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- UCI_N4/aol/summary.json +0 -0
- UCI_N4/jmlr_tables.tex +0 -469
- UCI_N4/ldlt-resnet/summary.json +0 -0
- UCI_N4/ldlt/summary.json +0 -0
- UCI_N4/ortho/summary.json +0 -0
- UCI_N4/sandwich/summary.json +0 -0
- UCI_N4/sdp/runs/abalone/fold_0/1762509990.1624336/events.out.tfevents.1762509990.auvsl-gpu-01.ise.illinois.edu.4159804.8534 +0 -3
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- UCI_N4/sdp/runs/abalone/fold_0/1762509993.7272043/events.out.tfevents.1762509993.auvsl-gpu-01.ise.illinois.edu.4159804.8554 +0 -3
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- UCI_N4/sdp/runs/abalone/fold_0/1762509995.9411156/events.out.tfevents.1762509995.auvsl-gpu-01.ise.illinois.edu.4159804.8568 +0 -3
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- UCI_N4/sdp/runs/abalone/fold_0/1762509996.5758202/events.out.tfevents.1762509996.auvsl-gpu-01.ise.illinois.edu.4159804.8572 +0 -3
- UCI_N4/sdp/runs/abalone/fold_0/1762509996.738359/events.out.tfevents.1762509996.auvsl-gpu-01.ise.illinois.edu.4159804.8573 +0 -3
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- UCI_N4/sdp/runs/abalone/fold_0/1762509997.378704/events.out.tfevents.1762509997.auvsl-gpu-01.ise.illinois.edu.4159804.8577 +0 -3
UCI_N4/aol/summary.json
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UCI_N4/jmlr_tables.tex
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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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\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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\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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\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{table}
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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{table}
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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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\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{table}
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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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}
|
| 164 |
-
\end{threeparttable}
|
| 165 |
-
\end{table}
|
| 166 |
-
|
| 167 |
-
\begin{table}[t]
|
| 168 |
-
\centering
|
| 169 |
-
\begin{threeparttable}
|
| 170 |
-
{
|
| 171 |
-
\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).}
|
| 172 |
-
\label{tab:signif:mean_test_acc}
|
| 173 |
-
\setlength{\tabcolsep}{3pt}
|
| 174 |
-
\begin{tabular}{@{}l c c c c c c @{}}
|
| 175 |
-
\toprule
|
| 176 |
-
& AOL & LDLT-L & LDLT-R & Orthogonal & Sandwich & SLL \\
|
| 177 |
-
\midrule
|
| 178 |
-
AOL & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} \\
|
| 179 |
-
LDLT-L & \textcolor{green}{$\blacktriangle$} & $\cdot$ & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & $\cdot$ & \textcolor{green}{$\blacktriangle$} \\
|
| 180 |
-
LDLT-R & \textcolor{green}{$\blacktriangle$} & \textcolor{red}{$\blacktriangledown$} & $\cdot$ & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & $\cdot$ \\
|
| 181 |
-
Orthogonal & \textcolor{green}{$\blacktriangle$} & \textcolor{red}{$\blacktriangledown$} & $\cdot$ & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & $\cdot$ \\
|
| 182 |
-
Sandwich & \textcolor{green}{$\blacktriangle$} & $\cdot$ & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & $\cdot$ & \textcolor{green}{$\blacktriangle$} \\
|
| 183 |
-
SLL & \textcolor{green}{$\blacktriangle$} & \textcolor{red}{$\blacktriangledown$} & $\cdot$ & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & $\cdot$ \\
|
| 184 |
-
\bottomrule
|
| 185 |
-
\end{tabular}
|
| 186 |
-
}
|
| 187 |
-
\end{threeparttable}
|
| 188 |
-
\end{table}
|
| 189 |
-
|
| 190 |
-
\begin{table}[t]
|
| 191 |
-
\centering
|
| 192 |
-
\begin{threeparttable}
|
| 193 |
-
{
|
| 194 |
-
\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).}
|
| 195 |
-
\label{tab:signif:mean_cert_acc_36}
|
| 196 |
-
\setlength{\tabcolsep}{3pt}
|
| 197 |
-
\begin{tabular}{@{}l c c c c c c @{}}
|
| 198 |
-
\toprule
|
| 199 |
-
& AOL & LDLT-L & LDLT-R & Orthogonal & Sandwich & SLL \\
|
| 200 |
-
\midrule
|
| 201 |
-
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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