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\begin{tabular}{cccccc} \toprule Layer & Procrustes & CKA & PWCCA & $\bar \rho_{\text{CCA}}$ & $R^2_{\text{CCA}}$ \\ \midrule 1 & 0.137 (8.7E-02) & 0.108 (1.4E-01) & 0.107 (1.4E-01) & 0.072 (7.6E-01) & 0.072 (7.6E-01) \\ 2 & -0.012 (5.5E-01) & 0.060 (2.8E-01) & 0.062 (2.7E-01) & 0.004 (5.1E-01) & 0.001 (5.0E-01) \\ 3 & -0.059 (7.2E-01) & 0.011 (4.6E-01) & -0.031 (6.2E-01) & -0.060 (2.8E-01) & -0.056 (2.9E-01) \\ 4 & 0.041 (3.4E-01) & 0.052 (3.0E-01) & -0.026 (6.0E-01) & -0.101 (1.6E-01) & -0.084 (2.0E-01) \\ 5 & 0.003 (4.9E-01) & 0.131 (9.7E-02) & -0.047 (6.8E-01) & -0.061 (2.7E-01) & -0.061 (2.7E-01) \\ 6 & 0.092 (1.8E-01) & 0.260 (4.5E-03) & -0.029 (6.1E-01) & -0.064 (2.6E-01) & -0.056 (2.9E-01) \\ 7 & 0.164 (5.2E-02) & 0.250 (6.1E-03) & 0.037 (3.6E-01) & 0.040 (6.5E-01) & 0.040 (6.5E-01) \\ 8 & 0.202 (2.2E-02) & 0.105 (1.5E-01) & 0.175 (4.1E-02) & 0.134 (9.1E-01) & 0.143 (9.2E-01) \\ \bottomrule \end{tabular}
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\begin{tabular}{cccccc} \toprule Layer & Procrustes & CKA & PWCCA & $\bar \rho_{\text{CCA}}$ & $R^2_{\text{CCA}}$ \\ \midrule 1 & 0.103 (6.5E-02) & 0.083 (1.1E-01) & 0.074 (1.4E-01) & 0.050 (7.7E-01) & 0.048 (7.6E-01) \\ 2 & -0.010 (5.6E-01) & 0.046 (2.5E-01) & 0.046 (2.5E-01) & 0.006 (5.3E-01) & 0.001 (5.0E-01) \\ 3 & -0.041 (7.3E-01) & 0.014 (4.2E-01) & -0.018 (6.0E-01) & -0.047 (2.5E-01) & -0.047 (2.4E-01) \\ 4 & 0.031 (3.2E-01) & 0.038 (2.9E-01) & -0.020 (6.2E-01) & -0.076 (1.3E-01) & -0.065 (1.7E-01) \\ 5 & 0.005 (4.7E-01) & 0.086 (1.0E-01) & -0.031 (6.8E-01) & -0.042 (2.7E-01) & -0.042 (2.7E-01) \\ 6 & 0.060 (1.9E-01) & 0.175 (5.1E-03) & -0.020 (6.2E-01) & -0.050 (2.3E-01) & -0.046 (2.5E-01) \\ 7 & 0.112 (4.9E-02) & 0.168 (6.8E-03) & 0.030 (3.3E-01) & 0.019 (6.1E-01) & 0.024 (6.4E-01) \\ 8 & 0.131 (2.7E-02) & 0.063 (1.8E-01) & 0.125 (3.3E-02) & 0.099 (9.3E-01) & 0.103 (9.4E-01) \\ \bottomrule \end{tabular}
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\begin{tabular}{lrr} \toprule Corruption & Procrustes & CKA \\ \midrule gaussian\_noise & 0.083 & 0.076 \\ shot\_noise & 0.171 & 0.161 \\ impulse\_noise & 0.104 & 0.083 \\ defocus\_blur & -0.025 & 0.021 \\ glass\_blur & 0.082 & 0.073 \\ motion\_blur & 0.033 & 0.035 \\ zoom\_blur & -0.023 & 0.020\\ snow & 0.087 & 0.060\\ frost & -0.062 & -0.081 \\ fog & -0.029 & -0.039 \\ brightness & 0.122 & 0.110\\ contrast & -0.225 & -0.145 \\ elastic\_transform & 0.137 & 0.122 \\ pixelate & 0.118 & 0.098 \\ jpeg\_compression & 0.149 & 0.102 \\ speckle\_noise & 0.028 & 0.033 \\ gaussian\_blur & 0.149 & 0.141 \\ spatter & 0.089 & 0.079 \\ saturate & 0.143 & 0.135 \\ \midrule Average & 0.060 & 0.057 \\ \bottomrule \end{tabular}
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\begin{tabular}{lrr} \toprule Corruption & Procrustes & CKA \\ \midrule gaussian\_noise & 0.057 & 0.050 \\ shot\_noise & 0.118 & 0.110 \\ impulse\_noise & 0.070& 0.055 \\ defocus\_blur & -0.016 & 0.013 \\ glass\_blur & 0.057 & 0.047 \\ motion\_blur & 0.021 & 0.022 \\ zoom\_blur & -0.014 & 0.013 \\ snow & 0.059 & 0.042 \\ frost & -0.046 & -0.059 \\ fog & -0.020 & -0.025 \\ brightness & 0.084 & 0.077 \\ contrast & -0.158 & -0.102 \\ elastic\_transform & 0.094 & 0.085 \\ pixelate & 0.081 & 0.066 \\ jpeg\_compression & 0.103 & 0.070\\ speckle\_noise & 0.019 & 0.022 \\ gaussian\_blur & 0.102 & 0.095 \\ spatter & 0.059 & 0.053 \\ saturate & 0.100 & 0.096 \\ \midrule Average & 0.041 & 0.038 \\ \bottomrule \end{tabular}
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\begin{tabular}{c}Ting-Yao Hu$^{\star}$ \qquad Ashish Shrivastava$^{\dagger}$ \qquad Jen-Hao Rick Chang$^{\dagger}$ \qquad Hema Koppula$^{\dagger}$, \\ Stefan Braun$^{\dagger}$ \qquad Kyuyeon Hwang$^{\dagger}$ \qquad Ozlem Kalinli$^{\dagger}$ \qquad Oncel Tuzel$^{\dagger}$\end{tabular}
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\begin{tabular}{c|cccc|cc} \toprule Exp.& \multicolumn{4}{c|}{Reward Setup} & Accuracy & Mean\\ \# & TP & TN & FP & FN & (\%) & Time (sec)\\ \midrule 1 & C'(t) & C'(t) & -C'(t) & -C'(t) & 96.867 & 48.61 \\ 2 & C'(t) & C'(t) & -10C'(t) & -10C'(t) & 96.801 & 48.37 \\ 3 & 1 & 1 & -C'(t) & -C'(t) & 96.212 & 10.53 \\ 4 & 10 & 10 & -C'(t) & -C'(t) & 95.424 & 3.68 \\ 5 & 100 & 100 & -C'(t) & -C'(t) & 91.220 & 0.73 \\ \bottomrule \end{tabular}
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\begin{tabular}{|l|l|l|l|l|l|l|l|} \hline Tool & Best model & Log Loss & TP & FP & FN & TN & AUC\\ \hline mljar-supervised & Stacked Ensemble & 1.2555 & 1085 & 42 & 9 & 267 & 0.9279\\\hline H2O & Deep Learning& 7.6809 & \textbf{1091} & 309 & \textbf{3} & 0 & 0.4986 \\\hline TPOT & Gradient Boosting& \textbf{1.1817} & 1087 & \textbf{41} & 7 & \textbf{268} & \textbf{0.9305}\\\hline \end{tabular}
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\begin{tabular}{|l|l|l|l|l|l|l|l|} \hline Tool & Best model & Log Loss & TP & FP & FN & TN & AUC \\ \hline mljar-supervised & Stacked Ensemble & \textbf{0.9109} & \textbf{1087} & \textbf{30} & \textbf{7} & \textbf{279} & \textbf{0.9483} \\\hline H2O & Stacked Ensemble& 1.0093 & 1084 & 31 & 10 & 278 & 0.9453 \\\hline TPOT & Logistic Regression& 1.1817 & 1085 & 41 & 9 & 268 & 0.9295\\\hline \end{tabular}
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\begin{tabular}{|l|l|l|l|l|l|l|l|} \hline Tool & Best model & Log Loss & TP & FP & FN & TN & AUC\\ \hline mljar-supervised & Stacked Ensemble & 0.8863 & \textbf{1088} & 30 & \textbf{6} & 279 & 0.9487 \\\hline H2O & Stacked Ensemble& \textbf{0.8370} & \textbf{1088} & \textbf{28} & \textbf{6} & \textbf{281} & \textbf{0.952} \\\hline TPOT & Logistic Regression& 1.034 & 1086 & 34 & 8 & 275 & 0.9413\\\hline \end{tabular}
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\begin{tabular}{|l|l|l|l|} \hline \multirow{2}{*}{Tool} & \multicolumn{3}{|c|}{Feature size} \\ \cline{2-4} & 50 & 100 & 200\\\hline mljar-supervised & 2:01 & 3:01 & 4:04\\\hline H2O & 1:20 & 2:03 & 2:41 \\\hline TPOT & 2:01 & 3:00 & 4:00\\\hline \end{tabular}
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\begin{tabular}{|l|l|l|l|} \hline Features subset size & Tool & Best model & Log Loss \\ \hline 50 & TPOT & Gradient Boosting & 1.1817 \\\hline 100 & H2O & Stacked Ensemble& 1.0093 \\\hline 200 & H2O & Stacked Ensemble& \textbf{0.8370} \\\hline \end{tabular}
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\begin{tabular}{|l|l|l|l|l|} \hline Feature subset size & Tool & Best model & Log Loss & Improvement (\%)\\ \hline 200 & TPOT & Logistic Regression& 1.034 &19.05\\\hline 200 & mljar-supervised & Ensemble & 0.8863 & 5.56\\\hline 200 & H2O & Stacked Ensemble& \textbf{0.8370} & - \\\hline \end{tabular}
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\begin{tabular}{|l|l|} \hline Metric & Value\\ \hline Log loss & 0.0766522\\\hline TP & 3257\\\hline FP & 24\\\hline FN & 67\\\hline TN & 859\\\hline AUC & 0.994897\\\hline Training time (in millisecond) & 2738 \\\hline Prediction time per row (in millisecond) & 0.288793\\\hline \end{tabular}
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\begin{tabular}{rrr|r|r} $n$ & $c$ & $f$ & Number of actions per player $(|A_i|)$ & Size of matrix / tensor $(= |A_i|^n)$\\ \midrule 2 & 10 & 3 & 66 & 4356 \\ 2 & 30 & 3 & 496 & 246016 \\ 2 & 15 & 4 & 816 & 665856 \\ 2 & 10 & 5 & 1001 & 1002001 \\ 2 & 10 & 6 & 3003 & 9018009 \\ \midrule 3 & 10 & 3 & 66 & 287496 \\ \midrule 4 & 8 & 3 & 45 & 4100625 \\ \midrule 5 & 6 & 3 & 28 & 17210368 \\ \end{tabular}
