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fuck latex seriously

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@book{em:86,
editor = "Engelmore, Robert and Morgan, Anthony",
title = "Blackboard Systems",
year = 1986,
address = "Reading, Mass.",
publisher = "Addison-Wesley",
}
@inproceedings{c:83,
author = "Clancey, William J.",
year = 1983,
title = "{Communication, Simulation, and Intelligent
Agents: Implications of Personal Intelligent Machines
for Medical Education}",
booktitle="Proceedings of the Eighth International Joint Conference on Artificial Intelligence {(IJCAI-83)}",
pages = "556-560",
address = "Menlo Park, Calif",
publisher = "{IJCAI Organization}",
}
@inproceedings{c:84,
author = "Clancey, William J.",
year = 1984,
title = "{Classification Problem Solving}",
booktitle = "Proceedings of the Fourth National
Conference on Artificial Intelligence",
pages = "45-54",
address = "Menlo Park, Calif.",
publisher="AAAI Press",
}
@article{r:80,
author = {Robinson, Arthur L.},
title = {New Ways to Make Microcircuits Smaller},
volume = {208},
number = {4447},
pages = {1019--1022},
year = {1980},
doi = {10.1126/science.208.4447.1019},
publisher = {American Association for the Advancement of Science},
issn = {0036-8075},
URL = {https://science.sciencemag.org/content/208/4447/1019},
eprint = {https://science.sciencemag.org/content/208/4447/1019.full.pdf},
journal = {Science},
}
@article{r:80x,
author = "Robinson, Arthur L.",
year = 1980,
title = "{New Ways to Make Microcircuits Smaller---Duplicate Entry}",
journal = "Science",
volume = 208,
pages = "1019-1026",
}
@article{hcr:83,
title = {Strategic explanations for a diagnostic consultation system},
journal = {International Journal of Man-Machine Studies},
volume = {20},
number = {1},
pages = {3-19},
year = {1984},
issn = {0020-7373},
doi = {https://doi.org/10.1016/S0020-7373(84)80003-6},
url = {https://www.sciencedirect.com/science/article/pii/S0020737384800036},
author = {Diane Warner Hasling and William J. Clancey and Glenn Rennels},
abstract = {This article examines the problem of automatte explanation of reasoning, especially as it relates to expert systems. By explanation we mean the ability of a program to discuss what it is doing in some understandable way. We first present a general framework in which to view explanation and review some of the research done in this area. We then focus on the explanation system for NEOMYCIN, a medical consultation program. A consultation program interactively helps a user to solve a problem. Our goal is to have NEOMYCIN explain its problem-solving strategies. An explanation of strategy describes the plan the program is using to reach a solution. Such an explanation is usually concrete, referring to aspects of the current problem situation. Abstract explanations articulate a general principle, which can be applied in different situations; such explanations are useful in teaching and in explaining by analogy. We describe the aspects of NEOMYCIN that make abstract strategic explanations possible—the representation of strategic knowledge explicitly and separately from domain knowledge— and demonstrate how this representation can be used to generate explanations.}
}
@article{hcrt:83,
author = "Hasling, Diane Warner and Clancey, William J. and Rennels, Glenn R. and Test, Thomas",
year = 1983,
title = "{Strategic Explanations in Consultation---Duplicate}",
journal = "The International Journal of Man-Machine Studies",
volume = 20,
number = 1,
pages = "3-19",
}
@techreport{r:86,
author = "Rice, James",
year = 1986,
title = "{Poligon: A System for Parallel Problem Solving}",
type = "Technical Report",
number = "KSL-86-19",
institution = "Dept.\ of Computer Science, Stanford Univ.",
}
@phdthesis{c:79,
author = "Clancey, William J.",
year = 1979,
title = "{Transfer of Rule-Based Expertise
through a Tutorial Dialogue}",
type = "{Ph.D.} diss.",
school = "Dept.\ of Computer Science, Stanford Univ.",
address = "Stanford, Calif.",
}
@unpublished{c:21,
author = "Clancey, William J.",
title = "{The Engineering of Qualitative Models}",
year = 2021,
note = "Forthcoming",
}
@misc{c:22,
title={Attention Is All You Need},
author={Ashish Vaswani and Noam Shazeer and Niki Parmar and Jakob Uszkoreit and Llion Jones and Aidan N. Gomez and Lukasz Kaiser and Illia Polosukhin},
year={2017},
eprint={1706.03762},
archivePrefix={arXiv},
primaryClass={cs.CL}
}
@misc{c:23,
title = "Pluto: The 'Other' Red Planet",
author = "{NASA}",
howpublished = "\url{https://www.nasa.gov/nh/pluto-the-other-red-planet}",
year = 2015,
note = "Accessed: 2018-12-06"
}
\ No newline at end of file
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\begin{table}
\caption{Results for real-world datasets: sample averages +/- one standard deviation across counterfactuals. Best outcomes are highlighted in bold. Asterisks indicate that the given value is more than one (*) or two (**) standard deviations away from the baseline (Wachter). \label{tab:results-real-world} \newline}
\centering
\resizebox{\linewidth}{!}{
\begin{tabular}[t]{llcccc}
\toprule
\multicolumn{2}{c}{ } & \multicolumn{2}{c}{MNIST} & \multicolumn{2}{c}{GMSC} \\
\cmidrule(l{3pt}r{3pt}){3-4} \cmidrule(l{3pt}r{3pt}){5-6}
Model & Generator & Unfaithfulness ↓ & Implausibility ↓ & Unfaithfulness ↓ & Implausibility ↓\\
\midrule
& ECCCo & \textbf{19.28 ± 5.01}** & 314.76 ± 32.36*\hphantom{*} & \textbf{79.16 ± 11.67}** & 18.26 ± 4.92**\\
& REVISE & 188.70 ± 26.18*\hphantom{*} & \textbf{255.26 ± 41.50}** & 186.40 ± 28.06\hphantom{*}\hphantom{*} & \textbf{5.34 ± 2.38}**\\
& Schut & 211.62 ± 27.13\hphantom{*}\hphantom{*} & 290.56 ± 40.66*\hphantom{*} & 200.98 ± 28.49\hphantom{*}\hphantom{*} & 6.50 ± 2.01**\\
\multirow{-4}{*}{\raggedright\arraybackslash JEM} & Wachter & 222.90 ± 26.56\hphantom{*}\hphantom{*} & 361.88 ± 39.74\hphantom{*}\hphantom{*} & 214.08 ± 45.35\hphantom{*}\hphantom{*} & 61.04 ± 2.58\hphantom{*}\hphantom{*}\\
\cmidrule{1-6}
& ECCCo & \textbf{15.99 ± 3.06}** & 294.72 ± 30.75** & \textbf{83.28 ± 13.26}** & 17.21 ± 4.46**\\
& REVISE & 173.59 ± 20.65** & \textbf{246.32 ± 37.46}** & 194.24 ± 35.41\hphantom{*}\hphantom{*} & \textbf{4.95 ± 1.26}**\\
& Schut & 204.36 ± 23.14\hphantom{*}\hphantom{*} & 290.64 ± 39.49*\hphantom{*} & 208.45 ± 34.60\hphantom{*}\hphantom{*} & 6.12 ± 1.91**\\
\multirow{-4}{*}{\raggedright\arraybackslash JEM Ensemble} & Wachter & 217.67 ± 23.78\hphantom{*}\hphantom{*} & 363.23 ± 39.24\hphantom{*}\hphantom{*} & 186.19 ± 33.88\hphantom{*}\hphantom{*} & 60.70 ± 44.32\hphantom{*}\hphantom{*}\\
\cmidrule{1-6}
& ECCCo & \textbf{41.95 ± 6.50}** & 591.58 ± 36.24\hphantom{*}\hphantom{*} & \textbf{75.93 ± 14.27}** & 17.20 ± 3.15**\\
