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UCI_N4/jmlr_tables.tex

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+% JMLR-ready tables for two-column papers
+% Required packages (no siunitx):
+% \usepackage{booktabs}
+% \usepackage{threeparttable}
+% \usepackage{threeparttablex} % for TableNotes + longtable
+% \usepackage{longtable}
+% Optional for landscape: \usepackage{pdflscape}
+
+\begin{table*}[t]
+\centering
+\begin{threeparttable}
+\caption{Model dimension ranges (min--max across all datasets and folds). Input/Output dimensions follow dataset label spaces.}
+\label{tab:model-ranges}
+\begin{tabular}{l r r r r r r}
+\toprule
+Algorithm & Width & Depth & Parameters & Padding & Input dim & Output dim \\
+\midrule
+AOL & 32--512 & 4--4 & 282--694837 & 10--524 & 3--262 & 2--100 \\
+Orthogonal & 32--512 & 4--4 & 285--694840 & 10--524 & 3--262 & 2--100 \\
+Sandwich & 32--512 & 4--4 & 615--1520140 & 10--524 & 3--262 & 2--100 \\
+SLL & 32--512 & 4--4 & 1558--1084073 & 10--524 & 3--262 & 2--100 \\
+LDLT-L & 32--512 & 4--4 & 3366--929297 & 10--524 & 3--262 & 2--100 \\
+LDLT-R & 32--512 & 4--4 & 3463--1063442 & 10--524 & 3--262 & 2--100 \\
+\bottomrule
+\end{tabular}
+\end{threeparttable}
+\end{table*}
+
+\begin{table*}[t]
+\centering
+\begin{threeparttable}
+\caption{Sorted mean$\pm$std across $N$ datasets for each algorithm.}
+\label{tab:metric_summary}
+\begin{tabular}{l r lllll}
+\toprule
+ &  &  & \multicolumn{4}{c}{Certified Accuracy} \\
+\cmidrule(lr){4-7}
+Algorithm & $N$ & Accuracy & 36/255 & 72/255 & 108/255 & 255/255 \\
+\midrule
+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$0.1874 \\
+Orthogonal & 121 & 0.6969\,\tiny$\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$0.2289 \\
+Sandwich & 121 & 0.7215\,\tiny$\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$0.2478} \\
+SLL & 121 & 0.6978\,\tiny$\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$0.2235 \\
+\midrule
+LDLT-L & 121 & \textbf{0.7223\,\tiny$\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$0.2287 \\
+LDLT-R & 121 & 0.7022\,\tiny$\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 \\
+\bottomrule
+\end{tabular}
+\end{threeparttable}
+\end{table*}
+
+\begin{table}[t]
+\centering
+\begin{threeparttable}
+{\small
+\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 $\alpha=0.05$.}
+\label{tab:overall:mean_test_acc}
+\setlength{\tabcolsep}{4pt}
+\begin{tabular}{@{}l r r r r r r@{}}
+\toprule
+Algorithm & \shortstack{Avg \\ rank} $\downarrow$ & \shortstack{sig \\ wins} & \shortstack{sig \\ losses} & \shortstack{net \\ wins} & \shortstack{win \\ share} & mean $r$ \\
+\midrule
+LDLT-L & 2.434 & 4 & 0 & 4 & 0.800 & 0.577 \\
+Sandwich & 2.566 & 4 & 0 & 4 & 0.800 & 0.517 \\
+LDLT-R & 3.438 & 1 & 2 & -1 & 0.200 & 0.629 \\
+SLL & 3.624 & 1 & 2 & -1 & 0.200 & 0.678 \\
+Orthogonal & 3.831 & 1 & 2 & -1 & 0.200 & 0.639 \\
+AOL & 5.107 & 0 & 5 & -5 & 0.000 & 0.000 \\
+\bottomrule
+\end{tabular}
+}
+\end{threeparttable}
+\end{table}
+
+\begin{table}[t]
+\centering
+\begin{threeparttable}
+{\small
+\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 $\alpha=0.05$.}
+\label{tab:overall:mean_cert_acc_36}
+\setlength{\tabcolsep}{4pt}
+\begin{tabular}{@{}l r r r r r r@{}}
+\toprule
+Algorithm & \shortstack{Avg \\ rank} $\downarrow$ & \shortstack{sig \\ wins} & \shortstack{sig \\ losses} & \shortstack{net \\ wins} & \shortstack{win \\ share} & mean $r$ \\
+\midrule
+Sandwich & 2.223 & 5 & 0 & 5 & 1.000 & 0.564 \\
+LDLT-R & 2.715 & 4 & 1 & 3 & 0.800 & 0.478 \\
+SLL & 3.248 & 2 & 2 & 0 & 0.400 & 0.624 \\
+Orthogonal & 3.380 & 2 & 2 & 0 & 0.400 & 0.627 \\
+LDLT-L & 3.760 & 1 & 4 & -3 & 0.200 & 0.737 \\
+AOL & 5.674 & 0 & 5 & -5 & 0.000 & 0.000 \\
+\bottomrule
+\end{tabular}
+}
+\end{threeparttable}
+\end{table}
+
+\begin{table}[t]
+\centering
+\begin{threeparttable}
+{\small
+\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 $\alpha=0.05$.}
+\label{tab:overall:mean_cert_acc_72}
+\setlength{\tabcolsep}{4pt}
+\begin{tabular}{@{}l r r r r r r@{}}
+\toprule
+Algorithm & \shortstack{Avg \\ rank} $\downarrow$ & \shortstack{sig \\ wins} & \shortstack{sig \\ losses} & \shortstack{net \\ wins} & \shortstack{win \\ share} & mean $r$ \\
+\midrule
+Sandwich & 1.979 & 5 & 0 & 5 & 1.000 & 0.662 \\
+LDLT-R & 2.628 & 4 & 1 & 3 & 0.800 & 0.542 \\
+SLL & 3.306 & 2 & 2 & 0 & 0.400 & 0.647 \\
+Orthogonal & 3.417 & 2 & 2 & 0 & 0.400 & 0.632 \\
+LDLT-L & 4.008 & 1 & 4 & -3 & 0.200 & 0.754 \\
+AOL & 5.661 & 0 & 5 & -5 & 0.000 & 0.000 \\
+\bottomrule
+\end{tabular}
+}
+\end{threeparttable}
+\end{table}
+
+\begin{table}[t]
+\centering
+\begin{threeparttable}
+{\small
+\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 $\alpha=0.05$.}
+\label{tab:overall:mean_cert_acc_108}
+\setlength{\tabcolsep}{4pt}
+\begin{tabular}{@{}l r r r r r r@{}}
+\toprule
+Algorithm & \shortstack{Avg \\ rank} $\downarrow$ & \shortstack{sig \\ wins} & \shortstack{sig \\ losses} & \shortstack{net \\ wins} & \shortstack{win \\ share} & mean $r$ \\
+\midrule
+Sandwich & 1.876 & 5 & 0 & 5 & 1.000 & 0.680 \\
+LDLT-R & 2.525 & 4 & 1 & 3 & 0.800 & 0.548 \\
+SLL & 3.318 & 2 & 2 & 0 & 0.400 & 0.662 \\
+Orthogonal & 3.364 & 2 & 2 & 0 & 0.400 & 0.677 \\
+LDLT-L & 4.194 & 1 & 4 & -3 & 0.200 & 0.824 \\
+AOL & 5.723 & 0 & 5 & -5 & 0.000 & 0.000 \\
+\bottomrule
+\end{tabular}
+}
+\end{threeparttable}
+\end{table}
+
+\begin{table}[t]
+\centering
+\begin{threeparttable}
+{\small
+\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 $\alpha=0.05$.}
+\label{tab:overall:mean_cert_acc_255}
+\setlength{\tabcolsep}{4pt}
+\begin{tabular}{@{}l r r r r r r@{}}
+\toprule
+Algorithm & \shortstack{Avg \\ rank} $\downarrow$ & \shortstack{sig \\ wins} & \shortstack{sig \\ losses} & \shortstack{net \\ wins} & \shortstack{win \\ share} & mean $r$ \\
+\midrule
+Sandwich & 2.029 & 5 & 0 & 5 & 1.000 & 0.663 \\
+LDLT-R & 2.517 & 4 & 1 & 3 & 0.800 & 0.584 \\
+Orthogonal & 3.409 & 2 & 2 & 0 & 0.400 & 0.600 \\
+SLL & 3.409 & 2 & 2 & 0 & 0.400 & 0.643 \\
+LDLT-L & 4.174 & 1 & 4 & -3 & 0.200 & 0.808 \\
+AOL & 5.463 & 0 & 5 & -5 & 0.000 & 0.000 \\
+\bottomrule
+\end{tabular}
+}
+\end{threeparttable}
+\end{table}
+
+\begin{table}[t]
+\centering
+\begin{threeparttable}
+{
+\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).}
+\label{tab:signif:mean_test_acc}
+\setlength{\tabcolsep}{3pt}
+\begin{tabular}{@{}l c c c c c c @{}}
+\toprule
+ & AOL & LDLT-L & LDLT-R & Orthogonal & Sandwich & SLL \\
+\midrule
+AOL & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} \\
+LDLT-L & \textcolor{green}{$\blacktriangle$} & $\cdot$ & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & $\cdot$ & \textcolor{green}{$\blacktriangle$} \\
+LDLT-R & \textcolor{green}{$\blacktriangle$} & \textcolor{red}{$\blacktriangledown$} & $\cdot$ & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & $\cdot$ \\
+Orthogonal & \textcolor{green}{$\blacktriangle$} & \textcolor{red}{$\blacktriangledown$} & $\cdot$ & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & $\cdot$ \\
+Sandwich & \textcolor{green}{$\blacktriangle$} & $\cdot$ & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & $\cdot$ & \textcolor{green}{$\blacktriangle$} \\
+SLL & \textcolor{green}{$\blacktriangle$} & \textcolor{red}{$\blacktriangledown$} & $\cdot$ & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & $\cdot$ \\
+\bottomrule
+\end{tabular}
+}
+\end{threeparttable}
+\end{table}
+
+\begin{table}[t]
+\centering
+\begin{threeparttable}
+{
+\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).}
+\label{tab:signif:mean_cert_acc_36}
+\setlength{\tabcolsep}{3pt}
+\begin{tabular}{@{}l c c c c c c @{}}
+\toprule
+ & AOL & LDLT-L & LDLT-R & Orthogonal & Sandwich & SLL \\
+\midrule
+AOL & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} \\
+LDLT-L & \textcolor{green}{$\blacktriangle$} & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} \\
+LDLT-R & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & $\cdot$ & \textcolor{green}{$\blacktriangle$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{green}{$\blacktriangle$} \\
+Orthogonal & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & \textcolor{red}{$\blacktriangledown$} & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & $\cdot$ \\
+Sandwich & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & $\cdot$ & \textcolor{green}{$\blacktriangle$} \\