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\begin{tabular}{l|rrrr} \toprule{} & \multicolumn{2}{c}{Training set} & \multicolumn{2}{c}{Validation set}\\ \midrule{} & \multicolumn{1}{c}{Press} & \multicolumn{1}{c}{No-press} & \multicolumn{1}{c}{Press} & \multicolumn{1}{c}{No-press}\\ \midrule \midrule Available games & 104456 & 31279 & 2000 & 2000\\ \midrule Excluded: non-standard map & 833 & 10659 & 17 & 705\\ Excluded: non-standard rules & 863 & 1 & 19 & 0\\ Excluded: min SCs not met & 2954 & 517 & 48 & 31\\ Excluded: unable to parse & 3554 & 79 & 78 & 4\\ \midrule Included & 96252 & 20023 & 1838 & 1260\\ \bottomrule \end{tabular}
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\begin{tabular}{ccccc} \hline Dataset & Sample & Dimension & Edges & Classes \\ \hline DBLP & 4057 & 334 & 7056 & 4 \\ ACM & 3025 & 1870 & 26256 & 3 \\ AMAP & 7650 & 745 & 287326 & 8 \\ AMAC & 13752 & 767 & 491722 & 10 \\ CITESEER & 3327 & 3703 & 4732 & 6 \\ CORA & 2708 & 1433 & 5429 & 7 \\ \hline \end{tabular}
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\begin{tabular}{ccccc|cc} \toprule \multirow{2}*{Model}& \multicolumn{4}{c}{Monster Kong} & \multicolumn{2}{c}{Flappy Bird\qquad\quad}\\ \cmidrule(r){2-7} & 1-5$^\S$ & 1-5 & 2-5 & 3-5 & 1-5$^\dag$ & 1-5$^\ddag$\\ \midrule MAOP & 0.34 & 0.15 & 0.14 & 0.12 & 0.30 & 0.34\\ \bottomrule \end{tabular}
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\begin{tabular}{cccc} \toprule Model& MonsterKong & FlappyBird & Freeway \\ \midrule MAOP& 100\% & 100\% & 98.75\%\\ \bottomrule \end{tabular}
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\begin{tabular}{ccc|cc} \toprule \multirow{2}*{Mask Number}& \multicolumn{2}{c|}{Training} & \multicolumn{2}{c}{Unseen}\\ \cmidrule(r){2-5} &Agent & All & Agent & All\\ \midrule 3 masks & 0.92 & 0.91 & 0.90 & 0.88 \\ 5 masks & 0.95 & 0.92 & 0.94 & 0.90 \\ 8 masks & 0.93 & 0.90 & 0.91 & 0.88 \\ \bottomrule \end{tabular}
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\begin{tabular}{lccc} & \textbf{Parameters} & \textbf{Interpolation} & \textbf{Extrapolation} \\ \hline Simple \textbf{LSTM} & 18M & 0.57 & 0.41 \\ Simple \textbf{RMC} & 38M & 0.53 & 0.38 \\ \hline Attentional \textbf{LSTM}, LSTM encoder & 24M & 0.57 & 0.38 \\ Attentional \textbf{LSTM}, bidir LSTM encoder & 26M & 0.58 & 0.42 \\ Attentional \textbf{RMC}, bidir LSTM encoder & 39M & 0.54 & 0.43 \\ \hline \textbf{Transformer} & 30M & \textbf{0.76} & \textbf{0.50} \\ \end{tabular}
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\begin{tabular}{ccccccccc} \toprule \multicolumn{1}{c}{} & \multicolumn{6}{c}{Classification Tasks} & \multicolumn{2}{c}{\multirow{2}{*}{Regression Tasks}} \\ \cline{2-7} \multicolumn{1}{c}{} & \multicolumn{2}{c}{Financial} & \multicolumn{4}{c}{Large-Scale} & \multicolumn{2}{c}{}\\ \cmidrule(lr){2-3} \cmidrule(lr){4-7} \cmidrule(lr){8-9} & UCICreditCard & GiveMeSomeCredit & news20 & rcv1 & url & webspam & E2006-tfidf & YearPredictionMSD\\ \midrule \#Train & 24,000 & 96,257 & 15,997 & 677,399 & 1,916,904 & 280,000 & 16,087 & 463,715\\ \#Test & 6,000 & 24,012 & 3,999 & 20,242 & 479,226 & 70,000 & 3,308 & 51,630\\ \#Feature & 90 & 92 & 1,355,191 & 47,236 & 3,231,961 & 16,609,143 & 150,360 & 90\\ \bottomrule \end{tabular}
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\begin{tabular}{cccc} \toprule \multicolumn{1}{c}{ \multirow{2.5}{*}{Dataset} } & \multicolumn{3}{c}{Speedup}\\ \cmidrule(lr){2-4} & SGD & SVRG & SAGA \\ \midrule UCICreditCard & 1.82 & 1.93 & 1.95\\ GiveMeSomeCredit & 1.89 & 2.15 & 2.11\\ new20 & 3.37 & 2.84 & 2.89\\ rcv1 & 3.70 & 2.64 & 2.28\\ url & 2.74 & 2.51 & 2.38\\ webspam & 1.96 & 1.97 & 1.99\\ E2006-tfidf & 3.32 & 2.89 & 2.51\\ YearPredictionMSD & 2.03 & 2.24 & 2.26\\ \bottomrule \end{tabular}
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\begin{tabular}{l|ll} Model & Top 1 Acc. & Top 5 Acc. \\ \toprule \textit{GLICO} & 43.84$\pm$0.25 & 70.73$\pm$0.07 \\ Baseline & 38.39$\pm$0.18 & 67.77$\pm$0.18 \\ No Classifier & 41.57$\pm$0.54 & 69.55$\pm$0.11 \\ No Noise & 43.31$\pm$0.02 & 70.05$\pm$0.02 \\ Lerp & 43.01$\pm$0.06 & 70.51$\pm$0.03 \\ Transductive & 44.79$\pm$0.12 & 71.28$\pm$0.09 \\ \bottomrule \end{tabular}
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\begin{tabular}{l|ll} Model & Top 1 Acc. & Top 5 Acc. \\ \toprule Latent Classifier & 43.08$\pm$0.06 & 70.22$\pm$0.05 \\ Hypercube Init & 44.21$\pm$0.61 & 70.89$\pm$0.46 \\ ResNet Init & 42.95$\pm$0.22 & 70.10$\pm$0.13 \\ Additive Noise & 41.02$\pm$0.43 & 68.10$\pm$0.11 \\ Cosine Loss & 41.01$\pm$0.27 & 68.45$\pm$0.31 \\ \bottomrule \end{tabular}
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\begin{tabular}{ccll} \toprule AutoAu. & Ours & Top-1 Accuracy & Top-5 Accuracy \\ \midrule & & 50.37$\pm$0.05 & 75.61$\pm$0.01 \\ & $\checkmark$ & 53.35$\pm$0.23 & 77.60$\pm$0.12 \\ $\checkmark$ & & 53.80$\pm$0.10 & 79.18$\pm$0.13 \\ $\checkmark$ & $\checkmark$ & \textbf{56.31$\pm$0.02} & 80.66$\pm$0.04 \\ \bottomrule \end{tabular}
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\begin{tabular}{l|ccc} \toprule Method & supervised only & 1000 unlabeled & 35k unlabeled \\ \midrule Baseline & 38.39$\pm$0.18 & - & - \\ MixMatch & 40.17 & 42.39 & 50.34 \\ Ours & 43.84$\pm$0.25 & 44.52$\pm$0.12 & 44.73$\pm$0.07 \\ \bottomrule \end{tabular}
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\begin{tabular}{cccc} \toprule Map Name & Replay Buffer Size & Behaviour Test Win Rate & Behaviour Policy \\ \hline 2s3z & 20k episodes & 91.2\% & VDN \\ 3s5z & 20k episodes & 77.5\% & VDN \\ 2s\_vs\_1sc & 20k episodes & 99.6\% & VDN \\ 3s\_vs\_5z & 20k episodes & 94.2\% & VDN \\ 1c3s5z & 30k episodes & 92.1\% & VDN \\ 3c7z & 30k episodes & 94.4\% & VDN \\ 5m\_vs\_6m & 50k episodes & 61.7\% & VDN \\ 10m\_vs\_11m & 50k episodes & 88.7\% & VDN \\ 3h\_vs\_4z & 50k episodes & 83.1\% & VDN \\ \toprule \end{tabular}
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\begin{tabular}{ccc} \toprule Map Name & Ally Units & Enemy Units \\ \hline 2s3z & 2 Stalkers \& 3 Zealots & 2 Stalkers \& 3 Zealots \\ 3s5z & 3 Stalkers \& 5 Zealots & 3 Stalkers \& 5 Zealots \\ 2s\_vs\_1sc & 2 Stalkers & 1 Spine Crawler \\ 3s\_vs\_5z & 3 Stalkers & 5 Zealots \\ 1c3s5z & 1 Colossus, 3 Stalkers \& 5 Zealots & 1 Colossus, 3 Stalkers \& 5 Zealots \\ 3c7z & 3 Colossi \& 7 Zealots & 3 Colossi \& 7 Zealots \\ 5m\_vs\_6m & 5 Marines & 6 Marines \\ 10m\_vs\_11m & 10 Marines & 11 Marines \\ 3h\_vs\_4z & 3 Hydralisks & 4 Zealots \\ \toprule \end{tabular}
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\begin{tabular}{ccccc} \hline Task & Metric & fp32 & RCT & Bitwidth \\ \hline CoLA & Matthew's corr & 56.53 & \textbf{57.29} & 18.0 \\ MRPC & F1 & 88.85 & \textbf{90.20} & 17.9 \\ QNLI & Accuracy & 90.66 & \textbf{90.87} & 17.7 \\ QQP & F1 & 87.49 & 86.74 & 17.6 \\ RTE & Accuracy & 65.70 & 65.34 & 18.8 \\ SST-2 & Accuracy & 92.32 & 91.97 & 18.2 \\ STS-B & Person corr. & 88.64 & \textbf{88.78} & 17.9 \\ \hline SQuADv1.1 & F1 & 88.46 & 87.62 & 18.2 \\ \hline \end{tabular}