& REVISE & 365.82 ± 15.35*\hphantom{*} & \textbf{249.49 ± 41.55}** & 196.75 ± 41.25\hphantom{*}\hphantom{*} & \textbf{4.84 ± 0.60}**\\
& Schut & 379.66 ± 17.16\hphantom{*}\hphantom{*} & 290.07 ± 42.65*\hphantom{*} & 212.00 ± 41.15\hphantom{*}\hphantom{*} & 6.44 ± 1.34**\\
\multirow{-4}{*}{\raggedright\arraybackslash MLP} & Wachter & 386.05 ± 16.60\hphantom{*}\hphantom{*} & 361.83 ± 42.18\hphantom{*}\hphantom{*} & 218.34 ± 53.26\hphantom{*}\hphantom{*} & 45.84 ± 39.39\hphantom{*}\hphantom{*}\\
\cmidrule{1-6}
& ECCCo & \textbf{31.43 ± 3.91}** & 490.88 ± 27.19\hphantom{*}\hphantom{*} & \textbf{73.86 ± 14.63}** & 17.92 ± 4.17**\\
& REVISE & 337.74 ± 11.89*\hphantom{*} & \textbf{247.67 ± 38.36}** & 207.21 ± 43.20\hphantom{*}\hphantom{*} & \textbf{5.78 ± 2.10}**\\
& Schut & 354.80 ± 13.05\hphantom{*}\hphantom{*} & 285.79 ± 41.33*\hphantom{*} & 205.36 ± 32.11\hphantom{*}\hphantom{*} & 7.00 ± 2.15**\\
\multirow{-4}{*}{\raggedright\arraybackslash MLP Ensemble} & Wachter & 360.79 ± 14.39\hphantom{*}\hphantom{*} & 357.73 ± 42.55\hphantom{*}\hphantom{*} & 213.71 ± 54.17\hphantom{*}\hphantom{*} & 73.09 ± 64.50\hphantom{*}\hphantom{*}\\
\bottomrule
\end{tabular}}
\end{table}
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\begin{table}
\caption{Results for synthetic datasets: sample averages +/- one standard deviation across counterfactuals. Best outcomes are highlighted in bold. Asterisks indicate that the given value is more than one (*) or two (**) standard deviations away from the baseline (Wachter). \label{tab:results-synthetic} \newline}
\centering
\resizebox{\linewidth}{!}{
\begin{tabular}[t]{llcccccc}
\toprule
\multicolumn{2}{c}{ } & \multicolumn{2}{c}{Linearly Separable} & \multicolumn{2}{c}{Moons} & \multicolumn{2}{c}{Circles} \\
\cmidrule(l{3pt}r{3pt}){3-4} \cmidrule(l{3pt}r{3pt}){5-6} \cmidrule(l{3pt}r{3pt}){7-8}
Model & Generator & Unfaithfulness ↓ & Implausibility ↓ & Unfaithfulness ↓ & Implausibility ↓ & Unfaithfulness ↓ & Implausibility ↓\\
\midrule
& ECCCo & \textbf{0.03 ± 0.06}** & \textbf{0.20 ± 0.08}** & \textbf{0.31 ± 0.30}*\hphantom{*} & \textbf{1.20 ± 0.15}** & 0.52 ± 0.36\hphantom{*}\hphantom{*} & 1.22 ± 0.46\hphantom{*}\hphantom{*}\\
& ECCCo (no CP) & 0.03 ± 0.06** & 0.20 ± 0.08** & 0.37 ± 0.30*\hphantom{*} & 1.21 ± 0.17** & 0.54 ± 0.39\hphantom{*}\hphantom{*} & 1.21 ± 0.46\hphantom{*}\hphantom{*}\\
& ECCCo (no EBM) & 0.16 ± 0.11\hphantom{*}\hphantom{*} & 0.34 ± 0.19\hphantom{*}\hphantom{*} & 0.91 ± 0.32\hphantom{*}\hphantom{*} & 1.71 ± 0.25\hphantom{*}\hphantom{*} & 0.70 ± 0.33\hphantom{*}\hphantom{*} & 1.30 ± 0.37\hphantom{*}\hphantom{*}\\
& REVISE & 0.19 ± 0.03\hphantom{*}\hphantom{*} & 0.41 ± 0.01** & 0.78 ± 0.23\hphantom{*}\hphantom{*} & 1.57 ± 0.26\hphantom{*}\hphantom{*} & \textbf{0.48 ± 0.16}*\hphantom{*} & \textbf{0.95 ± 0.32}*\hphantom{*}\\
& Schut & 0.39 ± 0.07\hphantom{*}\hphantom{*} & 0.73 ± 0.17\hphantom{*}\hphantom{*} & 0.67 ± 0.27\hphantom{*}\hphantom{*} & 1.50 ± 0.22*\hphantom{*} & 0.54 ± 0.43\hphantom{*}\hphantom{*} & 1.28 ± 0.53\hphantom{*}\hphantom{*}\\
\multirow{-6}{*}{\raggedright\arraybackslash JEM} & Wachter & 0.18 ± 0.10\hphantom{*}\hphantom{*} & 0.44 ± 0.17\hphantom{*}\hphantom{*} & 0.80 ± 0.27\hphantom{*}\hphantom{*} & 1.78 ± 0.24\hphantom{*}\hphantom{*} & 0.68 ± 0.34\hphantom{*}\hphantom{*} & 1.33 ± 0.32\hphantom{*}\hphantom{*}\\
\cmidrule{1-8}
& ECCCo & \textbf{0.29 ± 0.05}** & 0.23 ± 0.06** & 0.80 ± 0.62\hphantom{*}\hphantom{*} & 1.69 ± 0.40\hphantom{*}\hphantom{*} & 0.65 ± 0.53\hphantom{*}\hphantom{*} & 1.17 ± 0.41\hphantom{*}\hphantom{*}\\
& ECCCo (no CP) & 0.29 ± 0.05** & \textbf{0.23 ± 0.07}** & \textbf{0.79 ± 0.62}\hphantom{*}\hphantom{*} & 1.68 ± 0.42\hphantom{*}\hphantom{*} & \textbf{0.49 ± 0.35}\hphantom{*}\hphantom{*} & 1.19 ± 0.44\hphantom{*}\hphantom{*}\\
& ECCCo (no EBM) & 0.46 ± 0.05\hphantom{*}\hphantom{*} & 0.28 ± 0.04** & 1.34 ± 0.47\hphantom{*}\hphantom{*} & 1.68 ± 0.47\hphantom{*}\hphantom{*} & 0.84 ± 0.51\hphantom{*}\hphantom{*} & 1.23 ± 0.31\hphantom{*}\hphantom{*}\\
& REVISE & 0.56 ± 0.05\hphantom{*}\hphantom{*} & 0.41 ± 0.01\hphantom{*}\hphantom{*} & 1.45 ± 0.44\hphantom{*}\hphantom{*} & \textbf{1.64 ± 0.31}\hphantom{*}\hphantom{*} & 0.58 ± 0.52\hphantom{*}\hphantom{*} & \textbf{0.95 ± 0.32}\hphantom{*}\hphantom{*}\\
& Schut & 0.43 ± 0.06*\hphantom{*} & 0.47 ± 0.36\hphantom{*}\hphantom{*} & 1.45 ± 0.55\hphantom{*}\hphantom{*} & 1.73 ± 0.48\hphantom{*}\hphantom{*} & 0.58 ± 0.37\hphantom{*}\hphantom{*} & 1.23 ± 0.43\hphantom{*}\hphantom{*}\\
\multirow{-6}{*}{\raggedright\arraybackslash MLP} & Wachter & 0.51 ± 0.04\hphantom{*}\hphantom{*} & 0.40 ± 0.08\hphantom{*}\hphantom{*} & 1.32 ± 0.41\hphantom{*}\hphantom{*} & 1.69 ± 0.32\hphantom{*}\hphantom{*} & 0.83 ± 0.50\hphantom{*}\hphantom{*} & 1.24 ± 0.29\hphantom{*}\hphantom{*}\\
\bottomrule
\end{tabular}}
\end{table}
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\begin{table}
\caption{All results for all datasets: sample averages +/- one standard deviation over all counterfactuals. Best outcomes are highlighted in bold. Asterisks indicate that the given value is more than one (*) or two (**) standard deviations away from the baseline (Wachter). \label{tab:results-full} \newline}
\centering
\resizebox{\linewidth}{!}{
\begin{tabular}[t]{ccccccccc}
\toprule
Model & Data & Generator & Cost ↓ & Unfaithfulness ↓ & Implausibility ↓ & Redundancy ↑ & Uncertainty ↓ & Validity ↑\\
\midrule
& & ECCCo & 0.74 ± 0.21\hphantom{*}\hphantom{*} & 0.52 ± 0.36\hphantom{*}\hphantom{*} & 1.22 ± 0.46\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & \textbf{1.00 ± 0.00}**\\
& & ECCCo (no CP) & 0.72 ± 0.21\hphantom{*}\hphantom{*} & 0.54 ± 0.39\hphantom{*}\hphantom{*} & 1.21 ± 0.46\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & \textbf{1.00 ± 0.00}**\\
& & ECCCo (no EBM) & 0.52 ± 0.15\hphantom{*}\hphantom{*} & 0.70 ± 0.33\hphantom{*}\hphantom{*} & 1.30 ± 0.37\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & \textbf{1.00 ± 0.00}**\\
& & REVISE & 0.97 ± 0.34\hphantom{*}\hphantom{*} & \textbf{0.48 ± 0.16}*\hphantom{*} & \textbf{0.95 ± 0.32}*\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.50 ± 0.51\hphantom{*}\hphantom{*}\\
& & Schut & 1.06 ± 0.43\hphantom{*}\hphantom{*} & 0.54 ± 0.43\hphantom{*}\hphantom{*} & 1.28 ± 0.53\hphantom{*}\hphantom{*} & \textbf{0.26 ± 0.25}*\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & \textbf{1.00 ± 0.00}**\\
& \multirow[t]{-6}{*}{\centering\arraybackslash JEM} & Wachter & \textbf{0.44 ± 0.16}\hphantom{*}\hphantom{*} & 0.68 ± 0.34\hphantom{*}\hphantom{*} & 1.33 ± 0.32\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.98 ± 0.14\hphantom{*}\hphantom{*}\\