+SLL & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & \textcolor{red}{$\blacktriangledown$} & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & $\cdot$ \\
+\bottomrule
+\end{tabular}
+}
+\end{threeparttable}
+\end{table}
+
+\begin{table}[t]
+\centering
+\begin{threeparttable}
+{
+\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).}
+\label{tab:signif:mean_cert_acc_72}
+\setlength{\tabcolsep}{3pt}
+\begin{tabular}{@{}l c c c c c c @{}}
+\toprule
+ & AOL & LDLT-L & LDLT-R & Orthogonal & Sandwich & SLL \\
+\midrule
+AOL & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} \\
+LDLT-L & \textcolor{green}{$\blacktriangle$} & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} \\
+LDLT-R & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & $\cdot$ & \textcolor{green}{$\blacktriangle$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{green}{$\blacktriangle$} \\
+Orthogonal & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & \textcolor{red}{$\blacktriangledown$} & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & $\cdot$ \\
+Sandwich & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & $\cdot$ & \textcolor{green}{$\blacktriangle$} \\
+SLL & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & \textcolor{red}{$\blacktriangledown$} & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & $\cdot$ \\
+\bottomrule
+\end{tabular}
+}
+\end{threeparttable}
+\end{table}
+
+\begin{table}[t]
+\centering
+\begin{threeparttable}
+{
+\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).}
+\label{tab:signif:mean_cert_acc_108}
+\setlength{\tabcolsep}{3pt}
+\begin{tabular}{@{}l c c c c c c @{}}
+\toprule
+ & AOL & LDLT-L & LDLT-R & Orthogonal & Sandwich & SLL \\
+\midrule
+AOL & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} \\
+LDLT-L & \textcolor{green}{$\blacktriangle$} & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} \\
+LDLT-R & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & $\cdot$ & \textcolor{green}{$\blacktriangle$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{green}{$\blacktriangle$} \\
+Orthogonal & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & \textcolor{red}{$\blacktriangledown$} & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & $\cdot$ \\
+Sandwich & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & $\cdot$ & \textcolor{green}{$\blacktriangle$} \\
+SLL & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & \textcolor{red}{$\blacktriangledown$} & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & $\cdot$ \\
+\bottomrule
+\end{tabular}
+}
+\end{threeparttable}
+\end{table}
+
+\begin{table}[t]
+\centering
+\begin{threeparttable}
+{
+\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).}
+\label{tab:signif:mean_cert_acc_255}
+\setlength{\tabcolsep}{3pt}
+\begin{tabular}{@{}l c c c c c c @{}}
+\toprule
+ & AOL & LDLT-L & LDLT-R & Orthogonal & Sandwich & SLL \\
+\midrule
+AOL & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} \\
+LDLT-L & \textcolor{green}{$\blacktriangle$} & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} \\
+LDLT-R & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & $\cdot$ & \textcolor{green}{$\blacktriangle$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{green}{$\blacktriangle$} \\
+Orthogonal & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & \textcolor{red}{$\blacktriangledown$} & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & $\cdot$ \\
+Sandwich & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & $\cdot$ & \textcolor{green}{$\blacktriangle$} \\
+SLL & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & \textcolor{red}{$\blacktriangledown$} & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & $\cdot$ \\
+\bottomrule
+\end{tabular}
+}
+\end{threeparttable}
+\end{table}
+
+
+\begin{table*}[t]
+\centering
+\begin{threeparttable}
+\caption[Mean Accuracy]{Wilcoxon signed-rank tests (two-sided) for Mean Accuracy; $p$-values with Holm FWER corrections within-metric and global.}
+\label{tab:wilcoxon:mean_test_acc}
+\begingroup
+\setlength{\tabcolsep}{4pt}
+\begin{tabular}{ll r r r r r r r r r r r}
+\toprule
+\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}
+Alg A & Alg B & $n$ & wins$_A$ & wins$_B$ & ties & WinRate A & \shortstack{Median \\ $\Delta$ (A--B)} & $W$ & $p$ & $p_{\text{Holm,within}}$ & $p_{\text{Holm,global}}$ & $r$ \\
+\midrule
+AOL & LDLT-L & 121 & 16 & 105 & 0 & 0.1322 & -0.0568 & 412 & $2.3e-17^{***}$ & $3.4e-16^{***}$ & $0^{***}$ & 0.7708 \\
+AOL & Sandwich & 121 & 18 & 103 & 0 & 0.1488 & -0.0595 & 518 & $2.3e-16^{***}$ & $0^{***}$ & $0^{***}$ & 0.7459 \\
+AOL & SLL & 121 & 22 & 99 & 0 & 0.1818 & -0.0351 & 806 & $0^{***}$ & $0^{***}$ & $0^{***}$ & 0.6782 \\
+AOL & Orthogonal & 121 & 27 & 94 & 0 & 0.2231 & -0.0265 & 971 & $0^{***}$ & $0^{***}$ & $1.0e-10^{***}$ & 0.6394 \\
+AOL & LDLT-R & 121 & 25 & 96 & 0 & 0.2066 & -0.0313 & 1013 & $0^{***}$ & $0^{***}$ & $2.0e-10^{***}$ & 0.6295 \\
+Orthogonal & Sandwich & 121 & 31 & 89 & 1 & 0.2603 & -0.0126 & 1269 & $6.0e-10^{***}$ & $6.3e-09^{***}$ & $2.3e-08^{***}$ & 0.5643 \\
+LDLT-L & Orthogonal & 121 & 94 & 27 & 0 & 0.7769 & 0.0139 & 1309 & $7.0e-10^{***}$ & $6.6e-09^{***}$ & $2.6e-08^{***}$ & 0.5599 \\
+LDLT-L & SLL & 121 & 86 & 35 & 0 & 0.7107 & 0.0111 & 1503 & $1.5e-08^{***}$ & $1.2e-07^{***}$ & $5.1e-07^{***}$ & 0.5143 \\
+LDLT-L & LDLT-R & 121 & 87 & 33 & 1 & 0.7231 & 0.0108 & 1689 & $3.7e-07^{***}$ & $2.6e-06^{***}$ & $1.1e-05^{***}$ & 0.4639 \\
+Sandwich & SLL & 121 & 83 & 38 & 0 & 0.6860 & 0.0090 & 1789 & $8.8e-07^{***}$ & $5.3e-06^{***}$ & $2.4e-05^{***}$ & 0.4470 \\
+LDLT-R & Sandwich & 121 & 43 & 78 & 0 & 0.3554 & -0.0068 & 2364 & $6.0e-04^{***}$ & $3.0e-03^{**}$ & $9.1e-03^{**}$ & 0.3118 \\
+LDLT-R & SLL & 121 & 66 & 54 & 1 & 0.5496 & 0.0019 & 3070 & $1.4e-01$ & $5.7e-01$ & $8.6e-01$ & 0.1338 \\
+LDLT-R & Orthogonal & 121 & 71 & 50 & 0 & 0.5868 & 0.0025 & 3138 & $1.5e-01$ & $5.7e-01$ & $8.6e-01$ & 0.1298 \\
+Orthogonal & SLL & 121 & 60 & 61 & 0 & 0.4959 & -0.0004 & 3623 & $8.6e-01$ & $1.0e+00$ & $1.0e+00$ & 0.0158 \\
+LDLT-L & Sandwich & 121 & 59 & 62 & 0 & 0.4876 & -0.0002 & 3624 & $8.6e-01$ & $1.0e+00$ & $1.0e+00$ & 0.0155 \\
+\bottomrule
+\end{tabular}
+\begin{tablenotes}
+\item Stars mark significance ($^*\,p\!\le\!0.05$, $^{**}\,p\!\le\!0.01$, $^{***}\,p\!\le\!0.001$).
+\end{tablenotes}
+\endgroup
+\end{threeparttable}
+\end{table*}
+
+
+
+\begin{table*}[t]
+\centering
+\begin{threeparttable}
+\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.}
+\label{tab:wilcoxon:mean_cert_acc_36}
+\begingroup
+\setlength{\tabcolsep}{4pt}
+\begin{tabular}{ll r r r r r r r r r r r}
+\toprule
+\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}
+Alg A & Alg B & $n$ & wins$_A$ & wins$_B$ & ties & WinRate A & \shortstack{Median \\ $\Delta$ (A--B)} & $W$ & $p$ & $p_{\text{Holm,within}}$ & $p_{\text{Holm,global}}$ & $r$ \\
+\midrule
+AOL & SLL & 121 & 4 & 117 & 0 & 0.0331 & -0.1998 & 27 & $2.7e-21^{***}$ & $4.0e-20^{***}$ & $2.0e-19^{***}$ & 0.8613 \\
+AOL & Sandwich & 121 & 6 & 114 & 1 & 0.0537 & -0.2626 & 32 & $4.5e-21^{***}$ & $6.1e-20^{***}$ & $3.2e-19^{***}$ & 0.8601 \\
+AOL & LDLT-R & 121 & 4 & 117 & 0 & 0.0331 & -0.2302 & 47 & $4.4e-21^{***}$ & $6.1e-20^{***}$ & $3.2e-19^{***}$ & 0.8566 \\
+AOL & Orthogonal & 121 & 8 & 113 & 0 & 0.0661 & -0.2204 & 87 & $1.2e-20^{***}$ & $1.4e-19^{***}$ & $7.9e-19^{***}$ & 0.8472 \\
+AOL & LDLT-L & 121 & 17 & 104 & 0 & 0.1405 & -0.1415 & 554 & $5.0e-16^{***}$ & $0^{***}$ & $0^{***}$ & 0.7374 \\
+LDLT-L & Sandwich & 121 & 31 & 89 & 1 & 0.2603 & -0.0387 & 998 & $0^{***}$ & $1.0e-10^{***}$ & $2.0e-10^{***}$ & 0.6291 \\
+LDLT-L & LDLT-R & 121 & 40 & 81 & 0 & 0.3306 & -0.0297 & 1410 & $3.7e-09^{***}$ & $3.3e-08^{***}$ & $1.3e-07^{***}$ & 0.5361 \\
+Orthogonal & Sandwich & 121 & 28 & 93 & 0 & 0.2314 & -0.0238 & 1424 & $4.6e-09^{***}$ & $3.7e-08^{***}$ & $1.6e-07^{***}$ & 0.5327 \\
+Sandwich & SLL & 121 & 83 & 38 & 0 & 0.6860 & 0.0207 & 1530 & $2.3e-08^{***}$ & $1.6e-07^{***}$ & $7.4e-07^{***}$ & 0.5079 \\
+LDLT-L & Orthogonal & 121 & 48 & 73 & 0 & 0.3967 & -0.0200 & 1957 & $7.4e-06^{***}$ & $4.4e-05^{***}$ & $1.8e-04^{***}$ & 0.4075 \\
+LDLT-L & SLL & 121 & 47 & 73 & 1 & 0.3926 & -0.0085 & 2014 & $2.3e-05^{***}$ & $1.2e-04^{***}$ & $4.4e-04^{***}$ & 0.3862 \\