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\begin{tabular}{|l|l|} \hline \hline \textbf{\normalsize Variable} & \textbf{\normalsize Definition} \\ \hline \textbf{$y_j$} & Response connected to patient $j$ \\ \hline \textbf{$x_{ij}$} & ICD-9 code $i$ of patient $j$ \\ \hline \textbf{$b_{ij}$} & Specialist type for ICD-9 code $i$ of patient $j$ \\ \hline \textbf{$z_{ij}$} & Topic assignment for ICD code-9 $i$ of patient $j$ \\ \hline \textbf{$\theta_{j}$}& Topic mixture of patient $j$ \\ \hline \textbf{$\beta_{k}$} & Specialist mixture given topic $k$ \\ \hline \textbf{$\eta_{kt}$} & ICD-9 code mixture given topic $k$ and specialist $t$ \\ \hline \textbf{$\alpha$} & Dirichlet hyperparamter \\ \hline \textbf{$\iota$} & Dirichlet hyperparamter \\ \hline \textbf{$\zeta_k$} & Dirichlet hyperparamter \\ \hline \textbf{$g_j$} & Latent disease liability of patient $j$ \\ \hline \textbf{$w$} & Linear coefficients \\ \hline \textbf{$\tau$} & Precision variable of Gaussian distribution for regression coefficient $w$ \\ \hline \toprule \end{tabular}
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\begin{tabular}{lccccccccc}\toprule \multirow{2}{*}{Method} & \multicolumn{9}{c}{Number of Classes} \\\cmidrule{2-10} &4 &6 &8 &10 &20 &30 &40 &50 &60 \\\midrule SBM-GP & 96.98$\pm$0.5 & 95.55$\pm$0.9 &92.11$\pm$0.8 &91.04$\pm$0.7 &83.59$\pm$0.5 &77.63$\pm$0.9 &67.03$\pm$0.8 &64.20$\pm$1.0 &60.69$\pm$1.0\\ OVE &97.33$\pm$0.5 &96.60$\pm$0.9 &94.70$\pm$0.8 & 93.05$\pm$0.8 & -- & -- & -- & -- & --\\ LSM &97.30$\pm$0.9 &96.95$\pm$0.8 &95.16$\pm$0.8 &93.09$\pm$0.9 &89.23$\pm$1.3 &84.44$\pm$0.6 &72.90$\pm$1.2 &69.82$\pm$0.9 &65.53$\pm$0.9 \\ \midrule GP-Tree Rnd. (ours) & 97.80$\pm$0.8& 95.96$\pm$0.7 &93.49$\pm$0.9 &92.07$\pm$1.1 &85.32$\pm$1.6 & 77.45$\pm$1.0 & 68.97$\pm$0.8 & 62.77$\pm$1.2 & 58.49$\pm$0.8 \\ GP-Tree (ours) & 97.93$\pm$0.7 & 97.15$\pm$0.6 &94.67$\pm$0.9 &93.57$\pm$0.9 &88.77$\pm$1.4 &83.87$\pm$0.8 &\textbf{75.66$\pm$0.8} &\textbf{72.87$\pm$0.8} &\textbf{69.92$\pm$0.6} \\ \bottomrule \end{tabular}
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\begin{tabular}{lcccc}\toprule Method && CIFAR-10 && CIFAR-100 \\\midrule GPDNN && 81.16 $\pm$ 0.1 && -- \\ SV-DKL && 92.73 $\pm$ .05 && 70.61 $\pm$ 0.2 \\ \midrule GP-Tree (ours) && \textbf{93.25 $\pm$ 0.1} && \textbf{72.11 $\pm$ .05} \\ \bottomrule \end{tabular}
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\begin{tabular}{lccccccccccccccccccccc} \toprule \multirow{2}{*}{Method} &\multicolumn{21}{c}{Sessions} \\\cmidrule{2-22} &1& &2& &3& &4& &5& &6& &7& &8& &9& &10& &11 \\\midrule iCaRL & 68.68 && 52.65 && 48.61 && 44.16 && 36.62 && 29.52 && 27.83 && 26.26 && 24.01 && 23.89 && 21.16 \\ EEIL & 68.68 && 53.63 && 47.91 && 44.20 && 36.30 && 27.46 && 25.93 && 24.70 && 23.95 && 24.13 && 22.11\\ NCM & 68.68 && 57.12 && 44.21 && 28.78 && 26.71 && 25.66 && 24.62 && 21.52 && 20.12 && 20.06 && 19.87\\ TOPIC & 68.68 && 62.49 && 54.81 && 49.99 && 45.25 && 41.40 && 38.35 && 35.36 && 32.22 && 28.31 && 26.28\\ \midrule SDC & 64.10 && 60.58 && 57.00 && 53.57 && 52.09 && 49.87 && 48.20 && 46.38 && 44.04 && 43.81 && 42.39\\ PODNet & \textbf{75.93 } && \textbf{70.29} && \textbf{64.50} && 49.00 && 45.90 && 43.00 && 41.33 && 40.56 && 40.09 && 40.59 && 39.30\\ \midrule GP-Tree (ours) & 73.73 && 68.24 && 64.22 && \textbf{59.61} && \textbf{56.39} && \textbf{53.40} && \textbf{51.14} && \textbf{49.32} && \textbf{47.03} && \textbf{45.86} && \textbf{44.48} \\ \bottomrule \end{tabular}
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\begin{tabular}{lccccccccccccccccccccc} \toprule \multirow{2}{*}{Method} &\multicolumn{21}{c}{Sessions} \\\cmidrule{2-22} &1& &2& &3& &4& &5& &6& &7& &8& &9& &10& &11 \\\midrule Session Tree & 73.73 && \textbf{68.24} && 64.07 && 59.42 && 56.12 && 52.80 && 50.73 && 48.89 && 46.34 && 45.01 && 43.33\\ Rebuild Tree &73.73 && 67.71 && 63.50 && 59.03 && 55.73 && 52.73 && 50.49 && 48.85 && 46.17 && 44.84 && 43.20\\ GP-Tree & 73.73 && \textbf{68.24} && \textbf{64.22} && \textbf{59.61} && \textbf{56.39} && \textbf{53.40} && \textbf{51.14} && \textbf{49.32} && \textbf{47.03} && \textbf{45.86} && \textbf{44.48}\\ \bottomrule \end{tabular}
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\begin{tabular}{ll} \toprule Feature & Value Type\\ \midrule Age & Integral \\ Sex & Categorical \\ City of Birth & Categorical \\ Current / Migration City & Categorical \\ Duration of stay in current City (in months) & Integer \\ Married, divorced, widowed & Categorical \\ \bottomrule \end{tabular}
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\begin{tabular}{lllllll} \toprule Algorithm & F1 Score & Accuracy & TN & FP & FN & TP \\ \midrule SVM & 0.62 & 0.92 & 169 & 14 & 3 & 14 \\ Random Forest & 0.61 & 0.90 & 166 & 17 & 2 & 15 \\ XGBoost & 0.59 & 0.89 & 162 & 21 & 1 & 16 \\ MLP & 0.60 & 0.92 & 170 & 13 & 4 & 13 \\ Sequential Neural Network & 0.50 & 0.89 & 168 & 5 & 15 & 10 \\ \bottomrule \end{tabular}
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\begin{tabular}{lcc} \toprule Model Size & GPT-2 Perplexity& Our Perplexity \\ \midrule $117M$ & $21.11$ & $22.78$ \\ $345M$ & $16.03$ & - \\ $378M$ & - & $17.95$ \\ \bottomrule \end{tabular}
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\begin{tabular}{lcc} \toprule $d_x$ & $r$ & std \\ \midrule $680$ & $680$ & $8\cdot 10^{-4}$ \\ $576$ & $576$ & $1.5\cdot 10^{-3}$\\ $680$ & $128$ & $2.1\cdot 10^{-3}$ \\ \bottomrule \end{tabular}
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\begin{tabular}{lccc} \toprule $V$ &$L$ & $r$ & widths \\ \midrule 257 & 24 & & $144, 160, 168, 184, 192, 200, 224, 248, 264, 280, 336, 408, 480$ \\ 257 & 48 & & $104, 112, 120, 128, 136, 142, 144, 160, 176, 184, 200, 240, 288, 336$ \\ 500 & 24 & & $280, 336, 360, 384, 408, 424, 440, 480, 504, 528, 544, 576, 600$\\ 500 & 48 & & $200, 240, 272, 288, 296, 312, 336, 352, 376, 384, 408, 424$ \\ 2000 & 24 & $500$ & $280, 336, 408, 448, 480, 504, 528, 544, 576, 600, 628$ \\ 2000 & 48 & $500$ & $200, 240, 288, 320, 336, 352, 376, 384, 408, 424, 440$ \\ 2000 & 24 & & $200, 224, 248, 280, 336, 408, 480, 544, 704, 744, 792, 848, 1064$ \\ 2000 & 48 & & $144, 160, 176, 200, 240, 288, 336, 384, 496, 528, 560, 600, 752$ \\ 50257 & 24 & & $408, 480, 544, 592, 656, 704, 744, 792, 848, 1064$ \\ 50257 & 48 & & $336, 384, 432, 480, 512, 544, 576, 616, 768$ \\ \bottomrule \end{tabular}
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\begin{tabular}{lcccr} \toprule $V$ & $L$ & $d_x$ & $r$ & std \\ \midrule $257$ & $24$ & $264$ & & $5.1\cdot 10^{-4}$ \\ $257$ & $48$ & $184$ & & $6.8\cdot 10^{-4}$\\ $500$ & $24$ & $504$ & & $1.7\cdot 10^{-3}$ \\ $2000$ & $24$ & $528$ & $500$ & $1.5\cdot 10^{-3}$ \\ $50257$ & $48$ & $480$ & & $3.1\cdot 10^{-3}$ \\ \bottomrule \end{tabular}
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\begin{tabular}{lccc} \toprule $\nicefrac{H\cdot d_a}{d_x}$ & $L$ & $H$ & widths \\ \midrule $1$ & $\mathbf{18}$ & $12$ & $360,384,420,456$ \\ $1$ & $\mathbf{24}$ & $12$ & $420,456,480$ \\ $2$ & $\mathbf{12}$ & $12$ & $408,480$ \\ $2$ & $18$ & $18$ & $396$ \\ $2$ & $24$ & $24$ & $336$ \\ $4$ & $12$ & $12$ & $288,336$ \\ $4$ & $18$ & $12$ & $240,276$ \\ $4$ & $\mathbf{24}$ & $12$ & $204,240$ \\ $8$ & $\mathbf{12}$ & $12$ & $204,240$ \\ $8$ & $18$ & $12$ & $168,192$ \\ $8$ & $24$ & $12$ & $144,168$ \\ $16$ & $\mathbf{12}$ & $24$ & $144,168$ \\ \bottomrule \end{tabular}
