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results.tex
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\documentclass{article}
\usepackage{booktabs}
\usepackage{adjustbox}
\begin{document}
\section{Full DomainBed results}
% Total records: 1833734
\subsection{Model selection: training-domain validation set}
\subsubsection{ColoredMNIST}
\begin{center}
\adjustbox{max width=\textwidth}{%
\begin{tabular}{lcccc}
\toprule
\textbf{Algorithm} & \textbf{+90\%} & \textbf{+80\%} & \textbf{-90\%} & \textbf{Avg} \\
\midrule
ERM & 71.7 $\pm$ 0.1 & 72.9 $\pm$ 0.2 & 10.0 $\pm$ 0.1 & 51.5 \\
IRM & 72.5 $\pm$ 0.1 & 73.3 $\pm$ 0.5 & 10.2 $\pm$ 0.3 & 52.0 \\
GroupDRO & 73.1 $\pm$ 0.3 & 73.2 $\pm$ 0.2 & 10.0 $\pm$ 0.2 & 52.1 \\
Mixup & 72.7 $\pm$ 0.4 & 73.4 $\pm$ 0.1 & 10.1 $\pm$ 0.1 & 52.1 \\
MLDG & 71.5 $\pm$ 0.2 & 73.1 $\pm$ 0.2 & 9.8 $\pm$ 0.1 & 51.5 \\
CORAL & 71.6 $\pm$ 0.3 & 73.1 $\pm$ 0.1 & 9.9 $\pm$ 0.1 & 51.5 \\
MMD & 71.4 $\pm$ 0.3 & 73.1 $\pm$ 0.2 & 9.9 $\pm$ 0.3 & 51.5 \\
DANN & 71.4 $\pm$ 0.9 & 73.1 $\pm$ 0.1 & 10.0 $\pm$ 0.0 & 51.5 \\
CDANN & 72.0 $\pm$ 0.2 & 73.0 $\pm$ 0.2 & 10.2 $\pm$ 0.1 & 51.7 \\
MTL & 70.9 $\pm$ 0.2 & 72.8 $\pm$ 0.3 & 10.5 $\pm$ 0.1 & 51.4 \\
SagNet & 71.8 $\pm$ 0.2 & 73.0 $\pm$ 0.2 & 10.3 $\pm$ 0.0 & 51.7 \\
ARM & 82.0 $\pm$ 0.5 & 76.5 $\pm$ 0.3 & 10.2 $\pm$ 0.0 & 56.2 \\
VREx & 72.4 $\pm$ 0.3 & 72.9 $\pm$ 0.4 & 10.2 $\pm$ 0.0 & 51.8 \\
RSC & 71.9 $\pm$ 0.3 & 73.1 $\pm$ 0.2 & 10.0 $\pm$ 0.2 & 51.7 \\
\bottomrule
\end{tabular}}
\end{center}
\subsubsection{RotatedMNIST}
\begin{center}
\adjustbox{max width=\textwidth}{%
\begin{tabular}{lccccccc}
\toprule
\textbf{Algorithm} & \textbf{0} & \textbf{15} & \textbf{30} & \textbf{45} & \textbf{60} & \textbf{75} & \textbf{Avg} \\
\midrule
ERM & 95.9 $\pm$ 0.1 & 98.9 $\pm$ 0.0 & 98.8 $\pm$ 0.0 & 98.9 $\pm$ 0.0 & 98.9 $\pm$ 0.0 & 96.4 $\pm$ 0.0 & 98.0 \\
IRM & 95.5 $\pm$ 0.1 & 98.8 $\pm$ 0.2 & 98.7 $\pm$ 0.1 & 98.6 $\pm$ 0.1 & 98.7 $\pm$ 0.0 & 95.9 $\pm$ 0.2 & 97.7 \\