+LDLT-R & SLL & 121 & 76 & 43 & 2 & 0.6364 & 0.0095 & 2285 & $6.6e-04^{***}$ & $2.6e-03^{**}$ & $9.2e-03^{**}$ & 0.3123 \\
+LDLT-R & Sandwich & 121 & 44 & 77 & 0 & 0.3636 & -0.0089 & 2466 & $1.5e-03^{**}$ & $4.6e-03^{**}$ & $1.7e-02^{*}$ & 0.2878 \\
+LDLT-R & Orthogonal & 121 & 78 & 42 & 1 & 0.6488 & 0.0084 & 2756 & $2.2e-02^{*}$ & $4.4e-02^{*}$ & $2.0e-01$ & 0.2088 \\
+Orthogonal & SLL & 121 & 60 & 60 & 1 & 0.5000 & 0.0000 & 2916 & $6.2e-02$ & $6.2e-02$ & $4.9e-01$ & 0.1705 \\
+\bottomrule
+\end{tabular}
+\begin{tablenotes}
+\item Stars mark significance ($^*\,p\!\le\!0.05$, $^{**}\,p\!\le\!0.01$, $^{***}\,p\!\le\!0.001$).
+\end{tablenotes}
+\endgroup
+\end{threeparttable}
+\end{table*}
+
+
+
+\begin{table*}[t]
+\centering
+\begin{threeparttable}
+\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.}
+\label{tab:wilcoxon:mean_cert_acc_72}
+\begingroup
+\setlength{\tabcolsep}{4pt}
+\begin{tabular}{ll r r r r r r r r r r r}
+\toprule
+\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}
+Alg A & Alg B & $n$ & wins$_A$ & wins$_B$ & ties & WinRate A & \shortstack{Median \\ $\Delta$ (A--B)} & $W$ & $p$ & $p_{\text{Holm,within}}$ & $p_{\text{Holm,global}}$ & $r$ \\
+\midrule
+AOL & Sandwich & 121 & 6 & 114 & 1 & 0.0537 & -0.2723 & 58 & $8.5e-21^{***}$ & $1.3e-19^{***}$ & $5.9e-19^{***}$ & 0.8538 \\
+AOL & SLL & 121 & 3 & 116 & 2 & 0.0331 & -0.1967 & 59 & $1.3e-20^{***}$ & $1.8e-19^{***}$ & $8.6e-19^{***}$ & 0.8534 \\
+AOL & LDLT-R & 121 & 5 & 116 & 0 & 0.0413 & -0.2325 & 103 & $1.7e-20^{***}$ & $2.2e-19^{***}$ & $1.1e-18^{***}$ & 0.8435 \\
+AOL & Orthogonal & 121 & 8 & 113 & 0 & 0.0661 & -0.2085 & 149 & $5.2e-20^{***}$ & $6.3e-19^{***}$ & $3.3e-18^{***}$ & 0.8327 \\
+AOL & LDLT-L & 121 & 16 & 102 & 3 & 0.1446 & -0.1155 & 460 & $2.6e-16^{***}$ & $0^{***}$ & $0^{***}$ & 0.7539 \\
+LDLT-L & Sandwich & 121 & 21 & 100 & 0 & 0.1736 & -0.0748 & 670 & $0^{***}$ & $0^{***}$ & $0^{***}$ & 0.7101 \\
+Orthogonal & Sandwich & 121 & 18 & 103 & 0 & 0.1488 & -0.0370 & 698 & $0^{***}$ & $0^{***}$ & $0^{***}$ & 0.7037 \\
+Sandwich & SLL & 121 & 91 & 28 & 2 & 0.7603 & 0.0396 & 823 & $0^{***}$ & $0^{***}$ & $0^{***}$ & 0.6676 \\
+LDLT-L & LDLT-R & 121 & 30 & 90 & 1 & 0.2521 & -0.0625 & 988 & $0^{***}$ & $0^{***}$ & $2.0e-10^{***}$ & 0.6315 \\
+LDLT-L & SLL & 121 & 42 & 79 & 0 & 0.3471 & -0.0231 & 1813 & $1.2e-06^{***}$ & $7.2e-06^{***}$ & $3.1e-05^{***}$ & 0.4414 \\
+LDLT-L & Orthogonal & 121 & 44 & 77 & 0 & 0.3636 & -0.0192 & 1857 & $2.1e-06^{***}$ & $1.1e-05^{***}$ & $5.3e-05^{***}$ & 0.4310 \\
+LDLT-R & SLL & 121 & 79 & 41 & 1 & 0.6570 & 0.0156 & 1982 & $1.6e-05^{***}$ & $6.4e-05^{***}$ & $3.5e-04^{***}$ & 0.3937 \\
+LDLT-R & Sandwich & 121 & 44 & 77 & 0 & 0.3636 & -0.0238 & 2090 & $3.5e-05^{***}$ & $1.1e-04^{***}$ & $6.3e-04^{***}$ & 0.3761 \\
+LDLT-R & Orthogonal & 121 & 77 & 42 & 2 & 0.6446 & 0.0106 & 2346 & $1.2e-03^{**}$ & $2.4e-03^{**}$ & $1.5e-02^{*}$ & 0.2974 \\
+Orthogonal & SLL & 121 & 61 & 59 & 1 & 0.5083 & 0.0002 & 3188 & $2.5e-01$ & $2.5e-01$ & $9.9e-01$ & 0.1055 \\
+\bottomrule
+\end{tabular}
+\begin{tablenotes}
+\item Stars mark significance ($^*\,p\!\le\!0.05$, $^{**}\,p\!\le\!0.01$, $^{***}\,p\!\le\!0.001$).
+\end{tablenotes}
+\endgroup
+\end{threeparttable}
+\end{table*}
+
+
+
+\begin{table*}[t]
+\centering
+\begin{threeparttable}
+\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.}
+\label{tab:wilcoxon:mean_cert_acc_108}
+\begingroup
+\setlength{\tabcolsep}{4pt}
+\begin{tabular}{ll r r r r r r r r r r r}
+\toprule
+\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}
+Alg A & Alg B & $n$ & wins$_A$ & wins$_B$ & ties & WinRate A & \shortstack{Median \\ $\Delta$ (A--B)} & $W$ & $p$ & $p_{\text{Holm,within}}$ & $p_{\text{Holm,global}}$ & $r$ \\
+\midrule
+AOL & LDLT-R & 121 & 1 & 119 & 1 & 0.0124 & -0.2179 & 1 & $2.0e-21^{***}$ & $3.1e-20^{***}$ & $1.5e-19^{***}$ & 0.8675 \\
+AOL & SLL & 121 & 2 & 116 & 3 & 0.0289 & -0.1595 & 12 & $5.8e-21^{***}$ & $7.5e-20^{***}$ & $4.1e-19^{***}$ & 0.8648 \\
+AOL & Sandwich & 121 & 4 & 116 & 1 & 0.0372 & -0.2402 & 32 & $4.5e-21^{***}$ & $6.2e-20^{***}$ & $3.2e-19^{***}$ & 0.8601 \\
+AOL & Orthogonal & 121 & 6 & 113 & 2 & 0.0579 & -0.1817 & 72 & $1.8e-20^{***}$ & $2.1e-19^{***}$ & $1.2e-18^{***}$ & 0.8502 \\
+AOL & LDLT-L & 121 & 12 & 99 & 10 & 0.1405 & -0.0785 & 158 & $4.0e-18^{***}$ & $4.4e-17^{***}$ & $2.5e-16^{***}$ & 0.8237 \\
+LDLT-L & Sandwich & 121 & 17 & 104 & 0 & 0.1405 & -0.0905 & 492 & $1.3e-16^{***}$ & $0^{***}$ & $0^{***}$ & 0.7520 \\
+Orthogonal & Sandwich & 121 & 16 & 105 & 0 & 0.1322 & -0.0475 & 700 & $0^{***}$ & $0^{***}$ & $0^{***}$ & 0.7030 \\
+Sandwich & SLL & 121 & 93 & 26 & 2 & 0.7769 & 0.0480 & 764 & $0^{***}$ & $0^{***}$ & $0^{***}$ & 0.6820 \\
+LDLT-L & LDLT-R & 121 & 23 & 97 & 1 & 0.1942 & -0.0468 & 787 & $0^{***}$ & $0^{***}$ & $0^{***}$ & 0.6796 \\
+LDLT-L & Orthogonal & 121 & 35 & 84 & 2 & 0.2975 & -0.0276 & 1497 & $3.9e-08^{***}$ & $2.3e-07^{***}$ & $1.2e-06^{***}$ & 0.5038 \\
+LDLT-L & SLL & 121 & 37 & 82 & 2 & 0.3140 & -0.0208 & 1682 & $5.6e-07^{***}$ & $2.8e-06^{***}$ & $1.6e-05^{***}$ & 0.4588 \\
+LDLT-R & SLL & 121 & 82 & 35 & 4 & 0.6942 & 0.0178 & 1875 & $1.8e-05^{***}$ & $5.4e-05^{***}$ & $3.8e-04^{***}$ & 0.3963 \\
+LDLT-R & Sandwich & 121 & 41 & 79 & 1 & 0.3430 & -0.0213 & 1952 & $1.1e-05^{***}$ & $4.5e-05^{***}$ & $2.6e-04^{***}$ & 0.4010 \\
+LDLT-R & Orthogonal & 121 & 77 & 42 & 2 & 0.6446 & 0.0191 & 2543 & $6.5e-03^{**}$ & $1.3e-02^{*}$ & $6.5e-02$ & 0.2495 \\
+Orthogonal & SLL & 121 & 60 & 59 & 2 & 0.5041 & 0.0000 & 2941 & $9.6e-02$ & $9.6e-02$ & $6.7e-01$ & 0.1528 \\
+\bottomrule
+\end{tabular}
+\begin{tablenotes}
+\item Stars mark significance ($^*\,p\!\le\!0.05$, $^{**}\,p\!\le\!0.01$, $^{***}\,p\!\le\!0.001$).
+\end{tablenotes}
+\endgroup
+\end{threeparttable}
+\end{table*}
+
+
+
+\begin{table*}[t]
+\centering
+\begin{threeparttable}
+\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.}
+\label{tab:wilcoxon:mean_cert_acc_255}
+\begingroup
+\setlength{\tabcolsep}{4pt}
+\begin{tabular}{ll r r r r r r r r r r r}
+\toprule
+\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}
+Alg A & Alg B & $n$ & wins$_A$ & wins$_B$ & ties & WinRate A & \shortstack{Median \\ $\Delta$ (A--B)} & $W$ & $p$ & $p_{\text{Holm,within}}$ & $p_{\text{Holm,global}}$ & $r$ \\
+\midrule
+AOL & LDLT-R & 121 & 2 & 107 & 12 & 0.0661 & -0.0560 & 17 & $2.1e-19^{***}$ & $3.1e-18^{***}$ & $1.3e-17^{***}$ & 0.8629 \\
+AOL & SLL & 121 & 2 & 99 & 20 & 0.0992 & -0.0407 & 24 & $5.5e-18^{***}$ & $7.2e-17^{***}$ & $3.3e-16^{***}$ & 0.8599 \\
+AOL & Sandwich & 121 & 2 & 107 & 12 & 0.0661 & -0.0791 & 58 & $6.4e-19^{***}$ & $8.9e-18^{***}$ & $4.0e-17^{***}$ & 0.8511 \\
+AOL & Orthogonal & 121 & 5 & 100 & 16 & 0.1074 & -0.0347 & 109 & $1.3e-17^{***}$ & $1.5e-16^{***}$ & $7.6e-16^{***}$ & 0.8339 \\
+AOL & LDLT-L & 121 & 6 & 79 & 36 & 0.1983 & -0.0167 & 127 & $0^{***}$ & $0^{***}$ & $0^{***}$ & 0.8080 \\
+LDLT-L & Sandwich & 121 & 11 & 98 & 12 & 0.1405 & -0.0371 & 291 & $2.8e-16^{***}$ & $0^{***}$ & $0^{***}$ & 0.7836 \\
+Orthogonal & Sandwich & 121 & 16 & 95 & 10 & 0.1736 & -0.0340 & 427 & $0^{***}$ & $0^{***}$ & $0^{***}$ & 0.7486 \\
+Sandwich & SLL & 121 & 86 & 24 & 11 & 0.7562 & 0.0261 & 845 & $0^{***}$ & $4.0e-10^{***}$ & $1.8e-09^{***}$ & 0.6276 \\
+LDLT-L & LDLT-R & 121 & 20 & 89 & 12 & 0.2149 & -0.0193 & 847 & $1.0e-10^{***}$ & $6.0e-10^{***}$ & $3.1e-09^{***}$ & 0.6226 \\
+LDLT-L & SLL & 121 & 29 & 72 & 20 & 0.3223 & -0.0068 & 1312 & $1.9e-05^{***}$ & $9.4e-05^{***}$ & $3.8e-04^{***}$ & 0.4257 \\
+LDLT-R & SLL & 121 & 80 & 29 & 12 & 0.7107 & 0.0184 & 1331 & $4.7e-07^{***}$ & $2.8e-06^{***}$ & $1.4e-05^{***}$ & 0.4824 \\
+LDLT-L & Orthogonal & 121 & 34 & 71 & 16 & 0.3471 & -0.0067 & 1607 & $1.7e-04^{***}$ & $5.2e-04^{***}$ & $2.8e-03^{**}$ & 0.3666 \\
+LDLT-R & Orthogonal & 121 & 74 & 38 & 9 & 0.6488 & 0.0104 & 1829 & $1.1e-04^{***}$ & $4.3e-04^{***}$ & $1.8e-03^{**}$ & 0.3661 \\
+LDLT-R & Sandwich & 121 & 45 & 68 & 8 & 0.4050 & -0.0092 & 2100 & $1.3e-03^{**}$ & $2.7e-03^{**}$ & $1.6e-02^{*}$ & 0.3018 \\
+Orthogonal & SLL & 121 & 57 & 52 & 12 & 0.5207 & 0.0000 & 2967 & $9.3e-01$ & $9.3e-01$ & $1.0e+00$ & 0.0087 \\
+\bottomrule
+\end{tabular}
+\begin{tablenotes}
+\item Stars mark significance ($^*\,p\!\le\!0.05$, $^{**}\,p\!\le\!0.01$, $^{***}\,p\!\le\!0.001$).
+\end{tablenotes}
+\endgroup
+\end{threeparttable}
+\end{table*}