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\begin{tabular}{c} Matthew Horak \\ Lockheed Martin Space \\ matthew.horak@lmco.com \end{tabular}
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\begin{tabular}{c} Sowmya Chandrasekaran\\ Lockheed Martin Space \\ sowmya.s.chandrasekaran@lmco.com \end{tabular}
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\begin{tabular}{c} Giovanni Tobar\\ Lockheed Martin Space \\ giovanni.a.tobar@lmco.com \end{tabular}
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\begin{tabular}{c|cc} &Actual Positive& Actual Negative\\ \hline Predicted Positive & True Positive (TP) & False Positive (FP) \\ Predicted Negative & False Negative (FN) & True Negative (TN) \\ \end{tabular}
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\begin{tabular}{lll} \hline Features & ROC AUC & PR AUC \\ \hline General & $0.8277$ & $0.0336$ \\ Visit-specific & $0.8769$ & $0.1140$ \\ Both & $0.9126$ & $0.1516$ \\ \hline \end{tabular}
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\begin{tabular}{lccc} \hline \textbf{Model} & \textbf{Static} & \textbf{ROC AUC} & \textbf{PR AUC} \\ &\textbf{features} && \\ \hline Gradient boosting (BoW) & without & $ 0.8625 \pm 0.0297 $ & $ 0.1806 \pm 0.0446 $ \\ Gradient boosting (TF-IDF) & without & $ 0.8625 \pm 0.0297 $ & $ 0.1928 \pm 0.0658 $ \\ Gradient boosting (BoW) & with & $ 0.8934 \pm 0.0281 $ & $ 0.1958 \pm 0.0579 $ \\ Gradient boosting (TF-IDF) & with & $ 0.8948 \pm 0.0303 $ & $ 0.2036 \pm 0.0659 $ \\ \hline SWEM-mean & without & $ 0.8753 \pm 0.0233 $ & $ 0.2052 \pm 0.0778 $ \\ SWEM-concat & without & $ 0.8551 \pm 0.0302 $ & $ 0.1782 \pm 0.0754 $ \\ SWEM-max & without & $ 0.8957 \pm 0.0217 $ & $ 0.2279 \pm 0.0677 $ \\ SWEM-mean & with & $ 0.8932 \pm 0.0321 $ & $ 0.2112 \pm 0.0804 $ \\ SWEM-concat & with & $ 0.8696 \pm 0.0377 $ & $ 0.1784 \pm 0.0814 $ \\ SWEM-max & with & $ \mathbf{0.9062 \pm 0.0252} $ & $ \mathbf{0.2445 \pm 0.0867} $ \\ \hline \end{tabular}
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\begin{tabular}{lll} \hline Resampling technique & ROC AUC & PR AUC \\ \hline No resampling (baseline) & $0.8345$ & $0.0994$ \\ Over (SMOTE) & $0.844$ & $0.0961$ \\ Over (ADASYN) & $0.8455$ & $0.0985$ \\ Under (RepeatedEditedNN) & $0.8439$ & $0.1019$ \\ Under (InstanceHardnessThreshold) & $\mathbf{0.8515}$ & $0.1011$ \\ Both over- and under (SMOTEENN) & $0.8485$ & $\mathbf{0.1069}$ \\ \hline \end{tabular}
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\begin{tabular}{|c||c|c|c|c|c|c|} \hline \bfseries phase & \bfseries veh & \bfseries veh & \bfseries veh & \bfseries veh & \bfseries ped & \bfseries ped \\ \bfseries nr & \bfseries west & \bfseries east & \bfseries north & \bfseries south & \bfseries w\&e & \bfseries n\&s \\ \hline\hline 1 & r & r & r & r & r & r \\ \hline 2 & g & g & r & r & r & g \\ \hline 3 & g & g & r & r & r & r \\ \hline 4 & g & r & r & r & r & r \\ \hline 5 & g+left~g & r & r & r & r & r \\ \hline 6 & r & r & g & g & g & r \\ \hline 7 & r & r & g & g & r & r \\ \hline 8 & r & r & g & r & r & r \\ \hline \end{tabular}
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\begin{tabular}{ll} \hline \textbf{Hyperparameter} & \textbf{Value} \\ \hline train\_batch\_size & $8000$ \\ num\_sgd\_iter & $10$ \\ gamma & $0.98$ \\ lambda & $0.95$ \\ vf\_loss\_coeff & $0.1789$ \\ lr & $1.5e-5$ \\ \hline queue\_norm & $30$ \\ wave\_norm & $14$ \\ speed\_norm & $14$ \\ wait\_veh\_norm & $14$ \\ wait\_ped\_norm & $10$\\ elapsed\_norm & $10$\\ $\alpha_{veh}$ & $1$ \\ $\alpha_{ped}$ & $0.25$ \\ \hline \end{tabular}
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\begin{tabular}{ccccccc} \toprule \textbf{Classes}& \textbf{Scratch}& \textbf{Pretrained} & \textbf{SRNN} &\textbf{MRCL}&\textbf{OML} & \textbf{Ours}\\ \midrule 6 & 19.3 $\pm$ 4.0 & 16.9 & 34.2 & 41.8 $\pm$ 9.0 & 37.0 $\pm$ 6.8 & \textbf{49.4 $\pm$ 6.5} \\ 8 & 12.9 $\pm$ 1.3 & 13.0&29.2 & 36.8 $\pm$ 7.1 & 34.6 $\pm$ 4.2 & \textbf{45.3 $\pm$ 4.9}\\ 10 & 10.1 $\pm$ 0.9& 10.0& 25.8 & 34.4 $\pm$ 6.5 & 33.2 $\pm$ 4.6 & \textbf{42.7 $\pm$ 4.6}\\ 12 & 8.5 $\pm$ 0.9 & 8.5 & 23.1 &30.6 $\pm$ 4.9 & 29.5 $\pm$ 3.2 & \textbf{39.4 $\pm$ 3.0}\\ 14 & 9.1 $\pm$ 1.9 & 8.8 & 20.4 &29.6 $\pm$ 4.5 & 27.8 $\pm$ 2.5 & \textbf{37.0 $\pm$ 3.7}\\ 16 & 7.4 $\pm$ 1.8 & 10.8 & 18.1 &28.0 $\pm$ 3.5 & 25.2 $\pm$ 2.0 & \textbf{33.4 $\pm$ 2.1} \\ 18 & 5.5 $\pm$ 0.7 & 10.4 & 17.7 & 26.3 $\pm$ 3.3 & 23.9 $\pm$ 2.1 & \textbf{31.9 $\pm$ 2.2}\\ 20 & 6.2 $\pm$ 1.4 & 10.0 & 17.3 &25.5 $\pm$ 2.8 & 22.9 $\pm$ 1.6 & \textbf{29.7 $\pm$ 1.4} \\ \bottomrule \end{tabular}
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\begin{tabular}{lcccc} \toprule \textbf{Method} &\textbf{Standard} & \textbf{Pre-Training} &\textbf{OML} &\textbf{Ours} \\ \midrule Online & 4.64 $\pm$ 2.61 & 21.16 $\pm$ 2.71 & 64.72 $\pm$ 2.57 & \textbf{85.68 $\pm$ 2.10} \\ Approx. IID & 53.95 $\pm$ 5.50 & 54.29 $\pm$ 3.48 & 75.12 $\pm$ 3.24 & \textbf{88.66 $\pm$ 2.10} \\ MER & 54.88 $\pm$ 4.12 &62.76 $\pm$ 2.16 & 76.00 $\pm$ 2.07 & \textbf{91.28 $\pm$ 1.38} \\ EWC & 5.08 $\pm$ 2.47 &18.72 $\pm$ 3.97 & 64.44 $\pm$ 3.13 & \textbf{87.10 $\pm$ 1.40} \\ ER-Reservoir & 52.56 $\pm$ 2.12 &36.72 $\pm$ 3.06 & 68.16 $\pm$ 3.12 & \textbf{90.10 $\pm$ 1.35} \\ \bottomrule \end{tabular}
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\begin{tabular}{lcccc} \toprule \textbf{Method} &\textbf{Standard} & \textbf{Pre-Training} &\textbf{OML} &\textbf{Ours} \\ \midrule Online & 1.40 $\pm$ 0.43 & 11.80 $\pm$ 1.92 & 55.32 $\pm$ 2.25 & \textbf{80.10 $\pm$ 1.71} \\ Approx. IID & 48.02 $\pm$ 5.67 &46.02$\pm$ 2.83 & 67.03 $\pm$ 2.10 & \textbf{85.90 $\pm$ 1.76} \\ MER & 29.02 $\pm$ 4.01 &42.05$\pm$ 3.71 & 62.05 $\pm$ 2.19 & \textbf{83.42 $\pm$ 1.67} \\ EWC & 2.04 $\pm$ 0.35 &10.03 $\pm$ 1.53 & 56.03 $\pm$ 3.20 & \textbf{82.90 $\pm$ 1.27} \\ ER-Reservoir & 24.32 $\pm$ 5.37 &37.44 $\pm$ 1.67 & 60.92 $\pm$ 2.41 & \textbf{84.76 $\pm$ 1.12} \\ \bottomrule \end{tabular}
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\begin{tabular}{cccccccc} \toprule \textbf{Classes} & \textbf{DER} & \textbf{DER++} & \textbf{HAL} & \textbf{MERLIN} & \textbf{GSS} & \textbf{PODNet} & \textbf{Ours}\\ \midrule 6 & 27.22 $\pm$ 6.39 & 36.77$\pm$5.73 & 26.33 $\pm$ 3.44 & 22.78 & 35.00 & 42.68 $\pm$ 2.33 & \textbf{49.4 $\pm$ 5.5}\\ 8 & 22.29 $\pm$ 5.42 & {28.13 $\pm$ 3.46} & 20.63 $\pm$ 3.11 & 14.16 & 30.00 & 36.10 $\pm$ 2.00 & \textbf{45.3 $\pm$ 4.9}\\ 10 & 19.0 $\pm$ 2.69 & {23.5 $\pm$ 4.14} & 15.93 $\pm$ 4.14 & 11.24 & 24.33 & 31.48 $\pm$ 1.56 & \textbf{42.7 $\pm$ 4.6}\\ 12 & 15.58 $\pm$ 3.35 & {19.14 $\pm$ 3.51} & 14.86 $\pm$ 2.45 & 9.42 & 17.78 & 27.94 $\pm$ 1.42 & \textbf{39.4 $\pm$ 3.0}\\ 14 & 13.93 $\pm$ 2.18 & {17.14 $\pm$ 3.27} & 12.36 $\pm$ 1.58 & 7.53 & 17.14 & 25.15 $\pm$ 1.29 & \textbf{37.0 $\pm$ 3.7}\\ 16 & 13.33 $\pm$ 2.83 & {14.21 $\pm$ 2.83} & 10.75 $\pm$ 1.56 & 6.83 & 11.87 & 22.93 $\pm$ 1.29 & \textbf{33.4 $\pm$ 2.1}\\ 18 & 11.48 $\pm$ 1.97 & {13.15 $\pm$ 2.96} & 9.46 $\pm$ 1.55 & 6.16 & 12.41 & 21.14 $\pm$ 1.22 & \textbf{31.9 $\pm$ 2.2}\\ 20 & 9.68 $\pm$ 3.07 & {12.48 $\pm$ 2.08} & 8.9 $\pm$ 1.50 & 6.11 & 13.00 & 19.63 $\pm$ 1.14 & \textbf{29.7 $\pm$ 1.4}\\ \bottomrule \end{tabular}