GroupDRO & 95.6 $\pm$ 0.1 & 98.9 $\pm$ 0.1 & 98.9 $\pm$ 0.1 & 99.0 $\pm$ 0.0 & 98.9 $\pm$ 0.0 & 96.5 $\pm$ 0.2 & 98.0 \\
Mixup & 95.8 $\pm$ 0.3 & 98.9 $\pm$ 0.0 & 98.9 $\pm$ 0.0 & 98.9 $\pm$ 0.0 & 98.8 $\pm$ 0.1 & 96.5 $\pm$ 0.3 & 98.0 \\
MLDG & 95.8 $\pm$ 0.1 & 98.9 $\pm$ 0.1 & 99.0 $\pm$ 0.0 & 98.9 $\pm$ 0.1 & 99.0 $\pm$ 0.0 & 95.8 $\pm$ 0.3 & 97.9 \\
CORAL & 95.8 $\pm$ 0.3 & 98.8 $\pm$ 0.0 & 98.9 $\pm$ 0.0 & 99.0 $\pm$ 0.0 & 98.9 $\pm$ 0.1 & 96.4 $\pm$ 0.2 & 98.0 \\
MMD & 95.6 $\pm$ 0.1 & 98.9 $\pm$ 0.1 & 99.0 $\pm$ 0.0 & 99.0 $\pm$ 0.0 & 98.9 $\pm$ 0.0 & 96.0 $\pm$ 0.2 & 97.9 \\
DANN & 95.0 $\pm$ 0.5 & 98.9 $\pm$ 0.1 & 99.0 $\pm$ 0.0 & 99.0 $\pm$ 0.1 & 98.9 $\pm$ 0.0 & 96.3 $\pm$ 0.2 & 97.8 \\
CDANN & 95.7 $\pm$ 0.2 & 98.8 $\pm$ 0.0 & 98.9 $\pm$ 0.1 & 98.9 $\pm$ 0.1 & 98.9 $\pm$ 0.1 & 96.1 $\pm$ 0.3 & 97.9 \\
MTL & 95.6 $\pm$ 0.1 & 99.0 $\pm$ 0.1 & 99.0 $\pm$ 0.0 & 98.9 $\pm$ 0.1 & 99.0 $\pm$ 0.1 & 95.8 $\pm$ 0.2 & 97.9 \\
SagNet & 95.9 $\pm$ 0.3 & 98.9 $\pm$ 0.1 & 99.0 $\pm$ 0.1 & 99.1 $\pm$ 0.0 & 99.0 $\pm$ 0.1 & 96.3 $\pm$ 0.1 & 98.0 \\
ARM & 96.7 $\pm$ 0.2 & 99.1 $\pm$ 0.0 & 99.0 $\pm$ 0.0 & 99.0 $\pm$ 0.1 & 99.1 $\pm$ 0.1 & 96.5 $\pm$ 0.4 & 98.2 \\
VREx & 95.9 $\pm$ 0.2 & 99.0 $\pm$ 0.1 & 98.9 $\pm$ 0.1 & 98.9 $\pm$ 0.1 & 98.7 $\pm$ 0.1 & 96.2 $\pm$ 0.2 & 97.9 \\
RSC & 94.8 $\pm$ 0.5 & 98.7 $\pm$ 0.1 & 98.8 $\pm$ 0.1 & 98.8 $\pm$ 0.0 & 98.9 $\pm$ 0.1 & 95.9 $\pm$ 0.2 & 97.6 \\
\bottomrule
\end{tabular}}
\end{center}
\subsubsection{VLCS}
\begin{center}
\adjustbox{max width=\textwidth}{%
\begin{tabular}{lccccc}
\toprule
\textbf{Algorithm} & \textbf{C} & \textbf{L} & \textbf{S} & \textbf{V} & \textbf{Avg} \\
\midrule
ERM & 97.7 $\pm$ 0.4 & 64.3 $\pm$ 0.9 & 73.4 $\pm$ 0.5 & 74.6 $\pm$ 1.3 & 77.5 \\
IRM & 98.6 $\pm$ 0.1 & 64.9 $\pm$ 0.9 & 73.4 $\pm$ 0.6 & 77.3 $\pm$ 0.9 & 78.5 \\
GroupDRO & 97.3 $\pm$ 0.3 & 63.4 $\pm$ 0.9 & 69.5 $\pm$ 0.8 & 76.7 $\pm$ 0.7 & 76.7 \\
Mixup & 98.3 $\pm$ 0.6 & 64.8 $\pm$ 1.0 & 72.1 $\pm$ 0.5 & 74.3 $\pm$ 0.8 & 77.4 \\