UCI_N4/sdp/runs/abalone/fold_0/result.json

@@ -0,0 +1,46 @@
+{
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+}

UCI_N4/sdp/runs/abalone/fold_1/result.json

@@ -0,0 +1,46 @@
+{
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UCI_N4/sdp/runs/abalone/fold_2/result.json

@@ -0,0 +1,46 @@
+{
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UCI_N4/sdp/runs/abalone/fold_3/result.json

@@ -0,0 +1,46 @@
+{
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UCI_N4/sdp/runs/acute-inflammation/fold_0/result.json

@@ -0,0 +1,42 @@
+{
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UCI_N4/sdp/runs/acute-inflammation/fold_1/result.json

@@ -0,0 +1,42 @@
+{
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UCI_N4/sdp/runs/acute-inflammation/fold_2/result.json

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UCI_N4/sdp/runs/acute-inflammation/fold_3/result.json

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UCI_N4/sdp/runs/acute-nephritis/fold_0/result.json

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UCI_N4/sdp/runs/acute-nephritis/fold_1/result.json

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UCI_N4/sdp/runs/acute-nephritis/fold_2/result.json

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UCI_N4/sdp/runs/acute-nephritis/fold_3/result.json

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UCI_N4/sdp/runs/adult/fold_0/result.json

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UCI_N4/sdp/runs/adult/fold_1/result.json

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UCI_N4/sdp/runs/adult/fold_2/result.json

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UCI_N4/sdp/runs/adult/fold_3/result.json

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UCI_N4/sdp/runs/annealing/fold_0/result.json

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UCI_N4/sdp/runs/annealing/fold_1/result.json

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UCI_N4/sdp/runs/annealing/fold_2/result.json

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UCI_N4/sdp/runs/annealing/fold_3/result.json

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UCI_N4/sdp/runs/arrhythmia/fold_0/result.json

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UCI_N4/sdp/runs/audiology-std/fold_2/result.json

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UCI_N4/sdp/runs/audiology-std/fold_3/result.json

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UCI_N4/sdp/runs/balance-scale/fold_0/result.json

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UCI_N4/sdp/runs/balance-scale/fold_1/result.json

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UCI_N4/sdp/runs/balance-scale/fold_2/result.json

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UCI_N4/sdp/runs/balance-scale/fold_3/result.json

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UCI_N4/sdp/runs/blood/fold_0/result.json

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UCI_N4/sdp/runs/blood/fold_1/result.json

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UCI_N4/sdp/runs/blood/fold_2/result.json

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UCI_N4/sdp/runs/blood/fold_3/result.json

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UCI_N4/sdp/runs/car/fold_0/result.json

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UCI_N4/wilcoxon_pairwise_all.csv

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UCI_N4/wilcoxon_pairwise_all.json

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+]