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\begin{tabular}{cccc} \toprule \textbf{Classes} &\textbf{Scratch} &\textbf{MRCL} &\textbf{Ours}\\ \midrule 10 & 10.3$\pm$1.3 & 20.0 $\pm$ 4.3 & \textbf{43.9 $\pm$ 6.0}\\ 15 & 7.0 $\pm$0.8 &16.6 $\pm$ 2.5 & \textbf{37.5 $\pm$ 4.0}\\ 20 & 5.1$\pm$ 0.3 &13.8 $\pm$ 2.4 & \textbf{32.7 $\pm$ 2.8}\\ 25 & 4.2$\pm$ 0.8 &13.4 $\pm$ 1.7 & \textbf{29.3 $\pm$ 1.5}\\ 30 & 3.4 $\pm$ 0.1 &11.6 $\pm$ 2.3 & \textbf{26.0 $\pm$ 3.1}\\ \bottomrule \end{tabular}
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\begin{tabular}{cccccc} \toprule \textbf{Tasks} &\textbf{Pretrained} &\textbf{SRNN} &\textbf{MRCL} & \textbf{OML} &\textbf{Ours}\\ \midrule 1 & 0.03 & \textbf{0.01 $\pm$ 0.003} & 0.11 $\pm$ 0.10 & 0.08 & 0.08 $\pm$ 0.06\\ 2 & 0.42 & 0.32 $\pm$ 0.27 &0.23 $\pm$ 0.16 & 0.23 &\textbf{0.12 $\pm$ 0.13} \\ 3 & 0.73 & 0.41 $\pm$ 0.35 &0.37 $\pm$ 0.18 & 0.26 & \textbf{0.09 $\pm$ 0.05} \\ 4 & 0.87 & 0.50 $\pm$ 0.34 &0.28 $\pm$ 0.13 & 0.22 & \textbf{0.16 $\pm$ 0.13}\\ 5 & 1.03 & 0.64 $\pm$ 0.33 &0.28 $\pm$ 0.12 & 0.26 & \textbf{0.16 $\pm$ 0.10 }\\ 6 & 1.04 & 0.64 $\pm$ 0.40 & 0.34 $\pm$ 0.17 & 0.28 & \textbf{0.17 $\pm$ 0.08} \\ 7 & 1.40 & 0.87 $\pm$ 0.57 &0.33 $\pm$ 0.19 & 0.29 & \textbf{0.24 $\pm$ 0.13}\\ 8 & 1.22 & 0.76 $\pm$ 0.36 &0.30 $\pm$ 0.16 & 0.27 & \textbf{0.19 $\pm$ 0.10 } \\ 9 & 1.33 & 0.80 $\pm$ 0.37 &0.33 $\pm$ 0.18 & 0.32 & \textbf{0.22 $\pm$ 0.10}\\ 10 & 1.45 & 0.90 $\pm$ 0.45 &0.40 $\pm$ 0.23 & 0.35 & \textbf{0.22 $\pm$ 0.09 }\\ \bottomrule \end{tabular}
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\begin{tabular}{c|c} \toprule Task & max - min \\ \midrule a1 & 0.35\\ a2 & 0.39\\ a3 & 0.16\\ a4 & 0.31\\ a5 & 0.47\\ a6 & 0.31\\ a7 & 0.43\\ a8 & \textbf{0.04}\\ a9 & 0.17\\ \bottomrule \end{tabular}
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\begin{tabular}{l|ccc} \specialrule{.1em}{.05em}{.05em} Algorithm & F-measure & Precision & Recall \\ \hline VILMAP & 0.750 & \textbf{0.856} & 0.667 \\ PUDDLE & 0.706 & 0.682 & 0.733 \\ DiBS & 0.236 & 0.234 & 0.240 \\ AGu & \textbf{0.782} & 0.787 & \textbf{0.777} \\ TPs & 0.468 & 0.432 & 0.512 \\\specialrule{.1em}{.05em}{.05em} \end{tabular}
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\begin{tabular}{c|c|c|c|c|c|c} \hline \hline \textbf{Type} & \textbf{Dataset} & \textbf{Sampling rate} & \textbf{No of subjects} & \textbf{Total audio} & \textbf{Average length} & \textbf{Standard deviation} \\ \hline \hline \multirow{4}{*}{TB Cough} & TASK & 44.1 kHz & 14 & 91 mins & 6.5 mins & 1.23 mins \\ \cline{2-7} & Brooklyn & 44.1 kHz & 17 & 4.63 mins & 16.35 sec & 13 sec \\ \cline{2-7} & Wallacedene & 44.1 kHz & 16 & 4.98 mins & 18.69 sec & 4.95 sec \\ \cline{2-7} & \textbf{Total (TB Cough)} & \textbf{---} & \textbf{47} & \textbf{1.68 hours} & \textbf{2.14 min} & \textbf{28.37 sec} \\ \hline \hline \multirow{4}{*}{COVID-19 Cough} & Coswara & 44.1 kHz & 92 & 4.24 mins & 2.77 sec & 1.62 sec \\ \cline{2-7} & ComParE & 16 kHz & 119 & 13.43 mins & 6.77 sec & 2.11 sec \\ \cline{2-7} & Sarcos & 44.1 kHz & 18 & 0.87 mins & 2.91 sec & 2.23 sec \\ \cline{2-7} & \textbf{Total (COVID-19 Cough)} & \textbf{---} & \textbf{229} & \textbf{18.54 mins} & \textbf{4.85 sec} & \textbf{1.92 sec} \\ \hline \hline \multirow{4}{*}{Healthy Cough} & Coswara & 44.1 kHz & 1079 & 0.98 hours & 3.26 sec & 1.66 sec \\ \cline{2-7} & ComParE & 16 kHz & 398 & 40.89 mins & 6.16 sec & 2.26 sec \\ \cline{2-7} & Brooklyn & 44.1 kHz & 21 & 1.66 mins & 4.7 sec & 3.9 sec \\ \cline{2-7} & \textbf{Total (Healthy Cough)} & \textbf{---} & \textbf{1498} & \textbf{1.69 hours} & \textbf{4.05 sec} & \textbf{1.85 sec} \\ \hline \hline \end{tabular}
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\begin{tabular}{c|c|c|c|c|c|c} \hline \hline \textbf{Type} & \textbf{Dataset} & \textbf{Sampling rate} & \textbf{No of events} & \textbf{Total audio} & \textbf{Average length} & \textbf{Standard deviation} \\ \hline \hline \multirow{3}{*}{Sneeze} & Google Audio Set \& Freesound & 16 kHz & 1013 & 13.34 mins & 0.79 sec & 0.21 sec \\ \cline{2-7} & Google Audio Set \& Freesound + SMOTE & 16 kHz & 9750 & 2.14 hours & 0.79 sec & 0.23 sec \\ \cline{2-7} & \textbf{Total (Sneeze)} & \textbf{---} & \textbf{10763} & \textbf{2.14 hours} & \textbf{0.79 sec} & \textbf{0.23 sec} \\ \hline \hline \multirow{3}{*}{Speech} & Google Audio Set \& Freesound & 16 kHz & 2326 & 22.48 mins & 0.58 sec & 0.14 sec \\ \cline{2-7} & LibriSpeech & 16 kHz & 56 & 2.54 hours & 2.72 mins & 0.91 mins \\ \cline{2-7} & \textbf{Total (Speech)} & \textbf{---} & \textbf{2382} & \textbf{2.91 hours} & \textbf{4.39 sec} & \textbf{0.42 sec} \\ \hline \hline \multirow{3}{*}{Noise}& TASK dataset & 44.1 kHz & 12714 & 2.79 hours & 0.79 sec & 0.23 sec \\ \cline{2-7} & Google Audio Set \& Freesound & 16 kHz & 1027 & 11.13 mins & 0.65 sec & 0.26 sec \\ \cline{2-7} & \textbf{Total (Noise)} & \textbf{---} & \textbf{13741} & \textbf{2.79 hours} & \textbf{0.79 sec} & \textbf{0.23 sec} \\ \hline \hline \end{tabular}
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\begin{tabular}{c|c|c} \hline \hline \textbf{Hyperparameters} & \textbf{Description} & \textbf{Range} \\ \hline \hline \multirow{2}{*}{MFCCs ($\mathbb{M}$)} & \multirow{2}{*}{lower order MFCCs to keep} & $13 \times k$, where \\ & & $k=1, 2, 3, 4, 5$ \\ \hline \multirow{2}{*}{Frame length ($\mathbb{F}$)} & \multirow{2}{*}{into which audio is segmented} & $2^{k}$, where \\ & & $k=9, 10, 11, 12$ \\ \hline \multirow{2}{*}{Segments ($\mathbb{S}$)} & \multirow{2}{*}{no. of frames extracted from audio} & $10 \times k$, where \\ & & $k=7, 10, 12, 15$ \\ \hline \hline \end{tabular}
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\begin{tabular}{l|c|l} \hline \hline \textbf{Hyperparameters} & \textbf{Classifier} & \textbf{Range} \\ \hline \hline No. of conv filters ($\alpha_1$) & CNN & $3 \times 2^k$ where $k=3, 4, 5$ \\ \hline Kernel size ($\alpha_2$) & CNN & 2 and 3 \\ \hline Dropout rate ($\alpha_3$) & CNN, LSTM & 0.1 to 0.5 in steps of 0.2 \\ \hline Dense layer units ($\alpha_4$) & CNN, LSTM & $2^k$ where $k=4, 5$ \\ \hline LSTM units ($\alpha_5$) & LSTM & $2^k$ where $k=6, 7, 8$ \\ \hline Learning rate ($\alpha_6$) & LSTM & $10^k$ where, $k=-2,-3,-4$ \\ \hline Batch Size ($\alpha_7$) & CNN, LSTM & $2^k$ where $k=6, 7, 8$\\ \hline \hline \end{tabular}
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\begin{tabular}{c|c|c} \hline \hline \multicolumn{3}{c}{\textbf{\uppercase{Feature Extraction hyperparameters}}}\\ \hline \hline \multicolumn{2}{c|}{\textbf{Hyperparameters}} & \textbf{Values} \\ \hline $\mathbb{M}$ & MFCCs & $39$ \\ \hline $\mathbb{F}$ & frame length & $2^{10} = 1024$ \\ \hline $\mathbb{S}$ & no. of frames & $150$ \\ \hline \hline \multicolumn{3}{c}{\textbf{\uppercase{Classifier hyperparameters}}}\\ \hline \hline \textbf{Hyperparameters} & \textbf{Classifier} & \textbf{Values} \\ \hline No. of conv filters ($\alpha_1$) & CNN & $256$ \& $128$ \& $64$ \\ \hline Kernel size ($\alpha_2$) & CNN & $2$ \\ \hline Dropout rate (($\alpha_3$)) & CNN, LSTM & $0.3$ \\ \hline Dense layer units ($\alpha_4$) & \multirow{2}{*}{CNN, LSTM, Resnet50} & \multirow{2}{*}{$512$ \& $128$ \& $3$} \\[-0.2em] (for pre-training) & & \\ \hline Dense layer units ($\alpha_4$) & \multirow{2}{*}{CNN, LSTM, Resnet50} & \multirow{2}{*}{$16$ \& $2$ or $3$} \\[-0.2em] (for fine-tuning) & & \\ \hline LSTM units ($\alpha_5$) & LSTM & $512$ \& $256$ \& $128$ \\ \hline Learning rate ($\alpha_6$) & LSTM & $10^{-3} = 0.001$ \\ \hline Batch Size ($\alpha_7$) & CNN, LSTM, Resnet50 & $2^7 = 128$ \\ \hline \hline \end{tabular}