MLDG & 97.4 $\pm$ 0.2 & 65.2 $\pm$ 0.7 & 71.0 $\pm$ 1.4 & 75.3 $\pm$ 1.0 & 77.2 \\
CORAL & 98.3 $\pm$ 0.1 & 66.1 $\pm$ 1.2 & 73.4 $\pm$ 0.3 & 77.5 $\pm$ 1.2 & 78.8 \\
MMD & 97.7 $\pm$ 0.1 & 64.0 $\pm$ 1.1 & 72.8 $\pm$ 0.2 & 75.3 $\pm$ 3.3 & 77.5 \\
DANN & 99.0 $\pm$ 0.3 & 65.1 $\pm$ 1.4 & 73.1 $\pm$ 0.3 & 77.2 $\pm$ 0.6 & 78.6 \\
CDANN & 97.1 $\pm$ 0.3 & 65.1 $\pm$ 1.2 & 70.7 $\pm$ 0.8 & 77.1 $\pm$ 1.5 & 77.5 \\
MTL & 97.8 $\pm$ 0.4 & 64.3 $\pm$ 0.3 & 71.5 $\pm$ 0.7 & 75.3 $\pm$ 1.7 & 77.2 \\
SagNet & 97.9 $\pm$ 0.4 & 64.5 $\pm$ 0.5 & 71.4 $\pm$ 1.3 & 77.5 $\pm$ 0.5 & 77.8 \\
ARM & 98.7 $\pm$ 0.2 & 63.6 $\pm$ 0.7 & 71.3 $\pm$ 1.2 & 76.7 $\pm$ 0.6 & 77.6 \\
VREx & 98.4 $\pm$ 0.3 & 64.4 $\pm$ 1.4 & 74.1 $\pm$ 0.4 & 76.2 $\pm$ 1.3 & 78.3 \\
RSC & 97.9 $\pm$ 0.1 & 62.5 $\pm$ 0.7 & 72.3 $\pm$ 1.2 & 75.6 $\pm$ 0.8 & 77.1 \\
\bottomrule
\end{tabular}}
\end{center}
\subsubsection{PACS}
\begin{center}
\adjustbox{max width=\textwidth}{%
\begin{tabular}{lccccc}
\toprule
\textbf{Algorithm} & \textbf{A} & \textbf{C} & \textbf{P} & \textbf{S} & \textbf{Avg} \\
\midrule
ERM & 84.7 $\pm$ 0.4 & 80.8 $\pm$ 0.6 & 97.2 $\pm$ 0.3 & 79.3 $\pm$ 1.0 & 85.5 \\
IRM & 84.8 $\pm$ 1.3 & 76.4 $\pm$ 1.1 & 96.7 $\pm$ 0.6 & 76.1 $\pm$ 1.0 & 83.5 \\
GroupDRO & 83.5 $\pm$ 0.9 & 79.1 $\pm$ 0.6 & 96.7 $\pm$ 0.3 & 78.3 $\pm$ 2.0 & 84.4 \\
Mixup & 86.1 $\pm$ 0.5 & 78.9 $\pm$ 0.8 & 97.6 $\pm$ 0.1 & 75.8 $\pm$ 1.8 & 84.6 \\
MLDG & 85.5 $\pm$ 1.4 & 80.1 $\pm$ 1.7 & 97.4 $\pm$ 0.3 & 76.6 $\pm$ 1.1 & 84.9 \\
CORAL & 88.3 $\pm$ 0.2 & 80.0 $\pm$ 0.5 & 97.5 $\pm$ 0.3 & 78.8 $\pm$ 1.3 & 86.2 \\
MMD & 86.1 $\pm$ 1.4 & 79.4 $\pm$ 0.9 & 96.6 $\pm$ 0.2 & 76.5 $\pm$ 0.5 & 84.6 \\
DANN & 86.4 $\pm$ 0.8 & 77.4 $\pm$ 0.8 & 97.3 $\pm$ 0.4 & 73.5 $\pm$ 2.3 & 83.6 \\
CDANN & 84.6 $\pm$ 1.8 & 75.5 $\pm$ 0.9 & 96.8 $\pm$ 0.3 & 73.5 $\pm$ 0.6 & 82.6 \\
MTL & 87.5 $\pm$ 0.8 & 77.1 $\pm$ 0.5 & 96.4 $\pm$ 0.8 & 77.3 $\pm$ 1.8 & 84.6 \\
SagNet & 87.4 $\pm$ 1.0 & 80.7 $\pm$ 0.6 & 97.1 $\pm$ 0.1 & 80.0 $\pm$ 0.4 & 86.3 \\
ARM & 86.8 $\pm$ 0.6 & 76.8 $\pm$ 0.5 & 97.4 $\pm$ 0.3 & 79.3 $\pm$ 1.2 & 85.1 \\