UCI_N6/jmlr_tables.tex

@@ -0,0 +1,469 @@
+% JMLR-ready tables for two-column papers
+% Required packages (no siunitx):
+% \usepackage{booktabs}
+% \usepackage{threeparttable}
+% \usepackage{threeparttablex} % for TableNotes + longtable
+% \usepackage{longtable}
+% Optional for landscape: \usepackage{pdflscape}
+
+\begin{table*}[t]
+\centering
+\begin{threeparttable}
+\caption{Model dimension ranges (min--max across all datasets and folds). Input/Output dimensions follow dataset label spaces.}
+\label{tab:model-ranges}
+\begin{tabular}{l r r r r r r}
+\toprule
+Algorithm & Width & Depth & Parameters & Padding & Input dim & Output dim \\
+\midrule
+AOL & 32--512 & 6--6 & 502--1245037 & 10--524 & 3--262 & 2--100 \\
+Orthogonal & 32--512 & 6--6 & 507--1245042 & 10--524 & 3--262 & 2--100 \\
+Sandwich & 32--512 & 6--6 & 1057--2620542 & 10--524 & 3--262 & 2--100 \\
+SLL & 32--512 & 6--6 & 2326--1622697 & 10--524 & 3--262 & 2--100 \\
+LDLT-L & 32--512 & 6--6 & 5480--1454611 & 10--524 & 3--262 & 2--100 \\
+LDLT-R & 32--512 & 6--6 & 5577--1588756 & 10--524 & 3--262 & 2--100 \\
+\bottomrule
+\end{tabular}
+\end{threeparttable}
+\end{table*}
+
+\begin{table*}[t]
+\centering
+\begin{threeparttable}
+\caption{Sorted mean$\pm$std across $N$ datasets for each algorithm.}
+\label{tab:metric_summary}
+\begin{tabular}{l r lllll}
+\toprule
+ &  &  & \multicolumn{4}{c}{Certified Accuracy} \\
+\cmidrule(lr){4-7}
+Algorithm & $N$ & Accuracy & 36/255 & 72/255 & 108/255 & 255/255 \\
+\midrule
+AOL & 121 & 0.6049\,\tiny$\pm$0.2396 & 0.2918\,\tiny$\pm$0.3122 & 0.2161\,\tiny$\pm$0.2949 & 0.1740\,\tiny$\pm$0.2722 & 0.0837\,\tiny$\pm$0.1782 \\
+Orthogonal & 121 & 0.7036\,\tiny$\pm$0.1911 & 0.6071\,\tiny$\pm$0.2396 & 0.5068\,\tiny$\pm$0.2668 & 0.4233\,\tiny$\pm$0.2781 & 0.1983\,\tiny$\pm$0.2361 \\
+Sandwich & 121 & 0.7163\,\tiny$\pm$0.1879 & \textbf{0.6284\,\tiny$\pm$0.2414} & \textbf{0.5525\,\tiny$\pm$0.2633} & \textbf{0.4743\,\tiny$\pm$0.2773} & \textbf{0.2476\,\tiny$\pm$0.2509} \\
+SLL & 121 & 0.7011\,\tiny$\pm$0.1939 & 0.5866\,\tiny$\pm$0.2459 & 0.4810\,\tiny$\pm$0.2741 & 0.3932\,\tiny$\pm$0.2829 & 0.1882\,\tiny$\pm$0.2325 \\
+\midrule
+LDLT-L & 121 & \textbf{0.7245\,\tiny$\pm$0.1908} & 0.4665\,\tiny$\pm$0.3341 & 0.3863\,\tiny$\pm$0.3235 & 0.3226\,\tiny$\pm$0.3084 & 0.1562\,\tiny$\pm$0.2269 \\
+LDLT-R & 121 & 0.6970\,\tiny$\pm$0.2021 & 0.6114\,\tiny$\pm$0.2325 & 0.5253\,\tiny$\pm$0.2552 & 0.4516\,\tiny$\pm$0.2645 & 0.2138\,\tiny$\pm$0.2275 \\
+\bottomrule
+\end{tabular}
+\end{threeparttable}
+\end{table*}
+
+\begin{table}[t]
+\centering
+\begin{threeparttable}
+{\small
+\caption{Overall comparison on Mean Accuracy: average rank (lower is better) with Iman--Davenport $F=34.41$ (df=5,600), $p=1.11e-16$; Nemenyi CD$=0.969$. Counts are significant wins/losses after Holm within-metric at $\alpha=0.05$.}
+\label{tab:overall:mean_test_acc}
+\setlength{\tabcolsep}{4pt}
+\begin{tabular}{@{}l r r r r r r@{}}
+\toprule
+Algorithm & \shortstack{Avg \\ rank} $\downarrow$ & \shortstack{sig \\ wins} & \shortstack{sig \\ losses} & \shortstack{net \\ wins} & \shortstack{win \\ share} & mean $r$ \\
+\midrule
+LDLT-L & 2.525 & 4 & 0 & 4 & 0.800 & 0.533 \\
+Sandwich & 2.773 & 4 & 0 & 4 & 0.800 & 0.421 \\
+Orthogonal & 3.479 & 1 & 2 & -1 & 0.200 & 0.654 \\
+SLL & 3.545 & 1 & 2 & -1 & 0.200 & 0.621 \\
+LDLT-R & 3.628 & 1 & 2 & -1 & 0.200 & 0.560 \\
+AOL & 5.050 & 0 & 5 & -5 & 0.000 & 0.000 \\
+\bottomrule
+\end{tabular}
+}
+\end{threeparttable}
+\end{table}
+
+\begin{table}[t]
+\centering
+\begin{threeparttable}
+{\small
+\caption{Overall comparison on Mean Certified Accuracy (36/255): average rank (lower is better) with Iman--Davenport $F=71.33$ (df=5,600), $p=1.11e-16$; Nemenyi CD$=0.969$. Counts are significant wins/losses after Holm within-metric at $\alpha=0.05$.}
+\label{tab:overall:mean_cert_acc_36}
+\setlength{\tabcolsep}{4pt}
+\begin{tabular}{@{}l r r r r r r@{}}
+\toprule
+Algorithm & \shortstack{Avg \\ rank} $\downarrow$ & \shortstack{sig \\ wins} & \shortstack{sig \\ losses} & \shortstack{net \\ wins} & \shortstack{win \\ share} & mean $r$ \\
+\midrule
+Sandwich & 2.380 & 4 & 0 & 4 & 0.800 & 0.574 \\
+LDLT-R & 2.694 & 3 & 0 & 3 & 0.600 & 0.580 \\
+SLL & 3.128 & 2 & 2 & 0 & 0.400 & 0.696 \\
+Orthogonal & 3.252 & 2 & 1 & 1 & 0.400 & 0.671 \\
+LDLT-L & 4.004 & 1 & 4 & -3 & 0.200 & 0.645 \\
+AOL & 5.541 & 0 & 5 & -5 & 0.000 & 0.000 \\
+\bottomrule
+\end{tabular}
+}
+\end{threeparttable}
+\end{table}
+
+\begin{table}[t]
+\centering
+\begin{threeparttable}
+{\small
+\caption{Overall comparison on Mean Certified Accuracy (72/255): average rank (lower is better) with Iman--Davenport $F=111.54$ (df=5,600), $p=1.11e-16$; Nemenyi CD$=0.969$. Counts are significant wins/losses after Holm within-metric at $\alpha=0.05$.}
+\label{tab:overall:mean_cert_acc_72}
+\setlength{\tabcolsep}{4pt}
+\begin{tabular}{@{}l r r r r r r@{}}
+\toprule
+Algorithm & \shortstack{Avg \\ rank} $\downarrow$ & \shortstack{sig \\ wins} & \shortstack{sig \\ losses} & \shortstack{net \\ wins} & \shortstack{win \\ share} & mean $r$ \\
+\midrule
+Sandwich & 2.041 & 5 & 0 & 5 & 1.000 & 0.599 \\
+LDLT-R & 2.562 & 4 & 1 & 3 & 0.800 & 0.540 \\
+SLL & 3.260 & 2 & 2 & 0 & 0.400 & 0.729 \\
+Orthogonal & 3.273 & 2 & 2 & 0 & 0.400 & 0.707 \\
+LDLT-L & 4.153 & 1 & 4 & -3 & 0.200 & 0.776 \\
+AOL & 5.711 & 0 & 5 & -5 & 0.000 & 0.000 \\
+\bottomrule
+\end{tabular}
+}
+\end{threeparttable}
+\end{table}
+
+\begin{table}[t]
+\centering
+\begin{threeparttable}
+{\small
+\caption{Overall comparison on Mean Certified Accuracy (108/255): average rank (lower is better) with Iman--Davenport $F=129.26$ (df=5,600), $p=1.11e-16$; Nemenyi CD$=0.969$. Counts are significant wins/losses after Holm within-metric at $\alpha=0.05$.}
+\label{tab:overall:mean_cert_acc_108}
+\setlength{\tabcolsep}{4pt}
+\begin{tabular}{@{}l r r r r r r@{}}
+\toprule
+Algorithm & \shortstack{Avg \\ rank} $\downarrow$ & \shortstack{sig \\ wins} & \shortstack{sig \\ losses} & \shortstack{net \\ wins} & \shortstack{win \\ share} & mean $r$ \\
+\midrule
+Sandwich & 2.083 & 4 & 0 & 4 & 0.800 & 0.704 \\
+LDLT-R & 2.277 & 4 & 0 & 4 & 0.800 & 0.605 \\
+Orthogonal & 3.248 & 3 & 2 & 1 & 0.600 & 0.546 \\
+SLL & 3.430 & 2 & 3 & -1 & 0.400 & 0.702 \\
+LDLT-L & 4.236 & 1 & 4 & -3 & 0.200 & 0.828 \\
+AOL & 5.727 & 0 & 5 & -5 & 0.000 & 0.000 \\
+\bottomrule
+\end{tabular}
+}
+\end{threeparttable}
+\end{table}
+
+\begin{table}[t]
+\centering
+\begin{threeparttable}
+{\small
+\caption{Overall comparison on Mean Certified Accuracy (255/255): average rank (lower is better) with Iman--Davenport $F=91.19$ (df=5,600), $p=1.11e-16$; Nemenyi CD$=0.969$. Counts are significant wins/losses after Holm within-metric at $\alpha=0.05$.}