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\begin{tabular}{c|ll} \hline Dataset & \textbf{IMDB-Binary} & \textbf{Reddit-Binary} \\ \hline \# of Nodes & 19,773 & 859,254 \\ \# of Edges & 96,531 & 995,508 \\ \# of Graphs & 1,000 & 2,000 \\ Avg Degree & 4.88 & 1.16 \\ \hline \end{tabular}
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\begin{tabular}{c|llll} \hline Dataset & \textbf{OAG} & \textbf{Twitter} & \textbf{Weibo} & \textbf{Digg} \\ \hline \# of Nodes & 953,675 & 456,626 & 1,776,950 & 279,630 \\ \# of Edges & 4,151,463 & 12,508,413 & 308,489,739 & 1,548,126 \\ \# of Graphs & 499,848 & 499,160 & 779,164 & 244,128 \\ Avg Degree & 4.35 & 27.39 & 173.60 & 5.54 \\ \hline \end{tabular}
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\begin{tabular}{c|llllllll} \hline task & Target & DANN & MDD & DANE & UDAGCN & DSR & DIVA & DGDA(Ours)\\ \hline I$\rightarrow$R & ${90.0}_{\pm 1.6}$ & ${74.4}_{\pm 0.6}$ & ${67.3}_{\pm 2.0}$ & ${73.9}_{\pm 1.1}$ & ${73.7}_{\pm 0.9}$ & ${75.7}_{\pm 1.4}$ & ${75.9}_{\pm 0.7}$ & ${\textbf{78.1}}_{\pm 1.0}$ \\ R$\rightarrow$I & ${76.7}_{\pm 2.6}$ & ${73.8}_{\pm 1.4}$ & ${71.0}_{\pm 0.8}$ & ${72.1}_{\pm 1.6}$ & ${73.9}_{\pm 0.7}$ & ${73.2}_{\pm 1.1}$ & ${74.0}_{\pm 1.3}$ & ${\textbf{74.7}}_{\pm 0.9}$ \\ \hline \end{tabular}
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\begin{tabular}{l|lllllllllllll} \hline Methods &O$\rightarrow$T &O$\rightarrow$W &O$\rightarrow$D &T$\rightarrow$O &T$\rightarrow$W &T$\rightarrow$D &W$\rightarrow$O &W$\rightarrow$T &W$\rightarrow$D &D$\rightarrow$O &D$\rightarrow$T &D$\rightarrow$W & Avg\\ \hline Target & 53.3 & 53.2 & 62.9 & 43.0 & 53.2 & 62.9 & 43.0 & 53.3 & 62.9 & 43.0 & 53.3 & 53.2 & 53.1\\ DGDA-D & ${48.7}_{\pm 0.3}$ & ${42.3}_{\pm 0.6}$ & ${49.0}_{\pm 1.8}$ & ${40.3}_{\pm 0.1}$ & ${42.2}_{\pm 0.3}$ & ${45.1}_{\pm 1.9}$ & ${41.0}_{\pm 0.4}$ & ${48.3}_{\pm 0.4}$ & ${47.6}_{\pm 0.9}$ & ${41.0}_{\pm 0.4}$ & ${47.7}_{\pm 0.8}$ & ${42.0}_{\pm 0.6}$ & 44.6 \\ DGDA-O & ${48.6}_{\pm 0.5}$ & ${41.2}_{\pm 0.5}$ & ${46.3}_{\pm 1.1}$ & ${40.2}_{\pm 0.0}$ & ${41.7}_{\pm 0.9}$ & ${42.7}_{\pm 1.5}$ & ${40.3}_{\pm 0.1}$ & ${49.1}_{\pm 0.3}$ & ${44.5}_{\pm 1.8}$ & ${40.3}_{\pm 0.0}$ & ${48.0}_{\pm 0.7}$ & ${40.5}_{\pm 0.2}$ & 43.6 \\ DGDA-M & ${48.3}_{\pm 0.1}$ & ${41.0}_{\pm 0.6}$ & ${47.1}_{\pm 2.6}$ & ${40.2}_{\pm 0.0}$ & ${42.1}_{\pm 0.7}$ & ${43.0}_{\pm 2.3}$ & ${40.4}_{\pm 0.4}$ & ${48.8}_{\pm 0.2}$ & ${44.7}_{\pm 1.6}$ & ${40.2}_{\pm 0.0}$ & ${47.6}_{\pm 0.4}$ & ${41.0}_{\pm 0.6}$ & 43.7 \\ \hline DGDA & $\textbf{49.2}_{\pm 0.1}$ & $\textbf{42.9}_{\pm 0.4}$ & $\textbf{49.7}_{\pm 1.4}$ & $\textbf{40.3}_{\pm 0.4}$ & $\textbf{44.7}_{\pm 0.6}$ & $\textbf{46.7}_{\pm 1.7}$ & $\textbf{41.5}_{\pm 0.3}$ & $\textbf{49.9}_{\pm 0.3}$ & $\textbf{48.3}_{\pm 1.3}$ & $\textbf{41.1}_{\pm 0.4}$ & $\textbf{48.4}_{\pm 0.6}$ & $\textbf{42.7}_{\pm 0.8}$ & \textbf{45.5} \\ \hline \end{tabular}
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\begin{tabular}{c|cc} \hline \small{Parameter} & \textbf{IMDB\&Reddit} & \textbf{Ego-network}\\ \hline \small{Batch size} & 64 & 1024 \\ \small{Learning rate} & 0.001 & 0.01 \\ \small{Encoder hidden size} & 256 & 256 \\ \small{Dimension of $\bm{Z}_d$} & 256 & 64 \\ \small{Dimension of $\bm{Z}_y$} & 256 & 256 \\ \small{Dimension of $\bm{Z}_o$} & 128 & 128 \\ \small{Decoder hidden size} & 64 & 64 \\ \small{Dropout rate} & 0.2 & 0.5 \\ \small{Weight decay} & 0.0005 & 0.0005 \\ \small{$p_\text{drop}$} & 0.1 & 0.1 \\ \small{$p_\text{add}$} & 0.1 & 0.1 \\ \hline \end{tabular}
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\begin{tabular}{c|c} \hline Information Value & Predictive Power\\ \hline $0$ to $0.02$ & Useless for prediction\\ $0.02$ to $0.1$ & Weak predictor\\ $0.1$ to $0.3$ & Medium predictor\\ $0.3$ to $0.5$ & Strong predictor\\ $>0.5$ & Extremely strong predictor\\ \hline \end{tabular}
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\begin{tabular}{c|c} \hline Pearson Correlation Coefficient & Correlation\\ \hline $0$ to $0.2$ & Very weak or no correlation\\ $0.2$ to $0.4$ & Weak correlation\\ $0.4$ to $0.6$ & Moderate correlation\\ $0.6$ to $0.8$ & Strong correlation\\ $0.8$ to $1$ & Extremely strong correlation\\ \hline \end{tabular}
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\begin{tabular}{lcccc} \hline Dataset & \#Train & \#Valid & \#Test & \#Dim\\ \hline valley & 900 & - & 312 & 100\\ banknote & 1,000 & - & 372 & 4\\ gina & 2,800 & - & 668 & 970\\ spambase & 3,800 & - & 801 & 57\\ phoneme & 4,500 & - & 904 & 5\\ wind & 5,000 & - & 1,574 & 14\\ ailerons & 9,000 & 2,000 & 2,750 & 40\\ eeg-eye & 10,000 & 2,000 & 2,980 & 14\\ magic & 13,000 & 3,000 & 3,020 & 10\\ nomao & 22,000 & 6,000 & 6,000 & 118\\ bank & 35,211 & 4,000 & 6,000 & 51\\ vehicle & 60,000 & 18,528 & 20,000 & 100\\ \hline \end{tabular}
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\begin{tabular}{lccccc} \hline Dataset & FCT & TFC & RAND & IMP & SAFE\\ \hline valley & 9.80 & 228.93 & 0.55 & 0.65 & 0.73\\ banknote & 0.16 & 0.27 & 0.08 & 0.31 & 0.12\\ gina & 84.03 & 95.73 & 3.39 & 5.28 & 5.31\\ spambase & 23.84 & 262.11 & 2.85 & 3.23 & 3.17\\ phoneme & 10.83 & 2.48 & 0.46 & 0.58 & 0.51\\ wind & 25.03 & 22.87 & 2.13 & 2.39 & 2.33\\ ailerons & 80.73 & 336.53 & 2.12 & 2.57 & 2.72\\ egg-eye & 58.88 & 42.13 & 1.09 & 1.20 & 1.18\\ magic & 52.45 & 36.79 & 2.55 & 2.96 & 3.32\\ nomao & 104.59 & 1469.19 & 22.22 & 26.61 & 28.82\\ bank & 838.17 & 552.48 & 13.70 & 13.81 & 12.28\\ vehicle & 1355.19 & 2748.89 & 52.86 & 40.34 & 62.14\\ \hline \end{tabular}
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\begin{tabular}{lcccc} \hline Dataset & FCT & RAND & IMP & SAFE\\ \hline valley & 0.6991 & 0.4933 & 0.4947 & \textbf{0.4710}\\ banknote & 0.4405 & 0.3233 & 0.3174 & \textbf{0.1197}\\ gina & 0.5700 & 0.4639 & 0.4739 & \textbf{0.4163}\\ spambase & 0.5101 & 0.4571 & 0.4399 & \textbf{0.3587}\\ phoneme & \textbf{0.1947} & 0.3269 & 0.3294 & 0.2616\\ wind & 0.3707 & 0.3608 & 0.3570 & \textbf{0.3230}\\ ailerons & 0.4440 & 0.4590 & 0.3963 & \textbf{0.3330}\\ egg-eye & 0.3529 & 0.3768 & 0.3741 & \textbf{0.3212}\\ magic & \textbf{0.1847} & 0.3306 & 0.3384 & 0.2620\\ nomao & 0.5061 & 0.5032 & 0.4735 & \textbf{0.4065}\\ bank & 0.3713 & 0.4240 & 0.4072 & \textbf{0.2853}\\ \hline \end{tabular}
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\begin{tabular}{lcccc} \hline Dataset & \#Train & \#Valid & \#Test & \#Dim\\ \hline Data1 & 2,502,617 & 625,655 & 625,655 & 81\\ Data2 & 7,282,428 & 1,820,607 & 1,820,607 & 44\\ Data3 & 8,000,000 & 2,000,000 & 2,000,000 & 73\\ \hline \end{tabular}
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\begin{tabular}{cccccc} \hline Dataset & CLF & ORIG & RAND & IMP & SAFE\\ \hline & LR & 93.07 & 95.81 & 95.83 & \textbf{95.93}\\ Data1 & RF & 96.26 & 97.62 & 97.60 & \textbf{98.20}\\ & XGB & 97.04 & 96.59 & 97.35 & \textbf{97.46}\\ \hline & LR & 90.24 & 90.26 & 90.26 & \textbf{90.31}\\ Data2 & RF & 88.26 & 88.71 & 88.61 & \textbf{88.95}\\ & XGB & 90.13 & 90.33 & 90.44 & \textbf{90.61}\\ \hline & LR & 89.64 & 89.82 & 89.84 & \textbf{89.94}\\ Data3 & RF & 86.98 & 87.05 & 88.26 & \textbf{88.59}\\ & XGB & 89.77 & 89.74 & 89.92 & \textbf{90.37}\\ \hline \end{tabular}