\cmidrule{2-9}
& & ECCCo & 0.67 ± 0.19\hphantom{*}\hphantom{*} & 0.65 ± 0.53\hphantom{*}\hphantom{*} & 1.17 ± 0.41\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.09 ± 0.19** & \textbf{1.00 ± 0.00}\hphantom{*}\hphantom{*}\\
& & ECCCo (no CP) & 0.71 ± 0.16\hphantom{*}\hphantom{*} & \textbf{0.49 ± 0.35}\hphantom{*}\hphantom{*} & 1.19 ± 0.44\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.05 ± 0.16** & \textbf{1.00 ± 0.00}\hphantom{*}\hphantom{*}\\
& & ECCCo (no EBM) & 0.45 ± 0.11\hphantom{*}\hphantom{*} & 0.84 ± 0.51\hphantom{*}\hphantom{*} & 1.23 ± 0.31\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.15 ± 0.23*\hphantom{*} & \textbf{1.00 ± 0.00}\hphantom{*}\hphantom{*}\\
& & REVISE & 0.96 ± 0.31\hphantom{*}\hphantom{*} & 0.58 ± 0.52\hphantom{*}\hphantom{*} & \textbf{0.95 ± 0.32}\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & \textbf{0.00 ± 0.00}** & 0.50 ± 0.51\hphantom{*}\hphantom{*}\\
& & Schut & 0.57 ± 0.11\hphantom{*}\hphantom{*} & 0.58 ± 0.37\hphantom{*}\hphantom{*} & 1.23 ± 0.43\hphantom{*}\hphantom{*} & \textbf{0.43 ± 0.18}** & \textbf{0.00 ± 0.00}** & \textbf{1.00 ± 0.00}\hphantom{*}\hphantom{*}\\
\multirow[t]{-12}{*}{\centering\arraybackslash Circles} & \multirow[t]{-6}{*}{\centering\arraybackslash MLP} & Wachter & \textbf{0.40 ± 0.09}\hphantom{*}\hphantom{*} & 0.83 ± 0.50\hphantom{*}\hphantom{*} & 1.24 ± 0.29\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.53 ± 0.01\hphantom{*}\hphantom{*} & \textbf{1.00 ± 0.00}\hphantom{*}\hphantom{*}\\
\cmidrule{1-9}
& & ECCCo & 17.45 ± 2.92** & \textbf{79.16 ± 11.67}** & 18.26 ± 4.92** & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.10 ± 0.01\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& & REVISE & 3.43 ± 1.67** & 186.40 ± 28.06\hphantom{*}\hphantom{*} & \textbf{5.34 ± 2.38}** & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.51 ± 0.22\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& & Schut & \textbf{1.27 ± 0.33}** & 200.98 ± 28.49\hphantom{*}\hphantom{*} & 6.50 ± 2.01** & \textbf{0.77 ± 0.07}** & 0.07 ± 0.00\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& \multirow[t]{-4}{*}{\centering\arraybackslash JEM} & Wachter & 57.71 ± 0.47\hphantom{*}\hphantom{*} & 214.08 ± 45.35\hphantom{*}\hphantom{*} & 61.04 ± 2.58\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & \textbf{0.07 ± 0.00}\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
\cmidrule{2-9}
& & ECCCo & 17.43 ± 3.04** & \textbf{83.28 ± 13.26}** & 17.21 ± 4.46** & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.16 ± 0.11\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& & REVISE & 2.94 ± 1.13** & 194.24 ± 35.41\hphantom{*}\hphantom{*} & \textbf{4.95 ± 1.26}** & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.51 ± 0.29\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& & Schut & \textbf{1.03 ± 0.20}** & 208.45 ± 34.60\hphantom{*}\hphantom{*} & 6.12 ± 1.91** & \textbf{0.85 ± 0.05}** & 0.09 ± 0.04\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& \multirow[t]{-4}{*}{\centering\arraybackslash JEM Ensemble} & Wachter & 56.79 ± 44.68\hphantom{*}\hphantom{*} & 186.19 ± 33.88\hphantom{*}\hphantom{*} & 60.70 ± 44.32\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & \textbf{0.07 ± 0.00}\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
\cmidrule{2-9}
& & ECCCo & 17.05 ± 2.87** & \textbf{75.93 ± 14.27}** & 17.20 ± 3.15** & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.19 ± 0.08\hphantom{*}\hphantom{*} & \textbf{1.00 ± 0.00}**\\
& & REVISE & 2.93 ± 1.24** & 196.75 ± 41.25\hphantom{*}\hphantom{*} & \textbf{4.84 ± 0.60}** & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.38 ± 0.18\hphantom{*}\hphantom{*} & \textbf{1.00 ± 0.00}**\\
& & Schut & \textbf{1.49 ± 0.87}** & 212.00 ± 41.15\hphantom{*}\hphantom{*} & 6.44 ± 1.34** & \textbf{0.77 ± 0.13}** & 0.12 ± 0.01\hphantom{*}\hphantom{*} & \textbf{1.00 ± 0.00}**\\
& \multirow[t]{-4}{*}{\centering\arraybackslash MLP} & Wachter & 42.97 ± 39.50\hphantom{*}\hphantom{*} & 218.34 ± 53.26\hphantom{*}\hphantom{*} & 45.84 ± 39.39\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & \textbf{0.06 ± 0.06}\hphantom{*}\hphantom{*} & 0.50 ± 0.51\hphantom{*}\hphantom{*}\\
\cmidrule{2-9}
& & ECCCo & 16.63 ± 2.62** & \textbf{73.86 ± 14.63}** & 17.92 ± 4.17** & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.23 ± 0.07\hphantom{*}\hphantom{*} & \textbf{1.00 ± 0.00}**\\
& & REVISE & 3.73 ± 2.36** & 207.21 ± 43.20\hphantom{*}\hphantom{*} & \textbf{5.78 ± 2.10}** & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.33 ± 0.19\hphantom{*}\hphantom{*} & \textbf{1.00 ± 0.00}**\\
& & Schut & \textbf{1.20 ± 0.47}** & 205.36 ± 32.11\hphantom{*}\hphantom{*} & 7.00 ± 2.15** & \textbf{0.79 ± 0.09}** & 0.12 ± 0.01\hphantom{*}\hphantom{*} & \textbf{1.00 ± 0.00}**\\
\multirow[t]{-16}{*}{\centering\arraybackslash GMSC} & \multirow[t]{-4}{*}{\centering\arraybackslash MLP Ensemble} & Wachter & 69.30 ± 66.00\hphantom{*}\hphantom{*} & 213.71 ± 54.17\hphantom{*}\hphantom{*} & 73.09 ± 64.50\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & \textbf{0.06 ± 0.06}\hphantom{*}\hphantom{*} & 0.50 ± 0.51\hphantom{*}\hphantom{*}\\
\cmidrule{1-9}
& & ECCCo & 0.75 ± 0.17\hphantom{*}\hphantom{*} & \textbf{0.03 ± 0.06}** & \textbf{0.20 ± 0.08}** & 0.00 ± 0.00\hphantom{*}\hphantom{*} & \textbf{0.00 ± 0.00}\hphantom{*}\hphantom{*} & \textbf{1.00 ± 0.00}\hphantom{*}\hphantom{*}\\
& & ECCCo (no CP) & 0.75 ± 0.17\hphantom{*}\hphantom{*} & 0.03 ± 0.06** & 0.20 ± 0.08** & 0.00 ± 0.00\hphantom{*}\hphantom{*} & \textbf{0.00 ± 0.00}\hphantom{*}\hphantom{*} & \textbf{1.00 ± 0.00}\hphantom{*}\hphantom{*}\\
& & ECCCo (no EBM) & 0.70 ± 0.16\hphantom{*}\hphantom{*} & 0.16 ± 0.11\hphantom{*}\hphantom{*} & 0.34 ± 0.19\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & \textbf{0.00 ± 0.00}\hphantom{*}\hphantom{*} & \textbf{1.00 ± 0.00}\hphantom{*}\hphantom{*}\\
& & REVISE & \textbf{0.41 ± 0.15}\hphantom{*}\hphantom{*} & 0.19 ± 0.03\hphantom{*}\hphantom{*} & 0.41 ± 0.01** & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.36 ± 0.36\hphantom{*}\hphantom{*} & 0.50 ± 0.51\hphantom{*}\hphantom{*}\\
& & Schut & 1.15 ± 0.35\hphantom{*}\hphantom{*} & 0.39 ± 0.07\hphantom{*}\hphantom{*} & 0.73 ± 0.17\hphantom{*}\hphantom{*} & \textbf{0.25 ± 0.25}\hphantom{*}\hphantom{*} & \textbf{0.00 ± 0.00}\hphantom{*}\hphantom{*} & \textbf{1.00 ± 0.00}\hphantom{*}\hphantom{*}\\
& \multirow[t]{-6}{*}{\centering\arraybackslash JEM} & Wachter & 0.50 ± 0.13\hphantom{*}\hphantom{*} & 0.18 ± 0.10\hphantom{*}\hphantom{*} & 0.44 ± 0.17\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & \textbf{0.00 ± 0.00}\hphantom{*}\hphantom{*} & \textbf{1.00 ± 0.00}\hphantom{*}\hphantom{*}\\