+\label{tab:overall:mean_cert_acc_255}
+\setlength{\tabcolsep}{4pt}
+\begin{tabular}{@{}l r r r r r r@{}}
+\toprule
+Algorithm & \shortstack{Avg \\ rank} $\downarrow$ & \shortstack{sig \\ wins} & \shortstack{sig \\ losses} & \shortstack{net \\ wins} & \shortstack{win \\ share} & mean $r$ \\
+\midrule
+Sandwich & 2.037 & 5 & 0 & 5 & 1.000 & 0.652 \\
+LDLT-R & 2.508 & 4 & 1 & 3 & 0.800 & 0.597 \\
+SLL & 3.322 & 2 & 2 & 0 & 0.400 & 0.679 \\
+Orthogonal & 3.459 & 2 & 2 & 0 & 0.400 & 0.653 \\
+LDLT-L & 4.194 & 1 & 4 & -3 & 0.200 & 0.850 \\
+AOL & 5.479 & 0 & 5 & -5 & 0.000 & 0.000 \\
+\bottomrule
+\end{tabular}
+}
+\end{threeparttable}
+\end{table}
+
+\begin{table}[t]
+\centering
+\begin{threeparttable}
+{
+\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).}
+\label{tab:signif:mean_test_acc}
+\setlength{\tabcolsep}{3pt}
+\begin{tabular}{@{}l c c c c c c @{}}
+\toprule
+ & AOL & LDLT-L & LDLT-R & Orthogonal & Sandwich & SLL \\
+\midrule
+AOL & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} \\
+LDLT-L & \textcolor{green}{$\blacktriangle$} & $\cdot$ & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & $\cdot$ & \textcolor{green}{$\blacktriangle$} \\
+LDLT-R & \textcolor{green}{$\blacktriangle$} & \textcolor{red}{$\blacktriangledown$} & $\cdot$ & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & $\cdot$ \\
+Orthogonal & \textcolor{green}{$\blacktriangle$} & \textcolor{red}{$\blacktriangledown$} & $\cdot$ & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & $\cdot$ \\
+Sandwich & \textcolor{green}{$\blacktriangle$} & $\cdot$ & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & $\cdot$ & \textcolor{green}{$\blacktriangle$} \\
+SLL & \textcolor{green}{$\blacktriangle$} & \textcolor{red}{$\blacktriangledown$} & $\cdot$ & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & $\cdot$ \\
+\bottomrule
+\end{tabular}
+}
+\end{threeparttable}
+\end{table}
+
+\begin{table}[t]
+\centering
+\begin{threeparttable}
+{
+\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).}
+\label{tab:signif:mean_cert_acc_36}
+\setlength{\tabcolsep}{3pt}
+\begin{tabular}{@{}l c c c c c c @{}}
+\toprule
+ & AOL & LDLT-L & LDLT-R & Orthogonal & Sandwich & SLL \\
+\midrule
+AOL & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} \\
+LDLT-L & \textcolor{green}{$\blacktriangle$} & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} \\
+LDLT-R & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & $\cdot$ & $\cdot$ & $\cdot$ & \textcolor{green}{$\blacktriangle$} \\
+Orthogonal & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & $\cdot$ & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & $\cdot$ \\
+Sandwich & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & $\cdot$ & \textcolor{green}{$\blacktriangle$} & $\cdot$ & \textcolor{green}{$\blacktriangle$} \\
+SLL & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & \textcolor{red}{$\blacktriangledown$} & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & $\cdot$ \\
+\bottomrule
+\end{tabular}
+}
+\end{threeparttable}
+\end{table}
+
+\begin{table}[t]
+\centering
+\begin{threeparttable}
+{
+\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).}
+\label{tab:signif:mean_cert_acc_72}
+\setlength{\tabcolsep}{3pt}
+\begin{tabular}{@{}l c c c c c c @{}}
+\toprule
+ & AOL & LDLT-L & LDLT-R & Orthogonal & Sandwich & SLL \\
+\midrule
+AOL & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} \\
+LDLT-L & \textcolor{green}{$\blacktriangle$} & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} \\
+LDLT-R & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & $\cdot$ & \textcolor{green}{$\blacktriangle$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{green}{$\blacktriangle$} \\
+Orthogonal & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & \textcolor{red}{$\blacktriangledown$} & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & $\cdot$ \\
+Sandwich & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & $\cdot$ & \textcolor{green}{$\blacktriangle$} \\
+SLL & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & \textcolor{red}{$\blacktriangledown$} & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & $\cdot$ \\
+\bottomrule
+\end{tabular}
+}
+\end{threeparttable}
+\end{table}
+
+\begin{table}[t]
+\centering
+\begin{threeparttable}
+{
+\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).}
+\label{tab:signif:mean_cert_acc_108}
+\setlength{\tabcolsep}{3pt}
+\begin{tabular}{@{}l c c c c c c @{}}
+\toprule
+ & AOL & LDLT-L & LDLT-R & Orthogonal & Sandwich & SLL \\
+\midrule
+AOL & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} \\
+LDLT-L & \textcolor{green}{$\blacktriangle$} & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} \\
+LDLT-R & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & $\cdot$ & \textcolor{green}{$\blacktriangle$} & $\cdot$ & \textcolor{green}{$\blacktriangle$} \\
+Orthogonal & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & \textcolor{red}{$\blacktriangledown$} & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & \textcolor{green}{$\blacktriangle$} \\
+Sandwich & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & $\cdot$ & \textcolor{green}{$\blacktriangle$} & $\cdot$ & \textcolor{green}{$\blacktriangle$} \\
+SLL & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & $\cdot$ \\
+\bottomrule
+\end{tabular}
+}
+\end{threeparttable}
+\end{table}
+
+\begin{table}[t]
+\centering
+\begin{threeparttable}
+{
+\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).}
+\label{tab:signif:mean_cert_acc_255}
+\setlength{\tabcolsep}{3pt}
+\begin{tabular}{@{}l c c c c c c @{}}
+\toprule
+ & AOL & LDLT-L & LDLT-R & Orthogonal & Sandwich & SLL \\
+\midrule
+AOL & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} \\
+LDLT-L & \textcolor{green}{$\blacktriangle$} & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{red}{$\blacktriangledown$} \\
+LDLT-R & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & $\cdot$ & \textcolor{green}{$\blacktriangle$} & \textcolor{red}{$\blacktriangledown$} & \textcolor{green}{$\blacktriangle$} \\
+Orthogonal & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & \textcolor{red}{$\blacktriangledown$} & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & $\cdot$ \\
+Sandwich & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & $\cdot$ & \textcolor{green}{$\blacktriangle$} \\
+SLL & \textcolor{green}{$\blacktriangle$} & \textcolor{green}{$\blacktriangle$} & \textcolor{red}{$\blacktriangledown$} & $\cdot$ & \textcolor{red}{$\blacktriangledown$} & $\cdot$ \\
+\bottomrule