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\begin{tabular}{cccccccc} \toprule[1pt] \textbf{Dataset} & \textbf{Clients} & \textbf{Samples} & \textbf{Classes} & \multicolumn{2}{c}{\textbf{samples per client}} & \multicolumn{2}{c}{\textbf{classes per client}} \\ \cline{5-8} & \multicolumn{3}{c}{} & mean & stdev & min & max \\ \hline FEMNIST & 1,068 & 235,683 & 62 & 220 & 90 & 9 & 62 \\ Shakespeare & 528 & 625,127 & 70 & 1183 & 1218 & 2 & 70 \\ Sent140 & 3,790 & 171,809 & 2 & 45 & 28 & 1 & 2 \\ Production Dataset & 9,369 & 6,430,120 & 2,400 & 686 & 374 & 2 & 36 \\ \bottomrule[1pt] \end{tabular}
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\begin{tabular}{l|l|c|c|c} \toprule[1pt] \multicolumn{2}{l|}{} & 20\% Support & 50\% Support & 90\% Support \\ \hline \multirow{4}{*}{FEMNIST} & FedAvg & 76.79\% $\pm$ 0.45\% & 75.44\% $\pm$ 0.73\% & 77.05\% $\pm$ 1.43\% \\ & FedAvg(Meta) & 83.58\% $\pm$ 0.13\% & 87.84\% $\pm$ 0.11\% & 88.76\% $\pm$ 0.78\% \\ & FedMeta(MAML) & 88.46\% $\pm$ 0.25\% & 89.77\% $\pm$ 0.08\% & 89.31\% $\pm$ 0.15\%\\ & FedMeta(Meta-SGD) & \textbf{89.26\%} $\pm$ 0.12\% & \textbf{90.28\%} $\pm$ 0.02\% & \textbf{89.31\%} $\pm$ 0.09\% \\ \hline \multirow{4}{*}{Shakespeare} & FedAvg & 40.76\% $\pm$ 0.62\% & 42.01\% $\pm$ 0.43\% & 40.58\% $\pm$ 0.55\% \\ & FedAvg(Meta) & 38.71\% $\pm$ 0.51\% & 42.97\% $\pm$ 0.97\% & 43.48\% $\pm$ 0.64\% \\ & FedMeta(MAML) & \textbf{46.06\%} $\pm$ 0.85\% & \textbf{46.29\%} $\pm$ 0.84\% & \textbf{46.49\%} $\pm$ 0.77\%\\ & FedMeta(Meta-SGD) & 44.72\% $\pm$ 0.72\% & 45.24\% $\pm$ 0.53\% & 46.25\% $\pm$ 0.63\% \\ \hline \multirow{4}{*}{Sent140} & FedAvg & 71.53\% $\pm$ 0.18\% & 72.29\% $\pm$ 0.49\% & 73.38\% $\pm$ 0.38\% \\ & FedAvg(Meta) & 70.10\% $\pm$ 0.66\% & 73.88\% $\pm$ 0.06\% & 75.86\% $\pm$ 0.46\% \\ & FedMeta(MAML) & 76.37\% $\pm$ 0.06\% & 78.63\% $\pm$ 0.19\% & 79.53\% $\pm$ 0.25\%\\ & FedMeta(Meta-SGD) & \textbf{77.24\%} $\pm$ 0.32\% & \textbf{79.38\%} $\pm$ 0.09\% & \textbf{80.94\%} $\pm$ 0.29\% \\ \bottomrule[1pt] \end{tabular}
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\begin{tabular}{l|c|c} \toprule[1pt] & FedAvg & FedMeta($\alpha$, $\beta$)\\ \hline FEMNIST & 10e-5 & (0.001,0.0001)\\ Shakespeare & 0.001 & (0.1, 0.01)\\ Sent140 & 0.001 & (0.001, 0.0001)\\ \bottomrule[1pt] \end{tabular}
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\begin{tabular}{ccc} \toprule Step & \multicolumn{2}{c}{Number of trips}\\ \cmidrule(lr){2-3} & Porto & San Francisco\\ \midrule - & 1,710,670 (100.0\,\%) & 927,976 (100.0\,\%) \\ (1) & 1,638,681 (95.79\,\%) & 820,108 (88.37\,\%)\\ (2) & 1,638,681 (95.79\,\%) & 820,108 (88.37\,\%)\\ (3) & 1,630,112 (95.29\,\%) & 815,403 (87.87\,\%)\\ (4) & 1,545,240 (90.33\,\%) & 700,197 (75.44\,\%) \\ \bottomrule \end{tabular}
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\begin{tabular}{l|cccc}\toprule Setting & Cora & CiteSeer & ACM & BlogCatalog \\ \midrule Unsup. & 0.8997&0.9191&0.8742&0.8025\\ \midrule 1-shot &0.9058&0.9184&0.8858&0.8076\\ 3-shot &0.9070&0.9199&0.8867&0.8125\\ 5-shot &0.9096&0.9252&0.8906&0.8123\\ 10-shot &0.9155&0.9318&0.8955&0.8124\\ 15-shot &0.9226&0.9363&0.8953&0.8214\\ 20-shot &0.9214&0.9256&0.8965&0.8228\\ \bottomrule \end{tabular}
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\begin{tabular}{rrrr} \toprule & MLP & FCN & ResNet \\ \midrule DTW & 0.7575 & \textbf{0.0203} & \textbf{0.0245} \\ COTE & \textbf{0.0040} & 0.8445 & 0.8347 \\ MCNN & \textbf{0.0049} & 0.9834 & 0.9468 \\ BOSSVS & 0.1385 & 0.1660 & 0.1887 \\ PROP & 0.0616 & 0.2529 & 0.2360 \\ BOSS & \textbf{0.0076} & 0.8905 & 0.8740 \\ SE1 & 0.1299 & 0.0604 & 0.0576 \\ TSBF & 0.1634 & 0.0715 & 0.0811 \\ MLP & /\ & \textbf{0.0051} & \textbf{0.0049} \\ FCN & \textbf{0.0051} & /\ & 0.9169 \\ ResNet & \textbf{0.0049} & 0.9169 & /\ \\ \bottomrule \end{tabular}
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\begin{tabular}{rrrrrrrrrrrr} \toprule & DTW & COTE & MCNN & BOSSVS & PROP & BOSS & SE1 & TSBF & MLP & FCN & ResNet \\ \midrule DTW & & \textbf{2.056E-05} & \textbf{5.699E-05} & 5.141E-02 & \textbf{4.832E-05} & \textbf{2.760E-04} & \textbf{3.040E-03} & \textbf{1.311E-02} & 4.234E-01 & \textbf{1.451E-04} & \textbf{3.427E-04} \\ COTE & & & 2.287E-01 & \textbf{3.721E-05} & \textbf{5.911E-03} & 1.033E-01 & \textbf{1.208E-04} & \textbf{3.528E-04} & \textbf{5.240E-05} & 3.978E-01 & 4.351E-01 \\ MCNN & & & & \textbf{3.652E-04} & \textbf{1.354E-02} & 2.497E-01 & \textbf{3.634E-03} & \textbf{3.360E-03} & \textbf{8.023E-05} & 2.495E-01 & 3.757E-01 \\ BOSSVS & & & & & 2.140E-01 & \textbf{6.404E-04} & 1.763E-01 & 4.335E-01 & \textbf{4.628E-02} & \textbf{2.983E-03} & \textbf{5.067E-03} \\ PROP & & & & & & \textbf{3.739E-02} & 4.654E-01 & \textbf{1.440E-01} & \textbf{2.061E-02} & \textbf{2.673E-02} & \textbf{4.241E-02} \\ BOSS & & & & & & & \textbf{2.871E-02} & \textbf{1.759E-02} & \textbf{1.049E-03} & 1.879E-01 & 2.751E-01 \\ SE1 & & & & & & & & 1.770E-01 & \textbf{9.901E-03} & \textbf{1.208E-02} & \textbf{3.251E-02} \\ TSBF & & & & & & & & & 7.088E-02 & \textbf{1.510E-03} & \textbf{1.640E-03} \\ MLP & & & & & & & & & & \textbf{6.832E-05} & \textbf{3.045E-04} \\ FCN & & & & & & & & & & & 2.508E-01 \\ ResNet & & & & & & & & & & & \\ \bottomrule \end{tabular}
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\begin{tabular}{llll} \toprule \bf{Method} & \bf{Steps} & \bf{Time Complexity} & \bf{Space Complexity} \\\midrule \multirow{2}{*}{Linear search} & Distance Matrix & $O(N^2D)$ & $M(2N+1)$ \\ & Top-k & $O(N^2)$ & $2Mk$ \\\midrule \multirow{5}{*}{TNN} & Distance Segments & $O(\frac{N^2}{K}D)$ & $M\frac{N}{K}D$ \\ & Sort & $O(\frac{N^2}{K} \log(\frac{N}{K}))$ & $2M \frac{N}{K}$ \\ \cmidrule{2-4} & Distance to points & $O(Nn_fFKD)$ & $M(k+FK)D $ \\ & Top-k & $O(Nn_f(k+FK))$ & $2M(k+FK)$ \\ & Total & $O(\frac{N^2}{K} \log(\frac{N}{K})+Nn_fFKD)$ & $M\frac{N}{K}D + M(k+FK)D$ \\ \bottomrule \end{tabular}
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\begin{tabular}{cclrrr} \toprule \bf{Data set} & \bf{Device} & \bf{Algorithm} & \bf{Comparisons} & \bf{Query [ms]} & \bf{Total duration} \\ \midrule \multirow{4}{*}{Original Data set} & \multirow{2}{*}{\tt{CPU}} & Lin. Search & \tt{811'372} & \tt{9.03} & \tt{2:30:32} \\ & & TNN & \texttt{\textbf{28'579}} & \tt{1.03} & \tt{17:08} \\ & \multirow{2}{*}{\tt{GPU}} & Lin. Search & \tt{811'372} & \tt{2.55} & \tt{42:28} \\ & & TNN & \tt{81'611} & \texttt{\textbf{0.16}} & \texttt{\textbf{2:43}} \\\midrule \multirow{4}{*}{SRW Data set} & \multirow{2}{*}{\tt{CPU}} & Lin. Search & \tt{1'000'000} & \tt{11.95} & \tt{3:19:09} \\ & & TNN & \texttt{\textbf{58'408}} & \tt{1.60} & \tt{26:35} \\ & \multirow{2}{*}{\tt{GPU}} & Lin. Search & \tt{1'000'000} & \tt{2.51} & \tt{41:48} \\ & & TNN & \tt{93'555} & \texttt{\textbf{0.39}} & \texttt{\textbf{6:28}} \\\midrule \multirow{4}{*}{Random points} & \multirow{2}{*}{\tt{CPU}} & Linear Search & \tt{1'000'000} & \tt{7.43} & \tt{2:03:51} \\ & & TNN & \tt{999'940} & \tt{15.51} & \tt{4:18:34} \\ & \multirow{2}{*}{\tt{GPU}} & Linear Search & \tt{1'000'000} & \tt{1.72} & \tt{28:42} \\ & & TNN & \texttt{\textbf{998'588}} & \texttt{\textbf{1.36}} & \texttt{\textbf{22:40}} \\ \bottomrule \end{tabular}