\cmidrule{2-9}
& & ECCCo & 0.95 ± 0.16\hphantom{*}\hphantom{*} & \textbf{0.29 ± 0.05}** & 0.23 ± 0.06** & 0.00 ± 0.00\hphantom{*}\hphantom{*} & \textbf{0.00 ± 0.00}** & \textbf{1.00 ± 0.00}\hphantom{*}\hphantom{*}\\
& & ECCCo (no CP) & 0.94 ± 0.16\hphantom{*}\hphantom{*} & 0.29 ± 0.05** & \textbf{0.23 ± 0.07}** & 0.00 ± 0.00\hphantom{*}\hphantom{*} & \textbf{0.00 ± 0.00}** & \textbf{1.00 ± 0.00}\hphantom{*}\hphantom{*}\\
& & ECCCo (no EBM) & 0.60 ± 0.15\hphantom{*}\hphantom{*} & 0.46 ± 0.05\hphantom{*}\hphantom{*} & 0.28 ± 0.04** & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.02 ± 0.10** & \textbf{1.00 ± 0.00}\hphantom{*}\hphantom{*}\\
& & REVISE & \textbf{0.42 ± 0.14}\hphantom{*}\hphantom{*} & 0.56 ± 0.05\hphantom{*}\hphantom{*} & 0.41 ± 0.01\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.47 ± 0.50\hphantom{*}\hphantom{*} & 0.48 ± 0.50\hphantom{*}\hphantom{*}\\
& & Schut & 0.77 ± 0.17\hphantom{*}\hphantom{*} & 0.43 ± 0.06*\hphantom{*} & 0.47 ± 0.36\hphantom{*}\hphantom{*} & \textbf{0.20 ± 0.25}\hphantom{*}\hphantom{*} & \textbf{0.00 ± 0.00}** & \textbf{1.00 ± 0.00}\hphantom{*}\hphantom{*}\\
\multirow[t]{-12}{*}{\centering\arraybackslash Linearly Separable} & \multirow[t]{-6}{*}{\centering\arraybackslash MLP} & Wachter & 0.51 ± 0.15\hphantom{*}\hphantom{*} & 0.51 ± 0.04\hphantom{*}\hphantom{*} & 0.40 ± 0.08\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.59 ± 0.02\hphantom{*}\hphantom{*} & \textbf{1.00 ± 0.00}\hphantom{*}\hphantom{*}\\
\cmidrule{1-9}
& & ECCCo & 334.61 ± 46.37\hphantom{*}\hphantom{*} & \textbf{19.28 ± 5.01}** & 314.76 ± 32.36*\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 4.43 ± 0.56\hphantom{*}\hphantom{*} & \textbf{0.98 ± 0.12}\hphantom{*}\hphantom{*}\\
& & REVISE & 170.68 ± 63.26\hphantom{*}\hphantom{*} & 188.70 ± 26.18*\hphantom{*} & \textbf{255.26 ± 41.50}** & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 4.39 ± 0.91\hphantom{*}\hphantom{*} & 0.96 ± 0.20\hphantom{*}\hphantom{*}\\
& & Schut & \textbf{9.44 ± 1.60}** & 211.00 ± 27.21\hphantom{*}\hphantom{*} & 286.61 ± 39.85*\hphantom{*} & \textbf{0.99 ± 0.00}** & \textbf{1.08 ± 1.95}*\hphantom{*} & 0.24 ± 0.43\hphantom{*}\hphantom{*}\\
& \multirow[t]{-4}{*}{\centering\arraybackslash JEM} & Wachter & 128.36 ± 14.95\hphantom{*}\hphantom{*} & 222.90 ± 26.56\hphantom{*}\hphantom{*} & 361.88 ± 39.74\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 4.37 ± 0.98\hphantom{*}\hphantom{*} & 0.95 ± 0.21\hphantom{*}\hphantom{*}\\
\cmidrule{2-9}
& & ECCCo & 342.64 ± 41.14\hphantom{*}\hphantom{*} & \textbf{15.99 ± 3.06}** & 294.72 ± 30.75** & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 2.07 ± 0.06** & \textbf{1.00 ± 0.00}**\\
& & REVISE & 170.21 ± 58.02\hphantom{*}\hphantom{*} & 173.59 ± 20.65** & \textbf{246.32 ± 37.46}** & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 2.56 ± 0.83\hphantom{*}\hphantom{*} & 0.93 ± 0.26\hphantom{*}\hphantom{*}\\
& & Schut & \textbf{9.78 ± 1.02}** & 205.33 ± 24.07\hphantom{*}\hphantom{*} & 287.39 ± 39.33*\hphantom{*} & \textbf{0.99 ± 0.00}** & \textbf{0.32 ± 0.94}** & 0.11 ± 0.31\hphantom{*}\hphantom{*}\\
& \multirow[t]{-4}{*}{\centering\arraybackslash JEM Ensemble} & Wachter & 135.07 ± 16.79\hphantom{*}\hphantom{*} & 217.67 ± 23.78\hphantom{*}\hphantom{*} & 363.23 ± 39.24\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 2.93 ± 0.77\hphantom{*}\hphantom{*} & 0.94 ± 0.23\hphantom{*}\hphantom{*}\\
\cmidrule{2-9}
& & ECCCo & 605.17 ± 44.78\hphantom{*}\hphantom{*} & \textbf{41.95 ± 6.50}** & 591.58 ± 36.24\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.57 ± 0.00** & \textbf{1.00 ± 0.00}**\\
& & REVISE & 146.61 ± 36.96\hphantom{*}\hphantom{*} & 365.82 ± 15.35*\hphantom{*} & \textbf{249.49 ± 41.55}** & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.62 ± 0.30\hphantom{*}\hphantom{*} & 0.87 ± 0.34\hphantom{*}\hphantom{*}\\
& & Schut & \textbf{9.95 ± 0.37}** & 382.44 ± 17.81\hphantom{*}\hphantom{*} & 285.98 ± 42.48*\hphantom{*} & \textbf{0.99 ± 0.00}** & \textbf{0.05 ± 0.19}** & 0.06 ± 0.24\hphantom{*}\hphantom{*}\\
& \multirow[t]{-4}{*}{\centering\arraybackslash MLP} & Wachter & 136.08 ± 16.09\hphantom{*}\hphantom{*} & 386.05 ± 16.60\hphantom{*}\hphantom{*} & 361.83 ± 42.18\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.68 ± 0.36\hphantom{*}\hphantom{*} & 0.84 ± 0.36\hphantom{*}\hphantom{*}\\
\cmidrule{2-9}
& & ECCCo & 525.87 ± 34.00\hphantom{*}\hphantom{*} & \textbf{31.43 ± 3.91}** & 490.88 ± 27.19\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.29 ± 0.00** & \textbf{1.00 ± 0.00}**\\
& & REVISE & 146.60 ± 35.64\hphantom{*}\hphantom{*} & 337.74 ± 11.89*\hphantom{*} & \textbf{247.67 ± 38.36}** & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.39 ± 0.22\hphantom{*}\hphantom{*} & 0.85 ± 0.36\hphantom{*}\hphantom{*}\\
& & Schut & \textbf{9.98 ± 0.25}** & 359.54 ± 14.52\hphantom{*}\hphantom{*} & 283.99 ± 41.08*\hphantom{*} & \textbf{0.99 ± 0.00}** & \textbf{0.03 ± 0.14}** & 0.06 ± 0.24\hphantom{*}\hphantom{*}\\
\multirow[t]{-16}{*}{\centering\arraybackslash MNIST} & \multirow[t]{-4}{*}{\centering\arraybackslash MLP Ensemble} & Wachter & 137.53 ± 18.95\hphantom{*}\hphantom{*} & 360.79 ± 14.39\hphantom{*}\hphantom{*} & 357.73 ± 42.55\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.47 ± 0.64\hphantom{*}\hphantom{*} & 0.80 ± 0.40\hphantom{*}\hphantom{*}\\
\cmidrule{1-9}
& & ECCCo & 1.56 ± 0.44\hphantom{*}\hphantom{*} & \textbf{0.31 ± 0.30}*\hphantom{*} & \textbf{1.20 ± 0.15}** & 0.00 ± 0.00\hphantom{*}\hphantom{*} & \textbf{0.00 ± 0.00}** & \textbf{1.00 ± 0.00}**\\
& & ECCCo (no CP) & 1.56 ± 0.46\hphantom{*}\hphantom{*} & 0.37 ± 0.30*\hphantom{*} & 1.21 ± 0.17** & 0.00 ± 0.00\hphantom{*}\hphantom{*} & \textbf{0.00 ± 0.00}** & \textbf{1.00 ± 0.00}**\\
& & ECCCo (no EBM) & 0.80 ± 0.25\hphantom{*}\hphantom{*} & 0.91 ± 0.32\hphantom{*}\hphantom{*} & 1.71 ± 0.25\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & \textbf{0.00 ± 0.00}** & \textbf{1.00 ± 0.00}**\\
& & REVISE & 1.04 ± 0.43\hphantom{*}\hphantom{*} & 0.78 ± 0.23\hphantom{*}\hphantom{*} & 1.57 ± 0.26\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & \textbf{0.00 ± 0.00}** & \textbf{1.00 ± 0.00}**\\
& & Schut & 1.12 ± 0.31\hphantom{*}\hphantom{*} & 0.67 ± 0.27\hphantom{*}\hphantom{*} & 1.50 ± 0.22*\hphantom{*} & \textbf{0.08 ± 0.19}\hphantom{*}\hphantom{*} & \textbf{0.00 ± 0.00}** & 0.98 ± 0.14\hphantom{*}\hphantom{*}\\
& \multirow[t]{-6}{*}{\centering\arraybackslash JEM} & Wachter & \textbf{0.72 ± 0.24}\hphantom{*}\hphantom{*} & 0.80 ± 0.27\hphantom{*}\hphantom{*} & 1.78 ± 0.24\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.02 ± 0.10\hphantom{*}\hphantom{*} & 0.98 ± 0.14\hphantom{*}\hphantom{*}\\