+\end{tabular}
+}
+\end{threeparttable}
+\end{table}
+
+
+\begin{table*}[t]
+\centering
+\begin{threeparttable}
+\caption[Mean Accuracy]{Wilcoxon signed-rank tests (two-sided) for Mean Accuracy; $p$-values with Holm FWER corrections within-metric and global.}
+\label{tab:wilcoxon:mean_test_acc}
+\begingroup
+\setlength{\tabcolsep}{4pt}
+\begin{tabular}{ll r r r r r r r r r r r}
+\toprule
+\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}
+Alg A & Alg B & $n$ & wins$_A$ & wins$_B$ & ties & WinRate A & \shortstack{Median \\ $\Delta$ (A--B)} & $W$ & $p$ & $p_{\text{Holm,within}}$ & $p_{\text{Holm,global}}$ & $r$ \\
+\midrule
+AOL & LDLT-L & 121 & 16 & 105 & 0 & 0.1322 & -0.0632 & 409 & $2.1e-17^{***}$ & $3.2e-16^{***}$ & $0^{***}$ & 0.7715 \\
+AOL & Sandwich & 121 & 23 & 98 & 0 & 0.1901 & -0.0656 & 698 & $0^{***}$ & $0^{***}$ & $0^{***}$ & 0.7036 \\
+AOL & Orthogonal & 121 & 25 & 96 & 0 & 0.2066 & -0.0525 & 908 & $0^{***}$ & $0^{***}$ & $0^{***}$ & 0.6542 \\
+AOL & SLL & 121 & 24 & 97 & 0 & 0.1983 & -0.0445 & 1047 & $0^{***}$ & $1.0e-10^{***}$ & $4.0e-10^{***}$ & 0.6215 \\
+AOL & LDLT-R & 121 & 27 & 94 & 0 & 0.2231 & -0.0357 & 1307 & $7.0e-10^{***}$ & $7.8e-09^{***}$ & $2.4e-08^{***}$ & 0.5604 \\
+LDLT-L & SLL & 121 & 86 & 35 & 0 & 0.7107 & 0.0103 & 1511 & $1.7e-08^{***}$ & $1.7e-07^{***}$ & $5.0e-07^{***}$ & 0.5124 \\
+LDLT-L & LDLT-R & 121 & 87 & 34 & 0 & 0.7190 & 0.0125 & 1779 & $7.7e-07^{***}$ & $6.9e-06^{***}$ & $2.1e-05^{***}$ & 0.4494 \\
+LDLT-L & Orthogonal & 121 & 78 & 43 & 0 & 0.6446 & 0.0104 & 2002 & $1.3e-05^{***}$ & $1.0e-04^{***}$ & $2.8e-04^{***}$ & 0.3969 \\
+Orthogonal & Sandwich & 121 & 39 & 81 & 1 & 0.3264 & -0.0079 & 2171 & $1.3e-04^{***}$ & $9.4e-04^{***}$ & $2.5e-03^{**}$ & 0.3487 \\
+Sandwich & SLL & 121 & 80 & 41 & 0 & 0.6612 & 0.0063 & 2279 & $2.6e-04^{***}$ & $1.6e-03^{**}$ & $4.5e-03^{**}$ & 0.3318 \\
+LDLT-R & Sandwich & 121 & 47 & 74 & 0 & 0.3884 & -0.0101 & 2411 & $9.4e-04^{***}$ & $4.7e-03^{**}$ & $1.4e-02^{*}$ & 0.3008 \\
+LDLT-L & Sandwich & 121 & 64 & 56 & 1 & 0.5331 & 0.0008 & 3145 & $2.0e-01$ & $8.2e-01$ & $1.0e+00$ & 0.1158 \\
+LDLT-R & Orthogonal & 121 & 54 & 67 & 0 & 0.4463 & -0.0024 & 3206 & $2.1e-01$ & $8.2e-01$ & $1.0e+00$ & 0.1138 \\
+Orthogonal & SLL & 121 & 60 & 61 & 0 & 0.4959 & -0.0000 & 3382 & $4.3e-01$ & $8.5e-01$ & $1.0e+00$ & 0.0724 \\
+LDLT-R & SLL & 121 & 58 & 63 & 0 & 0.4793 & -0.0010 & 3627 & $8.7e-01$ & $8.7e-01$ & $1.0e+00$ & 0.0148 \\
+\bottomrule
+\end{tabular}
+\begin{tablenotes}
+\item Stars mark significance ($^*\,p\!\le\!0.05$, $^{**}\,p\!\le\!0.01$, $^{***}\,p\!\le\!0.001$).
+\end{tablenotes}
+\endgroup
+\end{threeparttable}
+\end{table*}
+
+
+
+\begin{table*}[t]
+\centering
+\begin{threeparttable}
+\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.}
+\label{tab:wilcoxon:mean_cert_acc_36}
+\begingroup
+\setlength{\tabcolsep}{4pt}
+\begin{tabular}{ll r r r r r r r r r r r}
+\toprule
+\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}
+Alg A & Alg B & $n$ & wins$_A$ & wins$_B$ & ties & WinRate A & \shortstack{Median \\ $\Delta$ (A--B)} & $W$ & $p$ & $p_{\text{Holm,within}}$ & $p_{\text{Holm,global}}$ & $r$ \\
+\midrule
+AOL & LDLT-R & 121 & 6 & 115 & 0 & 0.0496 & -0.2928 & 93 & $1.4e-20^{***}$ & $2.0e-19^{***}$ & $9.5e-19^{***}$ & 0.8458 \\
+AOL & SLL & 121 & 7 & 114 & 0 & 0.0579 & -0.2868 & 156 & $6.2e-20^{***}$ & $8.7e-19^{***}$ & $4.1e-18^{***}$ & 0.8310 \\
+AOL & Sandwich & 121 & 9 & 112 & 0 & 0.0744 & -0.3563 & 174 & $9.5e-20^{***}$ & $1.2e-18^{***}$ & $6.2e-18^{***}$ & 0.8268 \\
+AOL & Orthogonal & 121 & 9 & 112 & 0 & 0.0744 & -0.2985 & 184 & $1.2e-19^{***}$ & $1.4e-18^{***}$ & $7.6e-18^{***}$ & 0.8245 \\
+AOL & LDLT-L & 121 & 21 & 93 & 7 & 0.2025 & -0.1185 & 843 & $0^{***}$ & $1.0e-10^{***}$ & $3.0e-10^{***}$ & 0.6445 \\
+LDLT-L & Sandwich & 121 & 31 & 90 & 0 & 0.2562 & -0.0772 & 975 & $0^{***}$ & $0^{***}$ & $1.0e-10^{***}$ & 0.6384 \\
+LDLT-L & LDLT-R & 121 & 36 & 85 & 0 & 0.2975 & -0.0605 & 1205 & $1.0e-10^{***}$ & $1.2e-09^{***}$ & $5.1e-09^{***}$ & 0.5843 \\
+LDLT-L & SLL & 121 & 36 & 85 & 0 & 0.2975 & -0.0489 & 1305 & $7.0e-10^{***}$ & $5.5e-09^{***}$ & $2.4e-08^{***}$ & 0.5608 \\
+LDLT-L & Orthogonal & 121 & 42 & 79 & 0 & 0.3471 & -0.0531 & 1489 & $1.3e-08^{***}$ & $8.7e-08^{***}$ & $3.7e-07^{***}$ & 0.5176 \\
+Sandwich & SLL & 121 & 84 & 35 & 2 & 0.7025 & 0.0174 & 1683 & $5.7e-07^{***}$ & $3.4e-06^{***}$ & $1.6e-05^{***}$ & 0.4586 \\
+Orthogonal & Sandwich & 121 & 38 & 82 & 1 & 0.3182 & -0.0130 & 2067 & $4.3e-05^{***}$ & $2.1e-04^{***}$ & $9.0e-04^{***}$ & 0.3735 \\
+LDLT-R & SLL & 121 & 71 & 49 & 1 & 0.5909 & 0.0081 & 2331 & $6.7e-04^{***}$ & $2.7e-03^{**}$ & $1.1e-02^{*}$ & 0.3104 \\
+LDLT-R & Sandwich & 121 & 52 & 68 & 1 & 0.4339 & -0.0088 & 2802 & $3.0e-02^{*}$ & $9.1e-02$ & $3.0e-01$ & 0.1978 \\
+Orthogonal & SLL & 121 & 58 & 63 & 0 & 0.4793 & -0.0016 & 3123 & $1.4e-01$ & $2.8e-01$ & $1.0e+00$ & 0.1333 \\
+LDLT-R & Orthogonal & 121 & 76 & 45 & 0 & 0.6281 & 0.0060 & 3225 & $2.3e-01$ & $2.8e-01$ & $1.0e+00$ & 0.1093 \\
+\bottomrule
+\end{tabular}
+\begin{tablenotes}
+\item Stars mark significance ($^*\,p\!\le\!0.05$, $^{**}\,p\!\le\!0.01$, $^{***}\,p\!\le\!0.001$).
+\end{tablenotes}
+\endgroup
+\end{threeparttable}
+\end{table*}
+
+
+
+\begin{table*}[t]
+\centering
+\begin{threeparttable}
+\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.}
+\label{tab:wilcoxon:mean_cert_acc_72}
+\begingroup
+\setlength{\tabcolsep}{4pt}
+\begin{tabular}{ll r r r r r r r r r r r}
+\toprule
+\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}
+Alg A & Alg B & $n$ & wins$_A$ & wins$_B$ & ties & WinRate A & \shortstack{Median \\ $\Delta$ (A--B)} & $W$ & $p$ & $p_{\text{Holm,within}}$ & $p_{\text{Holm,global}}$ & $r$ \\
+\midrule
+AOL & SLL & 121 & 1 & 118 & 2 & 0.0165 & -0.2343 & 2 & $3.1e-21^{***}$ & $4.3e-20^{***}$ & $2.3e-19^{***}$ & 0.8672 \\
+AOL & LDLT-R & 121 & 1 & 120 & 0 & 0.0083 & -0.2920 & 21 & $2.3e-21^{***}$ & $3.5e-20^{***}$ & $1.7e-19^{***}$ & 0.8628 \\
+AOL & Orthogonal & 121 & 6 & 115 & 0 & 0.0496 & -0.2589 & 86 & $1.2e-20^{***}$ & $1.5e-19^{***}$ & $8.3e-19^{***}$ & 0.8473 \\
+AOL & Sandwich & 121 & 7 & 114 & 0 & 0.0579 & -0.3205 & 90 & $1.3e-20^{***}$ & $1.5e-19^{***}$ & $8.9e-19^{***}$ & 0.8465 \\
+AOL & LDLT-L & 121 & 10 & 93 & 18 & 0.1570 & -0.1040 & 284 & $0^{***}$ & $0^{***}$ & $0^{***}$ & 0.7759 \\
+LDLT-L & Sandwich & 121 & 21 & 99 & 1 & 0.1777 & -0.0916 & 608 & $0^{***}$ & $0^{***}$ & $0^{***}$ & 0.7223 \\
+LDLT-L & LDLT-R & 121 & 30 & 91 & 0 & 0.2479 & -0.0704 & 922 & $0^{***}$ & $0^{***}$ & $0^{***}$ & 0.6509 \\
+Orthogonal & Sandwich & 121 & 19 & 99 & 3 & 0.1694 & -0.0301 & 1122 & $1.0e-10^{***}$ & $8.0e-10^{***}$ & $5.4e-09^{***}$ & 0.5905 \\
