764 & $0^{***}$ & $0^{***}$ & $0^{***}$ & 0.6820 \\
417
- LDLT-L & LDLT-R & 121 & 23 & 97 & 1 & 0.1942 & -0.0468 & 787 & $0^{***}$ & $0^{***}$ & $0^{***}$ & 0.6796 \\
418
- LDLT-L & Orthogonal & 121 & 35 & 84 & 2 & 0.2975 & -0.0276 & 1497 & $3.9e-08^{***}$ & $2.3e-07^{***}$ & $1.2e-06^{***}$ & 0.5038 \\
419
- LDLT-L & SLL & 121 & 37 & 82 & 2 & 0.3140 & -0.0208 & 1682 & $5.6e-07^{***}$ & $2.8e-06^{***}$ & $1.6e-05^{***}$ & 0.4588 \\
420
- LDLT-R & SLL & 121 & 82 & 35 & 4 & 0.6942 & 0.0178 & 1875 & $1.8e-05^{***}$ & $5.4e-05^{***}$ & $3.8e-04^{***}$ & 0.3963 \\
421
- LDLT-R & Sandwich & 121 & 41 & 79 & 1 & 0.3430 & -0.0213 & 1952 & $1.1e-05^{***}$ & $4.5e-05^{***}$ & $2.6e-04^{***}$ & 0.4010 \\
422
- LDLT-R & Orthogonal & 121 & 77 & 42 & 2 & 0.6446 & 0.0191 & 2543 & $6.5e-03^{**}$ & $1.3e-02^{*}$ & $6.5e-02$ & 0.2495 \\
423
- Orthogonal & SLL & 121 & 60 & 59 & 2 & 0.5041 & 0.0000 & 2941 & $9.6e-02$ & $9.6e-02$ & $6.7e-01$ & 0.1528 \\
424
- \bottomrule
425
- \end{tabular}
426
- \begin{tablenotes}
427
- \item Stars mark significance ($^*\,p\!\le\!0.05$, $^{**}\,p\!\le\!0.01$, $^{***}\,p\!\le\!0.001$).
428
- \end{tablenotes}
429
- \endgroup
430
- \end{threeparttable}
431
- \end{table*}
432
-
433
-
434
-
435
- \begin{table*}[t]
436
- \centering
437
- \begin{threeparttable}
438
- \caption[Mean Certified Accuracy (255/255)]{Wilcoxon signed-rank tests (two-sided) for Mean Certified Accuracy (255/255); $p$-values with Holm FWER corrections within-metric and global.}
439
- \label{tab:wilcoxon:mean_cert_acc_255}
440
- \begingroup
441
- \setlength{\tabcolsep}{4pt}
442
- \begin{tabular}{ll r r r r r r r r r r r}
443
- \toprule
444
- \multicolumn{2}{c}{Algorithms} & \multicolumn{6}{c}{Run Statistics} & \multicolumn{5}{c}{Wilcoxon pairwise Statistics} \\\cmidrule(lr){1-2} \cmidrule(lr){3-8} \cmidrule(lr){9-13}
445
- Alg A & Alg B & $n$ & wins$_A$ & wins$_B$ & ties & WinRate A & \shortstack{Median \\ $\Delta$ (A--B)} & $W$ & $p$ & $p_{\text{Holm,within}}$ & $p_{\text{Holm,global}}$ & $r$ \\
446
- \midrule
447
- AOL & LDLT-R & 121 & 2 & 107 & 12 & 0.0661 & -0.0560 & 17 & $2.1e-19^{***}$ & $3.1e-18^{***}$ & $1.3e-17^{***}$ & 0.8629 \\
448
- AOL & SLL & 121 & 2 & 99 & 20 & 0.0992 & -0.0407 & 24 & $5.5e-18^{***}$ & $7.2e-17^{***}$ & $3.3e-16^{***}$ & 0.8599 \\
449
- AOL & Sandwich & 121 & 2 & 107 & 12 & 0.0661 & -0.0791 & 58 & $6.4e-19^{***}$ & $8.9e-18^{***}$ & $4.0e-17^{***}$ & 0.8511 \\
450
- AOL & Orthogonal & 121 & 5 & 100 & 16 & 0.1074 & -0.0347 & 109 & $1.3e-17^{***}$ & $1.5e-16^{***}$ & $7.6e-16^{***}$ & 0.8339 \\
451
- AOL & LDLT-L & 121 & 6 & 79 & 36 & 0.1983 & -0.0167 & 127 & $0^{***}$ & $0^{***}$ & $0^{***}$ & 0.8080 \\
452
- LDLT-L & Sandwich & 121 & 11 & 98 & 12 & 0.1405 & -0.0371 & 291 & $2.8e-16^{***}$ & $0^{***}$ & $0^{***}$ & 0.7836 \\
453
- Orthogonal & Sandwich & 121 & 16 & 95 & 10 & 0.1736 & -0.0340 & 427 & $0^{***}$ & $0^{***}$ & $0^{***}$ & 0.7486 \\
454
- Sandwich & SLL & 121 & 86 & 24 & 11 & 0.7562 & 0.0261 & 845 & $0^{***}$ & $4.0e-10^{***}$ & $1.8e-09^{***}$ & 0.6276 \\
455
- LDLT-L & LDLT-R & 121 & 20 & 89 & 12 & 0.2149 & -0.0193 & 847 & $1.0e-10^{***}$ & $6.0e-10^{***}$ & $3.1e-09^{***}$ & 0.6226 \\
456
- LDLT-L & SLL & 121 & 29 & 72 & 20 & 0.3223 & -0.0068 & 1312 & $1.9e-05^{***}$ & $9.4e-05^{***}$ & $3.8e-04^{***}$ & 0.4257 \\
457
- LDLT-R & SLL & 121 & 80 & 29 & 12 & 0.7107 & 0.0184 & 1331 & $4.7e-07^{***}$ & $2.8e-06^{***}$ & $1.4e-05^{***}$ & 0.4824 \\
458
- LDLT-L & Orthogonal & 121 & 34 & 71 & 16 & 0.3471 & -0.0067 & 1607 & $1.7e-04^{***}$ & $5.2e-04^{***}$ & $2.8e-03^{**}$ & 0.3666 \\
459
- LDLT-R & Orthogonal & 121 & 74 & 38 & 9 & 0.6488 & 0.0104 & 1829 & $1.1e-04^{***}$ & $4.3e-04^{***}$ & $1.8e-03^{**}$ & 0.3661 \\
460
- LDLT-R & Sandwich & 121 & 45 & 68 & 8 & 0.4050 & -0.0092 & 2100 & $1.3e-03^{**}$ & $2.7e-03^{**}$ & $1.6e-02^{*}$ & 0.3018 \\
461
- Orthogonal & SLL & 121 & 57 & 52 & 12 & 0.5207 & 0.0000 & 2967 & $9.3e-01$ & $9.3e-01$ & $1.0e+00$ & 0.0087 \\
462
- \bottomrule
463
- \end{tabular}
464
- \begin{tablenotes}
465
- \item Stars mark significance ($^*\,p\!\le\!0.05$, $^{**}\,p\!\le\!0.01$, $^{***}\,p\!\le\!0.001$).
466
- \end{tablenotes}
467
- \endgroup
468
- \end{threeparttable}
469
- \end{table*}
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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