\cmidrule{2-9}
& & ECCCo & 2.18 ± 1.05\hphantom{*}\hphantom{*} & 0.80 ± 0.62\hphantom{*}\hphantom{*} & 1.69 ± 0.40\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.15 ± 0.24*\hphantom{*} & \textbf{1.00 ± 0.00}\hphantom{*}\hphantom{*}\\
& & ECCCo (no CP) & 2.07 ± 1.15\hphantom{*}\hphantom{*} & \textbf{0.79 ± 0.62}\hphantom{*}\hphantom{*} & 1.68 ± 0.42\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.15 ± 0.24*\hphantom{*} & \textbf{1.00 ± 0.00}\hphantom{*}\hphantom{*}\\
& & ECCCo (no EBM) & 1.25 ± 0.92\hphantom{*}\hphantom{*} & 1.34 ± 0.47\hphantom{*}\hphantom{*} & 1.68 ± 0.47\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.43 ± 0.18\hphantom{*}\hphantom{*} & \textbf{1.00 ± 0.00}\hphantom{*}\hphantom{*}\\
& & REVISE & 0.79 ± 0.19*\hphantom{*} & 1.45 ± 0.44\hphantom{*}\hphantom{*} & \textbf{1.64 ± 0.31}\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.40 ± 0.22\hphantom{*}\hphantom{*} & \textbf{1.00 ± 0.00}\hphantom{*}\hphantom{*}\\
& & Schut & \textbf{0.73 ± 0.25}*\hphantom{*} & 1.45 ± 0.55\hphantom{*}\hphantom{*} & 1.73 ± 0.48\hphantom{*}\hphantom{*} & \textbf{0.31 ± 0.28}*\hphantom{*} & \textbf{0.00 ± 0.00}** & 0.90 ± 0.30\hphantom{*}\hphantom{*}\\
\multirow[t]{-12}{*}{\centering\arraybackslash Moons} & \multirow[t]{-6}{*}{\centering\arraybackslash MLP} & Wachter & 1.08 ± 0.83\hphantom{*}\hphantom{*} & 1.32 ± 0.41\hphantom{*}\hphantom{*} & 1.69 ± 0.32\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.52 ± 0.08\hphantom{*}\hphantom{*} & \textbf{1.00 ± 0.00}\hphantom{*}\hphantom{*}\\
\bottomrule
\end{tabular}}
\end{table}
AAAI/contents/table_all_valid.tex 0 → 100644
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\begin{table}
\caption{All results for all datasets: sample averages +/- one standard deviation over all valid counterfactuals. Best outcomes are highlighted in bold. Asterisks indicate that the given value is more than one (*) or two (**) standard deviations away from the baseline (Wachter). \label{tab:results-full-valid} \newline}
\centering
\resizebox{\linewidth}{!}{
\begin{tabular}[t]{ccccccccc}
\toprule
Model & Data & Generator & Cost ↓ & Unfaithfulness ↓ & Implausibility ↓ & Redundancy ↑ & Uncertainty ↓ & Validity ↑\\
\midrule
& & ECCCo & 0.74 ± 0.21\hphantom{*}\hphantom{*} & 0.52 ± 0.36\hphantom{*}\hphantom{*} & 1.22 ± 0.46\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& & ECCCo (no CP) & 0.72 ± 0.21\hphantom{*}\hphantom{*} & 0.54 ± 0.39\hphantom{*}\hphantom{*} & 1.21 ± 0.46\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& & ECCCo (no EBM) & 0.52 ± 0.15\hphantom{*}\hphantom{*} & 0.70 ± 0.33\hphantom{*}\hphantom{*} & 1.30 ± 0.37\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& & REVISE & 1.28 ± 0.14\hphantom{*}\hphantom{*} & \textbf{0.33 ± 0.01}** & \textbf{0.64 ± 0.00}** & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& & Schut & 1.06 ± 0.43\hphantom{*}\hphantom{*} & 0.54 ± 0.43\hphantom{*}\hphantom{*} & 1.28 ± 0.53\hphantom{*}\hphantom{*} & \textbf{0.26 ± 0.25}*\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& \multirow[t]{-6}{*}{\centering\arraybackslash JEM} & Wachter & \textbf{0.45 ± 0.15}\hphantom{*}\hphantom{*} & 0.68 ± 0.34\hphantom{*}\hphantom{*} & 1.33 ± 0.32\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
\cmidrule{2-9}
& & ECCCo & 0.67 ± 0.19\hphantom{*}\hphantom{*} & 0.65 ± 0.53\hphantom{*}\hphantom{*} & 1.17 ± 0.41\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.09 ± 0.19** & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& & ECCCo (no CP) & 0.71 ± 0.16\hphantom{*}\hphantom{*} & 0.49 ± 0.35\hphantom{*}\hphantom{*} & 1.19 ± 0.44\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.05 ± 0.16** & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& & ECCCo (no EBM) & 0.45 ± 0.11\hphantom{*}\hphantom{*} & 0.84 ± 0.51\hphantom{*}\hphantom{*} & 1.23 ± 0.31\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.15 ± 0.23*\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& & REVISE & 1.24 ± 0.15\hphantom{*}\hphantom{*} & \textbf{0.06 ± 0.01}** & \textbf{0.64 ± 0.00}** & 0.00 ± 0.00\hphantom{*}\hphantom{*} & \textbf{0.00 ± 0.00}** & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& & Schut & 0.57 ± 0.11\hphantom{*}\hphantom{*} & 0.58 ± 0.37\hphantom{*}\hphantom{*} & 1.23 ± 0.43\hphantom{*}\hphantom{*} & \textbf{0.43 ± 0.18}** & \textbf{0.00 ± 0.00}** & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
\multirow[t]{-12}{*}{\centering\arraybackslash Circles} & \multirow[t]{-6}{*}{\centering\arraybackslash MLP} & Wachter & \textbf{0.40 ± 0.09}\hphantom{*}\hphantom{*} & 0.83 ± 0.50\hphantom{*}\hphantom{*} & 1.24 ± 0.29\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.53 ± 0.01\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
\cmidrule{1-9}
& & ECCCo & 17.45 ± 2.92** & \textbf{79.16 ± 11.67}** & 18.26 ± 4.92** & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.10 ± 0.01\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& & REVISE & 3.43 ± 1.67** & 186.40 ± 28.06\hphantom{*}\hphantom{*} & \textbf{5.34 ± 2.38}** & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.51 ± 0.22\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& & Schut & \textbf{1.27 ± 0.33}** & 200.98 ± 28.49\hphantom{*}\hphantom{*} & 6.50 ± 2.01** & \textbf{0.77 ± 0.07}** & 0.07 ± 0.00\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& \multirow[t]{-4}{*}{\centering\arraybackslash JEM} & Wachter & 57.71 ± 0.47\hphantom{*}\hphantom{*} & 214.08 ± 45.35\hphantom{*}\hphantom{*} & 61.04 ± 2.58\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & \textbf{0.07 ± 0.00}\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
\cmidrule{2-9}
& & ECCCo & 17.43 ± 3.04** & \textbf{83.28 ± 13.26}** & 17.21 ± 4.46** & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.16 ± 0.11\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& & REVISE & 2.94 ± 1.13** & 194.24 ± 35.41\hphantom{*}\hphantom{*} & \textbf{4.95 ± 1.26}** & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.51 ± 0.29\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& & Schut & \textbf{1.03 ± 0.20}** & 208.45 ± 34.60\hphantom{*}\hphantom{*} & 6.12 ± 1.91** & \textbf{0.85 ± 0.05}** & 0.09 ± 0.04\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& \multirow[t]{-4}{*}{\centering\arraybackslash JEM Ensemble} & Wachter & 56.79 ± 44.68\hphantom{*}\hphantom{*} & 186.19 ± 33.88\hphantom{*}\hphantom{*} & 60.70 ± 44.32\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & \textbf{0.07 ± 0.00}\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
\cmidrule{2-9}