+LDLT-L & SLL & 121 & 34 & 86 & 1 & 0.2851 & -0.0486 & 1161 & $1.0e-10^{***}$ & $8.0e-10^{***}$ & $4.1e-09^{***}$ & 0.5901 \\
+Sandwich & SLL & 121 & 93 & 28 & 0 & 0.7686 & 0.0368 & 1188 & $1.0e-10^{***}$ & $8.0e-10^{***}$ & $4.0e-09^{***}$ & 0.5883 \\
+LDLT-L & Orthogonal & 121 & 35 & 85 & 1 & 0.2934 & -0.0477 & 1257 & $5.0e-10^{***}$ & $2.6e-09^{***}$ & $1.9e-08^{***}$ & 0.5672 \\
+LDLT-R & SLL & 121 & 82 & 39 & 0 & 0.6777 & 0.0152 & 1961 & $7.7e-06^{***}$ & $3.1e-05^{***}$ & $1.8e-04^{***}$ & 0.4066 \\
+LDLT-R & Sandwich & 121 & 49 & 72 & 0 & 0.4050 & -0.0105 & 2635 & $6.4e-03^{**}$ & $1.9e-02^{*}$ & $8.3e-02$ & 0.2481 \\
+LDLT-R & Orthogonal & 121 & 74 & 47 & 0 & 0.6116 & 0.0114 & 2675 & $8.7e-03^{**}$ & $1.9e-02^{*}$ & $1.0e-01$ & 0.2387 \\
+Orthogonal & SLL & 121 & 62 & 59 & 0 & 0.5124 & 0.0025 & 2936 & $5.1e-02$ & $5.1e-02$ & $4.6e-01$ & 0.1774 \\
+\bottomrule
+\end{tabular}
+\begin{tablenotes}
+\item Stars mark significance ($^*\,p\!\le\!0.05$, $^{**}\,p\!\le\!0.01$, $^{***}\,p\!\le\!0.001$).
+\end{tablenotes}
+\endgroup
+\end{threeparttable}
+\end{table*}
+
+
+
+\begin{table*}[t]
+\centering
+\begin{threeparttable}
+\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.}
+\label{tab:wilcoxon:mean_cert_acc_108}
+\begingroup
+\setlength{\tabcolsep}{4pt}
+\begin{tabular}{ll r r r r r r r r r r r}
+\toprule
+\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}
+Alg A & Alg B & $n$ & wins$_A$ & wins$_B$ & ties & WinRate A & \shortstack{Median \\ $\Delta$ (A--B)} & $W$ & $p$ & $p_{\text{Holm,within}}$ & $p_{\text{Holm,global}}$ & $r$ \\
+\midrule
+AOL & SLL & 121 & 1 & 113 & 7 & 0.0372 & -0.1619 & 31 & $4.4e-20^{***}$ & $5.3e-19^{***}$ & $2.9e-18^{***}$ & 0.8596 \\
+AOL & LDLT-R & 121 & 1 & 120 & 0 & 0.0083 & -0.2368 & 43 & $4.0e-21^{***}$ & $6.0e-20^{***}$ & $2.9e-19^{***}$ & 0.8576 \\
+AOL & Orthogonal & 121 & 3 & 114 & 4 & 0.0413 & -0.1930 & 53 & $2.4e-20^{***}$ & $3.2e-19^{***}$ & $1.6e-18^{***}$ & 0.8544 \\
+AOL & Sandwich & 121 & 4 & 115 & 2 & 0.0413 & -0.2776 & 82 & $2.3e-20^{***}$ & $3.2e-19^{***}$ & $1.6e-18^{***}$ & 0.8478 \\
+AOL & LDLT-L & 121 & 5 & 91 & 25 & 0.1446 & -0.0716 & 108 & $5.0e-16^{***}$ & $0^{***}$ & $0^{***}$ & 0.8278 \\
+LDLT-L & Sandwich & 121 & 16 & 103 & 2 & 0.1405 & -0.0699 & 532 & $8.0e-16^{***}$ & $0^{***}$ & $0^{***}$ & 0.7384 \\
+LDLT-L & LDLT-R & 121 & 25 & 95 & 1 & 0.2107 & -0.0751 & 711 & $0^{***}$ & $0^{***}$ & $0^{***}$ & 0.6977 \\
+Orthogonal & Sandwich & 121 & 20 & 97 & 4 & 0.1818 & -0.0322 & 1002 & $0^{***}$ & $2.0e-10^{***}$ & $1.1e-09^{***}$ & 0.6159 \\
+Sandwich & SLL & 121 & 92 & 27 & 2 & 0.7686 & 0.0456 & 1046 & $0^{***}$ & $2.0e-10^{***}$ & $9.0e-10^{***}$ & 0.6134 \\
+LDLT-L & Orthogonal & 121 & 31 & 86 & 4 & 0.2727 & -0.0380 & 1169 & $5.0e-10^{***}$ & $3.2e-09^{***}$ & $1.9e-08^{***}$ & 0.5738 \\
+LDLT-L & SLL & 121 & 31 & 83 & 7 & 0.2851 & -0.0308 & 1220 & $6.0e-09^{***}$ & $3.0e-08^{***}$ & $1.9e-07^{***}$ & 0.5447 \\
+LDLT-R & SLL & 121 & 92 & 29 & 0 & 0.7603 & 0.0294 & 1470 & $9.3e-09^{***}$ & $3.7e-08^{***}$ & $2.9e-07^{***}$ & 0.5220 \\
+LDLT-R & Orthogonal & 121 & 84 & 37 & 0 & 0.6942 & 0.0207 & 2239 & $1.7e-04^{***}$ & $5.2e-04^{***}$ & $3.1e-03^{**}$ & 0.3412 \\
+Orthogonal & SLL & 121 & 69 & 50 & 2 & 0.5785 & 0.0077 & 2708 & $2.2e-02^{*}$ & $4.5e-02^{*}$ & $2.4e-01$ & 0.2095 \\
+LDLT-R & Sandwich & 121 & 59 & 62 & 0 & 0.4876 & -0.0023 & 3035 & $9.0e-02$ & $9.0e-02$ & $7.2e-01$ & 0.1540 \\
+\bottomrule
+\end{tabular}
+\begin{tablenotes}
+\item Stars mark significance ($^*\,p\!\le\!0.05$, $^{**}\,p\!\le\!0.01$, $^{***}\,p\!\le\!0.001$).
+\end{tablenotes}
+\endgroup
+\end{threeparttable}
+\end{table*}
+
+
+
+\begin{table*}[t]
+\centering
+\begin{threeparttable}
+\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.}
+\label{tab:wilcoxon:mean_cert_acc_255}
+\begingroup
+\setlength{\tabcolsep}{4pt}
+\begin{tabular}{ll r r r r r r r r r r r}
+\toprule
+\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}
+Alg A & Alg B & $n$ & wins$_A$ & wins$_B$ & ties & WinRate A & \shortstack{Median \\ $\Delta$ (A--B)} & $W$ & $p$ & $p_{\text{Holm,within}}$ & $p_{\text{Holm,global}}$ & $r$ \\
+\midrule
+AOL & LDLT-R & 121 & 0 & 107 & 14 & 0.0579 & -0.0753 & 0 & $2.8e-19^{***}$ & $4.2e-18^{***}$ & $1.7e-17^{***}$ & 0.8679 \\
+AOL & SLL & 121 & 1 & 99 & 21 & 0.0950 & -0.0435 & 4 & $4.5e-18^{***}$ & $5.8e-17^{***}$ & $2.7e-16^{***}$ & 0.8666 \\
+AOL & LDLT-L & 121 & 3 & 78 & 40 & 0.1901 & -0.0180 & 36 & $0^{***}$ & $0^{***}$ & $0^{***}$ & 0.8496 \\
+AOL & Orthogonal & 121 & 2 & 97 & 22 & 0.1074 & -0.0518 & 61 & $3.6e-17^{***}$ & $4.4e-16^{***}$ & $0^{***}$ & 0.8466 \\
+AOL & Sandwich & 121 & 3 & 107 & 11 & 0.0702 & -0.0914 & 67 & $5.5e-19^{***}$ & $7.7e-18^{***}$ & $3.4e-17^{***}$ & 0.8488 \\
+Orthogonal & Sandwich & 121 & 12 & 97 & 12 & 0.1488 & -0.0259 & 367 & $0^{***}$ & $0^{***}$ & $0^{***}$ & 0.7616 \\
+LDLT-L & Sandwich & 121 & 12 & 98 & 11 & 0.1446 & -0.0363 & 385 & $0^{***}$ & $0^{***}$ & $0^{***}$ & 0.7584 \\
+LDLT-L & LDLT-R & 121 & 22 & 86 & 13 & 0.2355 & -0.0305 & 669 & $0^{***}$ & $0^{***}$ & $1.0e-10^{***}$ & 0.6706 \\
+Sandwich & SLL & 121 & 83 & 28 & 10 & 0.7273 & 0.0187 & 1014 & $7.0e-10^{***}$ & $5.1e-09^{***}$ & $2.4e-08^{***}$ & 0.5846 \\
+LDLT-L & SLL & 121 & 24 & 77 & 20 & 0.2810 & -0.0083 & 1120 & $8.3e-07^{***}$ & $5.0e-06^{***}$ & $2.1e-05^{***}$ & 0.4905 \\
+LDLT-L & Orthogonal & 121 & 30 & 70 & 21 & 0.3347 & -0.0077 & 1191 & $4.5e-06^{***}$ & $1.8e-05^{***}$ & $1.1e-04^{***}$ & 0.4585 \\
+LDLT-R & SLL & 121 & 80 & 29 & 12 & 0.7107 & 0.0156 & 1368 & $8.5e-07^{***}$ & $5.0e-06^{***}$ & $2.1e-05^{***}$ & 0.4716 \\
+LDLT-R & Orthogonal & 121 & 76 & 34 & 11 & 0.6736 & 0.0123 & 1722 & $7.3e-05^{***}$ & $2.2e-04^{***}$ & $1.5e-03^{**}$ & 0.3780 \\
+LDLT-R & Sandwich & 121 & 44 & 68 & 9 & 0.4008 & -0.0070 & 2043 & $1.1e-03^{**}$ & $2.3e-03^{**}$ & $1.6e-02^{*}$ & 0.3074 \\
+Orthogonal & SLL & 121 & 53 & 51 & 17 & 0.5083 & 0.0000 & 2606 & $6.9e-01$ & $6.9e-01$ & $1.0e+00$ & 0.0393 \\
+\bottomrule
+\end{tabular}
+\begin{tablenotes}
+\item Stars mark significance ($^*\,p\!\le\!0.05$, $^{**}\,p\!\le\!0.01$, $^{***}\,p\!\le\!0.001$).
+\end{tablenotes}
+\endgroup
+\end{threeparttable}
+\end{table*}

UCI_N6/wilcoxon_pairwise_all.csv

@@ -0,0 +1,76 @@
+metric,alg_a,alg_b,n_common,n_nonzero,wins_a,wins_b,ties,win_rate_a_over_b,mean_diff_a_minus_b,median_diff_a_minus_b,W_stat,p_two_sided,z_equiv,effect_size_r,p_holm_global,p_holm_within_metric
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UCI_N6/wilcoxon_pairwise_all.json

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