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\begin{tabular}{lrrr} \toprule \bf{Method} & \bf{Creation [s]} & \bf{Query [ms]} & \bf{Total duration} \\\midrule Linear search CPU & \tt{- } & \tt{9.03} & \tt{2:30:32} \\ TNN CPU & \tt{1.00} & \tt{1.03} & \tt{17:08} \\ Scaled masked KDTree & \tt{0.11} & \tt{9.25} & \tt{2:35:06} \\ Scaled masked cKDTree & \tt{0.03} & \texttt{\textbf{0.70}} & \texttt{\textbf{11:35}} \\ \midrule TNN GPU & \tt{7.00} & \texttt{\textbf{0.16}} & \texttt{\textbf{2:43}} \\ Linear search GPU & \tt{- } & \tt{2.55} & \tt{42:28} \\ \bottomrule \end{tabular}
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\begin{tabular}{cccc} \hline Algorithm & Lipschitz Bound & Largest Gradient & Ratio \\ \hline ReLU & 9.22& 2.91& 3.17 \\ SDP & 2.91& 1.30& 2.24 \\ 2-Layer FullSort & 5.85& 4.16& 1.41\\ 3-Layer GroupSort-10 & 6.36& 5.29& \textbf{1.20}\\ 4-Layer OPLU & 10.77& 3.90& 2.76\\ \hline \end{tabular}
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\begin{tabular}{lll} \toprule Symbol & Type & Definition \\ \midrule $a_{jm}$ & variable & node $m$ splits on feature $j$ \\ $b_{vm}$ & variable & node $m$'s threshold is left/right of $v$ \\ $b'_{m}$ & variable & node $m$'s continuous threshold value \\ $c_{t}$ & variable & leaf node $t$ predicts class $0$ or $1$ \\ $s_{im0}$ & variable & sample $i$ can move left of node $m$ \\ $s_{im1}$ & variable & sample $i$ can move right of node $m$ \\ $e_{i}$ & variable & sample $i$ can be misclassified \\ \midrule $X_{ij}$ & constant & value of data row $i$ in feature $j$ \\ $y_{i}$ & constant & class label of data row $i$ \\ $\Delta^l_{j}$ & constant & left perturbation range for feature $j$ \\ $\Delta^r_{j}$ & constant & right perturbation range for feature $j$ \\ $n$ & constant & number of samples \\ $p$ & constant & number of features \\ \midrule $A(t)$ & set & ancestors of node $t$ \\ $A_l(t)$ & set & ... with left branch on the path to $t$ \\ $A_r(t)$ & set & ... with right branch on the path to $t$ \\ $\mathcal{T}_B$ & set & all decision nodes \\ $\mathcal{T}_L$ & set & all leaf nodes \\ $V_j$ & set & unique values in feature $j$ \\ \bottomrule \end{tabular}
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\begin{tabular}{l|ccc} \toprule{} & Mean adv. & Mean rank & Wins \\ Algorithm & accuracy & & \\ \midrule TREANT & .692 \tiny $\pm$ .013 & 5.167 \tiny $\pm$ .604 & 7 \\ Binary-MILP & .714 \tiny $\pm$ .013 & 3.958 \tiny $\pm$ .576 & 10 \\ MILP & .720 \tiny $\pm$ .015 & 2.917 \tiny $\pm$ .454 & 12 \\ RC2-MaxSAT & .724 \tiny $\pm$ .014 & 2.667 \tiny $\pm$ .393 & 10 \\ GROOT & .726 \tiny $\pm$ .015 & 2.375 \tiny $\pm$ .450 & 16 \\ Binary-MILP-warm & .726 \tiny $\pm$ .015 & 2.083 \tiny $\pm$ .399 & 16 \\ LSU-MaxSAT & .729 \tiny $\pm$ .014 & 2.125 \tiny $\pm$ .303 & 13 \\ MILP-warm & \textbf{.735} \tiny $\pm$ .015 & \textbf{1.583} \tiny $\pm$ .225 & \textbf{17} \\ \bottomrule \end{tabular}
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\begin{tabular}{cccc} \textbf{Architecture} & \textbf{T4} & \textbf{V100} & \textbf{A100} \\ \midrule \textbf{SMs} & 40 & 80 & 108 \\ \textbf{Global Memory Size} & 16 GB & 16 or 32 GB & 40 or 80 GB \\ \textbf{Memory BW} & 320 GB/s & 900 GB/s & 1.6 or 1.9 TB/s \\ \textbf{L2 cache} & 4 MB & 6 MB & 40 MB \\ \bottomrule \end{tabular}
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\begin{tabular}{ccccc} \toprule NAS Method & NAS Formulation & Weight-sharing & Update Method & Search Stopping Criterion \\ \midrule REINFORCE & Single-path & No & policy gradients & policy entropy \\\midrule Evolution & Single-path & No & mutation & population diversity \\\midrule FP-NAS & Supernet & Yes & gradient descent & entropy of architecture parameters \\ \bottomrule \end{tabular}
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\begin{tabular}{ccc} \toprule Indicators & Accuracy & GPU secs. \\ \midrule Baseline (1-epoch training) & 68.4(5.93) & 19786 \\ $\hat{R}$ & 69.06(2.15) & 254.6 \\ $\hat{\kappa}$ & 69.27(0.73) & 1574 \\ $\mathrm{MSE}$ & 69.68(0.88) & 2447.7 \\ $\hat{\kappa}$, $\hat{R}$ & 69.89(0.98) & 1716.1 \\ $\hat{R}$, $\mathrm{MSE}$ & 70.00(0.42) & 2667.4 \\ $\hat{\kappa}$, $\mathrm{MSE}$ & 70.18(0.04) & 2704 \\ $\hat{\kappa}$, $\hat{R}$, $\mathrm{MSE}$ & 70.42(0.36) & 3668.5 \\ \bottomrule \end{tabular}
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\begin{tabular}{lccccc} \toprule &\multicolumn{2}{c}{\textbf{Co-authorship Data}} & \multicolumn{3}{c}{\textbf{Co-citation Data}} \\ \cmidrule(lr){2-3} \cmidrule(lr){4-6} \textbf{Method} &DBLP &Cora&Pubmed &Citeseer & Cora \\ \cmidrule(l){1-1}\cmidrule(l){2-2} \cmidrule(l){3-3} \cmidrule(l){4-4} \cmidrule(l){5-5} \cmidrule(l){6-6} MLP $+$ HLR & 63.6 $\pm$ 4.7 & 59.8 $\pm$ 4.7 & 64.7 $\pm$ 3.1 & 56.1 $\pm$ 2.6 & 61.0 $\pm$ 4.1\\ [3pt] HGNN & 69.2 $\pm$ 5.1 & 63.2 $\pm$ 3.1 & 66.8 $\pm$ 3.7 & 56.7 $\pm$ 3.8 & \textbf{70.0 $\pm$ 2.9} \\ [3pt] FastHyperGCN & 68.1 $\pm$ 9.6 & 61.1 $\pm$ 8.2 & 65.7 $\pm$ 11.1 & 56.2 $\pm$ 8.1 & 61.3 $\pm$ 10.3 \\ [3pt] HyperGCN & 70.9 $\pm$ 8.3 & 63.9 $\pm$ 7.3 & 68.3 $\pm$ 9.5 & 57.3 $\pm$ 7.3 & 62.5 $\pm$ 9.7 \\ [3pt] \midrule HyperSAGE ($p=2$) & 71.5 $\pm$ 4.4 & 69.8 $\pm$ 2.6 & 71.3 $\pm$ 2.4 & 59.8 $\pm$ 3.3 &62.9 $\pm$ 2.1 \\ HyperSAGE ($p=1$) & 77.2 $\pm$ 4.3 & \textbf{72.4 $\pm$ 1.6} & 72.6 $\pm$ 2.1 & \textbf{61.8 $\pm$ 2.3} & 69.3 $\pm$ 2.7 \\ HyperSAGE ($p=0.01$) & \textbf{77.4 $\pm$ 3.8} & 72.1 $\pm$ 1.8 & \textbf{72.9 $\pm$ 1.3} & 61.3 $\pm$ 2.4 & 68.2 $\pm$ 2.4 \\ HyperSAGE ($p=-1$) & 70.9 $\pm$ 2.3 & 67.4 $\pm$ 2.1 & 68.3 $\pm$ 3.1 & 59.8 $\pm$ 2.0 & 62.3 $\pm$ 5.7 \\ \bottomrule \end{tabular}
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\begin{tabular}{lcccccccc} \toprule &\multicolumn{4}{c}{DBLP} & \multicolumn{4}{c}{Pubmed} \\ \cmidrule(lr){2-5} \cmidrule(lr){6-9} &$\alpha = 2$ &$\alpha = 3$ &$\alpha = 5$ &$\alpha = 10$ &$\alpha = 2$ &$\alpha = 3$ &$\alpha = 5$ &$\alpha = 10$\\ \cmidrule(l){2-2} \cmidrule(l){3-3} \cmidrule(l){4-4} \cmidrule(l){5-5} \cmidrule(l){6-6} \cmidrule(l){7-7} \cmidrule(l){8-8} \cmidrule(l){9-9} $p = -1$ & 59.6& 61.2 &69.9 &70.9 &60.1 & 60.2 & 67.9 & 66.4 \\ $p = 0.01$ & 61.2 & 64.8 & 73.1 & \textbf{77.4} & 65.5 & 67.4 & \textbf{73.4}& 72.9 \\ $p = 1$ & 62.3 & 64.5 & 73.1 &77.2 &64.8 & 64.3 &72.2 & 72.6 \\ $p = 2$ & 63.1 & 63.8 & 71.9 & 71.5 & 63.7 & 63.9 & 70.8& 71.3\\ $p = 3$ & 62.7 & 63.6 &71.3 & 71.4 & 62.2 & 61.3 & 70.1 & 67.9 \\ $p = 5$ & 62.8&63.3 &69.4 & 70.6 &62.1 &60.4 &69.3 & 68.0\\ \bottomrule \end{tabular}
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\begin{tabular}{lcccccccc} \toprule &\multicolumn{2}{c}{DBLP} & \multicolumn{2}{c}{Pubmed} &\multicolumn{2}{c}{Citeseer} & \multicolumn{2}{c}{Cora (citation)}\\ \cmidrule(lr){2-3} \cmidrule(lr){4-5} \cmidrule(lr){6-7} \cmidrule(lr){8-9} \textbf{Method} &Seen &Unseen &Seen &Unseen &Seen &Unseen &Seen &Unseen\\ \cmidrule(l){2-2} \cmidrule(l){3-3} \cmidrule(l){4-4} \cmidrule(l){5-5} \cmidrule(l){6-6} \cmidrule(l){7-7} \cmidrule(l){8-8} \cmidrule(l){9-9} MLP + HLR & 64.5 &58.7 &66.8 &62.4 &60.1 &58.2 &65.7 &64.2 \\ HyperSAGE $(p = 0.01)$ & 78.1 & 73.1 & 81.0 &80.4 & 69.2 & 67.1 &68.2 &65.7 \\ HyperSAGE $(p = 1)$ & 78.1 & 73.2 &78.5 &76.4 & 69.3&67.9 & 71.3&66.8 \\ HyperSAGE $(p = 2)$ & 76.1 &70.2 &71.2 &69.8 & 65.9 & 63.8 &65.9 &64.5 \\ \bottomrule \end{tabular}