& & ECCCo & 17.05 ± 2.87\hphantom{*}\hphantom{*} & \textbf{75.93 ± 14.27}** & 17.20 ± 3.15\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.19 ± 0.08\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& & REVISE & 2.93 ± 1.24*\hphantom{*} & 196.75 ± 41.25\hphantom{*}\hphantom{*} & \textbf{4.84 ± 0.60}** & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.38 ± 0.18\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& & Schut & \textbf{1.49 ± 0.87}** & 212.00 ± 41.15\hphantom{*}\hphantom{*} & 6.44 ± 1.34\hphantom{*}\hphantom{*} & \textbf{0.77 ± 0.13}** & 0.12 ± 0.01\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& \multirow[t]{-4}{*}{\centering\arraybackslash MLP} & Wachter & 4.48 ± 0.18\hphantom{*}\hphantom{*} & 184.03 ± 48.16\hphantom{*}\hphantom{*} & 7.49 ± 0.89\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & \textbf{0.12 ± 0.00}\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
\cmidrule{2-9}
& & ECCCo & 16.63 ± 2.62\hphantom{*}\hphantom{*} & \textbf{73.86 ± 14.63}** & 17.92 ± 4.17\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.23 ± 0.07\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& & REVISE & 3.73 ± 2.36\hphantom{*}\hphantom{*} & 207.21 ± 43.20\hphantom{*}\hphantom{*} & \textbf{5.78 ± 2.10}** & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.33 ± 0.19\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& & Schut & \textbf{1.20 ± 0.47}** & 205.36 ± 32.11\hphantom{*}\hphantom{*} & 7.00 ± 2.15*\hphantom{*} & \textbf{0.79 ± 0.09}** & 0.12 ± 0.01\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
\multirow[t]{-16}{*}{\centering\arraybackslash GMSC} & \multirow[t]{-4}{*}{\centering\arraybackslash MLP Ensemble} & Wachter & 4.97 ± 0.47\hphantom{*}\hphantom{*} & 177.20 ± 25.86\hphantom{*}\hphantom{*} & 10.27 ± 3.21\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & \textbf{0.11 ± 0.00}\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
\cmidrule{1-9}
& & ECCCo & 0.75 ± 0.17\hphantom{*}\hphantom{*} & \textbf{0.03 ± 0.06}** & \textbf{0.20 ± 0.08}** & 0.00 ± 0.00\hphantom{*}\hphantom{*} & \textbf{0.00 ± 0.00}\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& & ECCCo (no CP) & 0.75 ± 0.17\hphantom{*}\hphantom{*} & 0.03 ± 0.06** & 0.20 ± 0.08** & 0.00 ± 0.00\hphantom{*}\hphantom{*} & \textbf{0.00 ± 0.00}\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& & ECCCo (no EBM) & 0.70 ± 0.16\hphantom{*}\hphantom{*} & 0.16 ± 0.11\hphantom{*}\hphantom{*} & 0.34 ± 0.19\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & \textbf{0.00 ± 0.00}\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& & REVISE & \textbf{0.41 ± 0.14}\hphantom{*}\hphantom{*} & 0.15 ± 0.00** & 0.41 ± 0.01** & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.72 ± 0.02\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& & Schut & 1.15 ± 0.35\hphantom{*}\hphantom{*} & 0.39 ± 0.07\hphantom{*}\hphantom{*} & 0.73 ± 0.17\hphantom{*}\hphantom{*} & \textbf{0.25 ± 0.25}\hphantom{*}\hphantom{*} & \textbf{0.00 ± 0.00}\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& \multirow[t]{-6}{*}{\centering\arraybackslash JEM} & Wachter & 0.50 ± 0.13\hphantom{*}\hphantom{*} & 0.18 ± 0.10\hphantom{*}\hphantom{*} & 0.44 ± 0.17\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & \textbf{0.00 ± 0.00}\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
\cmidrule{2-9}
& & ECCCo & 0.95 ± 0.16\hphantom{*}\hphantom{*} & \textbf{0.29 ± 0.05}** & 0.23 ± 0.06** & 0.00 ± 0.00\hphantom{*}\hphantom{*} & \textbf{0.00 ± 0.00}** & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& & ECCCo (no CP) & 0.94 ± 0.16\hphantom{*}\hphantom{*} & 0.29 ± 0.05** & \textbf{0.23 ± 0.07}** & 0.00 ± 0.00\hphantom{*}\hphantom{*} & \textbf{0.00 ± 0.00}** & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& & ECCCo (no EBM) & 0.60 ± 0.15\hphantom{*}\hphantom{*} & 0.46 ± 0.05\hphantom{*}\hphantom{*} & 0.28 ± 0.04** & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.02 ± 0.10** & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& & REVISE & \textbf{0.39 ± 0.15}\hphantom{*}\hphantom{*} & 0.52 ± 0.04\hphantom{*}\hphantom{*} & 0.41 ± 0.01\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.98 ± 0.00\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& & Schut & 0.77 ± 0.17\hphantom{*}\hphantom{*} & 0.43 ± 0.06*\hphantom{*} & 0.47 ± 0.36\hphantom{*}\hphantom{*} & \textbf{0.20 ± 0.25}\hphantom{*}\hphantom{*} & \textbf{0.00 ± 0.00}** & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
\multirow[t]{-12}{*}{\centering\arraybackslash Linearly Separable} & \multirow[t]{-6}{*}{\centering\arraybackslash MLP} & Wachter & 0.51 ± 0.15\hphantom{*}\hphantom{*} & 0.51 ± 0.04\hphantom{*}\hphantom{*} & 0.40 ± 0.08\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.59 ± 0.02\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
\cmidrule{1-9}
& & ECCCo & 334.98 ± 46.54\hphantom{*}\hphantom{*} & \textbf{19.27 ± 5.02}** & 314.54 ± 32.54*\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & \textbf{4.50 ± 0.00}** & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& & REVISE & 170.06 ± 62.45\hphantom{*}\hphantom{*} & 188.54 ± 26.22*\hphantom{*} & \textbf{254.32 ± 41.55}** & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 4.57 ± 0.14\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& & Schut & \textbf{7.63 ± 2.55}** & 199.70 ± 28.43\hphantom{*}\hphantom{*} & 273.01 ± 39.60** & \textbf{0.99 ± 0.00}** & 4.56 ± 0.13\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& \multirow[t]{-4}{*}{\centering\arraybackslash JEM} & Wachter & 128.13 ± 14.81\hphantom{*}\hphantom{*} & 222.81 ± 26.22\hphantom{*}\hphantom{*} & 361.38 ± 39.55\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 4.58 ± 0.16\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
\cmidrule{2-9}
& & ECCCo & 342.64 ± 41.14\hphantom{*}\hphantom{*} & \textbf{15.99 ± 3.06}** & 294.72 ± 30.75** & 0.00 ± 0.00\hphantom{*}\hphantom{*} & \textbf{2.07 ± 0.06}** & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& & REVISE & 171.95 ± 58.81\hphantom{*}\hphantom{*} & 173.05 ± 20.38** & \textbf{246.20 ± 37.74}** & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 2.76 ± 0.45\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& & Schut & \textbf{7.96 ± 2.49}** & 186.91 ± 22.98*\hphantom{*} & 264.68 ± 37.58** & \textbf{0.99 ± 0.00}** & 3.02 ± 0.26\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& \multirow[t]{-4}{*}{\centering\arraybackslash JEM Ensemble} & Wachter & 134.98 ± 16.95\hphantom{*}\hphantom{*} & 217.37 ± 23.93\hphantom{*}\hphantom{*} & 362.91 ± 39.40\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 3.10 ± 0.31\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
\cmidrule{2-9}
& & ECCCo & 605.17 ± 44.78\hphantom{*}\hphantom{*} & \textbf{41.95 ± 6.50}** & 591.58 ± 36.24\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & \textbf{0.57 ± 0.00}** & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& & REVISE & 146.76 ± 37.07\hphantom{*}\hphantom{*} & 365.69 ± 14.90*\hphantom{*} & 245.36 ± 39.69** & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.72 ± 0.18\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& & Schut & \textbf{9.25 ± 1.31}** & 371.12 ± 19.99\hphantom{*}\hphantom{*} & \textbf{245.11 ± 35.72}** & \textbf{0.99 ± 0.00}** & 0.75 ± 0.23\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& \multirow[t]{-4}{*}{\centering\arraybackslash MLP} & Wachter & 135.08 ± 15.68\hphantom{*}\hphantom{*} & 384.76 ± 16.52\hphantom{*}\hphantom{*} & 359.21 ± 42.03\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.81 ± 0.22\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
\cmidrule{2-9}
& & ECCCo & 525.87 ± 34.00\hphantom{*}\hphantom{*} & \textbf{31.43 ± 3.91}** & 490.88 ± 27.19\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & \textbf{0.29 ± 0.00}** & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& & REVISE & 146.38 ± 35.18\hphantom{*}\hphantom{*} & 337.21 ± 11.68*\hphantom{*} & \textbf{244.84 ± 37.17}** & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.45 ± 0.16\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& & Schut & \textbf{9.75 ± 1.00}** & 344.60 ± 13.64*\hphantom{*} & 252.53 ± 37.92** & \textbf{0.99 ± 0.00}** & 0.55 ± 0.21\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
\multirow[t]{-16}{*}{\centering\arraybackslash MNIST} & \multirow[t]{-4}{*}{\centering\arraybackslash MLP Ensemble} & Wachter & 134.48 ± 17.69\hphantom{*}\hphantom{*} & 358.51 ± 13.18\hphantom{*}\hphantom{*} & 352.63 ± 39.93\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.58 ± 0.67\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
\cmidrule{1-9}
& & ECCCo & 1.56 ± 0.44\hphantom{*}\hphantom{*} & \textbf{0.31 ± 0.30}*\hphantom{*} & \textbf{1.20 ± 0.15}** & 0.00 ± 0.00\hphantom{*}\hphantom{*} & \textbf{0.00 ± 0.00}** & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& & ECCCo (no CP) & 1.56 ± 0.46\hphantom{*}\hphantom{*} & 0.37 ± 0.30*\hphantom{*} & 1.21 ± 0.17** & 0.00 ± 0.00\hphantom{*}\hphantom{*} & \textbf{0.00 ± 0.00}** & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& & ECCCo (no EBM) & 0.80 ± 0.25\hphantom{*}\hphantom{*} & 0.91 ± 0.32\hphantom{*}\hphantom{*} & 1.71 ± 0.25\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & \textbf{0.00 ± 0.00}** & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& & REVISE & 1.04 ± 0.43\hphantom{*}\hphantom{*} & 0.78 ± 0.23\hphantom{*}\hphantom{*} & 1.57 ± 0.26\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & \textbf{0.00 ± 0.00}** & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& & Schut & 1.13 ± 0.29\hphantom{*}\hphantom{*} & 0.66 ± 0.25\hphantom{*}\hphantom{*} & 1.47 ± 0.10** & \textbf{0.07 ± 0.18}\hphantom{*}\hphantom{*} & \textbf{0.00 ± 0.00}** & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& \multirow[t]{-6}{*}{\centering\arraybackslash JEM} & Wachter & \textbf{0.73 ± 0.24}\hphantom{*}\hphantom{*} & 0.78 ± 0.23\hphantom{*}\hphantom{*} & 1.75 ± 0.19\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.02 ± 0.11\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
\cmidrule{2-9}
& & ECCCo & 2.18 ± 1.05\hphantom{*}\hphantom{*} & 0.80 ± 0.62\hphantom{*}\hphantom{*} & 1.69 ± 0.40\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.15 ± 0.24*\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& & ECCCo (no CP) & 2.07 ± 1.15\hphantom{*}\hphantom{*} & \textbf{0.79 ± 0.62}\hphantom{*}\hphantom{*} & 1.68 ± 0.42\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.15 ± 0.24*\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& & ECCCo (no EBM) & 1.25 ± 0.92\hphantom{*}\hphantom{*} & 1.34 ± 0.47\hphantom{*}\hphantom{*} & 1.68 ± 0.47\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.43 ± 0.18\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& & REVISE & 0.79 ± 0.19*\hphantom{*} & 1.45 ± 0.44\hphantom{*}\hphantom{*} & 1.64 ± 0.31\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.40 ± 0.22\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
& & Schut & \textbf{0.78 ± 0.17}*\hphantom{*} & 1.39 ± 0.50\hphantom{*}\hphantom{*} & \textbf{1.59 ± 0.26}\hphantom{*}\hphantom{*} & \textbf{0.28 ± 0.25}*\hphantom{*} & \textbf{0.00 ± 0.00}** & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
\multirow[t]{-12}{*}{\centering\arraybackslash Moons} & \multirow[t]{-6}{*}{\centering\arraybackslash MLP} & Wachter & 1.08 ± 0.83\hphantom{*}\hphantom{*} & 1.32 ± 0.41\hphantom{*}\hphantom{*} & 1.69 ± 0.32\hphantom{*}\hphantom{*} & 0.00 ± 0.00\hphantom{*}\hphantom{*} & 0.52 ± 0.08\hphantom{*}\hphantom{*} & 1.00 ± 0.00\hphantom{*}\hphantom{*}\\
\bottomrule
\end{tabular}}
\end{table}
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\begin{table}
\caption{EBM hyperparemeter choices for our experiments. \label{tab:ebmparams} \newline}
\centering
\fontsize{8}{10}\selectfont
\begin{tabular}[t]{rrrr}
\toprule
Dataset & SGLD Steps & Batch Size & $\lambda$\\
\midrule
Linearly Separable & 30 & 50 & 0.10\\
Moons & 30 & 10 & 0.10\\
Circles & 20 & 100 & 0.01\\
MNIST & 25 & 10 & 0.01\\
GMSC & 30 & 10 & 0.10\\
\bottomrule
\end{tabular}
\end{table}
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\begin{table}
\caption{Generator hyperparameters. \label{tab:genparams} \newline}
\centering
\fontsize{8}{10}\selectfont
\begin{tabular}[t]{rrrrr}
\toprule
Dataset & $\eta$ & $\lambda_1$ & $\lambda_2$ & $\lambda_3$\\
\midrule
Linearly Separable & 0.01 & 0.25 & 0.75 & 0.75\\
Moons & 0.05 & 0.25 & 0.75 & 0.75\\
Circles & 0.01 & 0.25 & 0.75 & 0.75\\
MNIST & 0.10 & 0.10 & 0.25 & 0.25\\
GMSC & 0.05 & 0.10 & 0.50 & 0.50\\
\bottomrule
\end{tabular}
\end{table}
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\begin{table}
\caption{Paremeter choices for our experiments. \label{tab:params} \newline}
\centering
\resizebox{\linewidth}{!}{
\begin{tabular}[t]{rrrrrrrr}
\toprule
\multicolumn{2}{c}{ } & \multicolumn{4}{c}{Network Architecture} & \multicolumn{2}{c}{Training} \\
\cmidrule(l{3pt}r{3pt}){3-6} \cmidrule(l{3pt}r{3pt}){7-8}
Dataset & Sample Size & Hidden Units & Hidden Layers & Activation & Ensemble Size & Epochs & Batch Size\\
\midrule
Linearly Separable & 1000 & 16 & 3 & swish & 5 & 100 & 100\\
Moons & 2500 & 32 & 3 & relu & 5 & 500 & 128\\
Circles & 1000 & 32 & 3 & swish & 5 & 100 & 100\\
MNIST & 10000 & 128 & 1 & swish & 5 & 100 & 128\\
GMSC & 13370 & 128 & 2 & swish & 5 & 100 & 250\\
\bottomrule
\end{tabular}}
\end{table}
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\begin{table}
\caption{Various standard performance metrics for our different models grouped by dataset. \label{tab:perf} \newline}
\centering
\fontsize{8}{10}\selectfont
\begin{tabular}[t]{rrrrr}
\toprule
\multicolumn{2}{c}{ } & \multicolumn{3}{c}{Performance Metrics} \\
\cmidrule(l{3pt}r{3pt}){3-5}
Dataset & Model & Accuracy & Precision & F1-Score\\
\midrule
& JEM & 0.99 & 0.99 & 0.99\\
\multirow[t]{-2}{*}{\raggedleft\arraybackslash Linearly Separable} & MLP & 0.99 & 0.99 & 0.99\\
\cmidrule{1-5}
& JEM & 1.00 & 1.00 & 1.00\\
\multirow[t]{-2}{*}{\raggedleft\arraybackslash Moons} & MLP & 1.00 & 1.00 & 1.00\\
\cmidrule{1-5}
& JEM & 0.98 & 0.98 & 0.98\\
\multirow[t]{-2}{*}{\raggedleft\arraybackslash Circles} & MLP & 1.00 & 1.00 & 1.00\\
\cmidrule{1-5}
& JEM & 0.83 & 0.84 & 0.83\\
& JEM Ensemble & 0.90 & 0.90 & 0.89\\
& MLP & 0.95 & 0.95 & 0.95\\
\multirow[t]{-4}{*}{\raggedleft\arraybackslash MNIST} & MLP Ensemble & 0.95 & 0.95 & 0.95\\
\cmidrule{1-5}
& JEM & 0.73 & 0.75 & 0.73\\
& JEM Ensemble & 0.73 & 0.75 & 0.73\\
& MLP & 0.75 & 0.75 & 0.75\\
\multirow[t]{-4}{*}{\raggedleft\arraybackslash GMSC} & MLP Ensemble & 0.75 & 0.75 & 0.75\\
\bottomrule
\end{tabular}
\end{table}
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\begin{table}
\caption{Results for real-world datasets. Standard deviations across samples are shown in parentheses. Best outcomes are highlighted in bold. Asterisks indicate that the given value is more than one (*) or two (**) standard deviations away from the baseline (Wachter). \label{tab:results-real} \newline}
\centering
\resizebox{\linewidth}{!}{
\begin{tabular}[t]{>{}cccccccc}
\toprule
\multicolumn{2}{c}{ } & \multicolumn{2}{c}{California Housing} & \multicolumn{2}{c}{GMSC} & \multicolumn{2}{c}{MNIST} \\
\cmidrule(l{3pt}r{3pt}){3-4} \cmidrule(l{3pt}r{3pt}){5-6} \cmidrule(l{3pt}r{3pt}){7-8}
Model & Generator & Non-conformity ↓ & Implausibility ↓ & Non-conformity ↓ & Implausibility ↓ & Non-conformity ↓ & Implausibility ↓\\
\midrule
& ECCCo & \textbf{236.79 (51.16)} & 39.78 (3.18) & \textbf{41.65 (17.24)**} & 40.57 (8.74)** & \textbf{116.09 (30.70)**} & 281.33 (41.51)**\\
& REVISE & 284.51 (52.74) & \textbf{5.58 (0.81)**} & 74.89 (15.82)** & \textbf{6.01 (5.75)**} & 348.74 (65.65)** & \textbf{246.69 (36.69)**}\\
& Schut & 263.55 (60.56) & 8.00 (2.03) & 76.23 (15.54)** & 6.02 (0.72)** & 355.58 (64.84)** & 270.06 (40.41)**\\
\multirow{-4}{*}{\centering\arraybackslash \textbf{JEM}} & Wachter & 274.55 (51.17) & 7.32 (1.80) & 146.02 (64.48) & 128.93 (74.00) & 694.08 (50.86) & 630.99 (33.01)\\
\cmidrule{1-8}
& ECCCo & \textbf{249.44 (58.53)} & 35.09 (5.56) & \textbf{26.55 (12.94)**} & 33.65 (8.33)** & \textbf{89.89 (27.26)**} & 240.59 (37.41)**\\
& REVISE & 268.45 (66.87) & \textbf{5.44 (0.74)**} & 52.47 (14.12)** & 6.69 (3.37)** & 292.52 (53.13)** & \textbf{240.50 (35.73)**}\\
& Schut & 279.38 (63.23) & 7.64 (1.47) & 56.34 (15.00)** & \textbf{6.27 (1.06)**} & 319.45 (59.02)** & 266.80 (40.46)**\\
\multirow{-4}{*}{\centering\arraybackslash \textbf{JEM Ensemble}} & Wachter & 268.59 (68.66) & 7.16 (1.46) & 125.72 (70.80) & 126.55 (93.75) & 582.52 (58.46) & 543.90 (44.24)\\
\cmidrule{1-8}
& ECCCo & \textbf{230.92 (48.86)} & 37.53 (5.40) & \textbf{46.90 (15.80)**} & 37.78 (8.40)** & \textbf{212.45 (36.70)**} & 649.63 (58.80)\\
& REVISE & 281.10 (53.01) & \textbf{5.34 (0.67)**} & 81.08 (19.53)** & \textbf{4.60 (0.72)**} & 839.79 (77.14)* & \textbf{244.33 (38.69)**}\\
& Schut & 285.12 (56.00) & 6.48 (1.18)** & 90.67 (20.80)** & 5.56 (0.81)** & 842.80 (82.01)* & 264.94 (42.18)**\\
\multirow{-4}{*}{\centering\arraybackslash \textbf{MLP}} & Wachter & 262.50 (56.87) & 9.21 (10.41) & 191.68 (30.86) & 200.23 (15.05) & 982.32 (61.81) & 561.23 (45.08)\\
\cmidrule{1-8}
& ECCCo & \textbf{212.47 (59.27)*} & 38.17 (6.18) & \textbf{74.65 (144.69)*} & 71.87 (145.19) & \textbf{162.21 (36.21)**} & 587.65 (95.01)\\
& REVISE & 284.65 (49.52) & \textbf{5.64 (1.13)*} & 80.90 (14.59)** & \textbf{5.20 (1.52)**} & 741.30 (125.98)* & \textbf{242.76 (41.16)**}\\
& Schut & 269.19 (46.08) & 7.30 (1.94) & 85.63 (19.15)** & 6.00 (0.99)** & 754.35 (132.26) & 266.94 (42.55)**\\
\multirow{-4}{*}{\centering\arraybackslash \textbf{MLP Ensemble}} & Wachter & 278.09 (73.65) & 7.32 (1.75) & 220.05 (17.41) & 203.65 (14.77) & 871.09 (92.36) & 536.24 (48.73)\\
\bottomrule
\end{tabular}}
\end{table}
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\begin{table}
\caption{Results for synthetic datasets. Standard deviations across samples are shown in parentheses. Best outcomes are highlighted in bold. Asterisks indicate that the given value is more than one (*) or two (**) standard deviations away from the baseline (Wachter). \label{tab:results-synth} \newline}
\centering
\resizebox{\linewidth}{!}{
\begin{tabular}[t]{>{}cccccccc}
\toprule
\multicolumn{2}{c}{ } & \multicolumn{2}{c}{Circles} & \multicolumn{2}{c}{Linearly Separable} & \multicolumn{2}{c}{Moons} \\
\cmidrule(l{3pt}r{3pt}){3-4} \cmidrule(l{3pt}r{3pt}){5-6} \cmidrule(l{3pt}r{3pt}){7-8}
Model & Generator & Non-conformity ↓ & Implausibility ↓ & Non-conformity ↓ & Implausibility ↓ & Non-conformity ↓ & Implausibility ↓\\
\midrule
& ECCCo & \textbf{0.63 (1.58)} & 1.44 (1.37) & 0.10 (0.06)** & 0.19 (0.03)** & \textbf{0.57 (0.58)**} & \textbf{1.29 (0.21)*}\\
& ECCCo (no CP) & 0.64 (1.61) & 1.45 (1.38) & \textbf{0.10 (0.07)**} & \textbf{0.19 (0.03)**} & 0.63 (0.64)* & 1.30 (0.21)*\\
& ECCCo (no EBM) & 1.41 (1.51) & 1.50 (1.38) & 0.37 (0.28) & 0.38 (0.26) & 1.73 (1.34) & 1.73 (1.42)\\
& REVISE & 0.96 (0.32)* & \textbf{0.95 (0.32)*} & 0.41 (0.02)** & 0.41 (0.01)** & 1.59 (0.55) & 1.55 (0.20)\\
& Schut & 0.99 (0.80) & 1.28 (0.53) & 0.66 (0.23) & 0.66 (0.22) & 1.55 (0.61) & 1.42 (0.16)*\\
\multirow{-6}{*}{\centering\arraybackslash \textbf{JEM}} & Wachter & 1.41 (1.50) & 1.51 (1.35) & 0.44 (0.16) & 0.44 (0.15) & 1.77 (0.48) & 1.67 (0.15)\\
\cmidrule{1-8}
& ECCCo & \textbf{0.37 (0.65)**} & 1.30 (0.68) & \textbf{0.03 (0.02)**} & 0.69 (0.10) & 1.68 (1.74) & 2.02 (0.86)\\
& ECCCo (no CP) & 0.50 (0.85)* & 1.28 (0.66) & \textbf{0.03 (0.02)**} & 0.68 (0.10) & \textbf{1.34 (1.66)} & 2.11 (0.88)\\
& ECCCo (no EBM) & 2.00 (1.46) & 1.83 (1.00) & 1.25 (0.87) & 1.84 (1.10) & 2.98 (1.89) & 2.29 (1.75)\\
& REVISE & 1.16 (1.05) & \textbf{0.95 (0.32)*} & 1.10 (0.10) & \textbf{0.40 (0.01)**} & 2.46 (1.05) & \textbf{1.54 (0.27)*}\\
& Schut & 1.60 (1.15) & 1.24 (0.44) & 0.81 (0.10)* & 0.47 (0.24) & 2.71 (1.15) & 1.62 (0.42)\\
\multirow{-6}{*}{\centering\arraybackslash \textbf{MLP}} & Wachter & 1.67 (1.05) & 1.31 (0.43) & 0.94 (0.11) & 0.44 (0.15) & 2.95 (1.42) & 1.84 (1.33)\\
\bottomrule
\end{tabular}}
\end{table}
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