VREx & 86.0 $\pm$ 1.6 & 79.1 $\pm$ 0.6 & 96.9 $\pm$ 0.5 & 77.7 $\pm$ 1.7 & 84.9 \\
RSC & 85.4 $\pm$ 0.8 & 79.7 $\pm$ 1.8 & 97.6 $\pm$ 0.3 & 78.2 $\pm$ 1.2 & 85.2 \\
\bottomrule
\end{tabular}}
\end{center}
\subsubsection{OfficeHome}
\begin{center}
\adjustbox{max width=\textwidth}{%
\begin{tabular}{lccccc}
\toprule
\textbf{Algorithm} & \textbf{A} & \textbf{C} & \textbf{P} & \textbf{R} & \textbf{Avg} \\
\midrule
ERM & 61.3 $\pm$ 0.7 & 52.4 $\pm$ 0.3 & 75.8 $\pm$ 0.1 & 76.6 $\pm$ 0.3 & 66.5 \\
IRM & 58.9 $\pm$ 2.3 & 52.2 $\pm$ 1.6 & 72.1 $\pm$ 2.9 & 74.0 $\pm$ 2.5 & 64.3 \\
GroupDRO & 60.4 $\pm$ 0.7 & 52.7 $\pm$ 1.0 & 75.0 $\pm$ 0.7 & 76.0 $\pm$ 0.7 & 66.0 \\
Mixup & 62.4 $\pm$ 0.8 & 54.8 $\pm$ 0.6 & 76.9 $\pm$ 0.3 & 78.3 $\pm$ 0.2 & 68.1 \\
MLDG & 61.5 $\pm$ 0.9 & 53.2 $\pm$ 0.6 & 75.0 $\pm$ 1.2 & 77.5 $\pm$ 0.4 & 66.8 \\
CORAL & 65.3 $\pm$ 0.4 & 54.4 $\pm$ 0.5 & 76.5 $\pm$ 0.1 & 78.4 $\pm$ 0.5 & 68.7 \\
MMD & 60.4 $\pm$ 0.2 & 53.3 $\pm$ 0.3 & 74.3 $\pm$ 0.1 & 77.4 $\pm$ 0.6 & 66.3 \\
DANN & 59.9 $\pm$ 1.3 & 53.0 $\pm$ 0.3 & 73.6 $\pm$ 0.7 & 76.9 $\pm$ 0.5 & 65.9 \\
CDANN & 61.5 $\pm$ 1.4 & 50.4 $\pm$ 2.4 & 74.4 $\pm$ 0.9 & 76.6 $\pm$ 0.8 & 65.8 \\
MTL & 61.5 $\pm$ 0.7 & 52.4 $\pm$ 0.6 & 74.9 $\pm$ 0.4 & 76.8 $\pm$ 0.4 & 66.4 \\
SagNet & 63.4 $\pm$ 0.2 & 54.8 $\pm$ 0.4 & 75.8 $\pm$ 0.4 & 78.3 $\pm$ 0.3 & 68.1 \\
ARM & 58.9 $\pm$ 0.8 & 51.0 $\pm$ 0.5 & 74.1 $\pm$ 0.1 & 75.2 $\pm$ 0.3 & 64.8 \\
VREx & 60.7 $\pm$ 0.9 & 53.0 $\pm$ 0.9 & 75.3 $\pm$ 0.1 & 76.6 $\pm$ 0.5 & 66.4 \\
RSC & 60.7 $\pm$ 1.4 & 51.4 $\pm$ 0.3 & 74.8 $\pm$ 1.1 & 75.1 $\pm$ 1.3 & 65.5 \\
\bottomrule
\end{tabular}}
\end{center}
\subsubsection{TerraIncognita}
\begin{center}
\adjustbox{max width=\textwidth}{%
\begin{tabular}{lccccc}
\toprule
\textbf{Algorithm} & \textbf{L100} & \textbf{L38} & \textbf{L43} & \textbf{L46} & \textbf{Avg} \\
\midrule
ERM & 49.8 $\pm$ 4.4 & 42.1 $\pm$ 1.4 & 56.9 $\pm$ 1.8 & 35.7 $\pm$ 3.9 & 46.1 \\
IRM & 54.6 $\pm$ 1.3 & 39.8 $\pm$ 1.9 & 56.2 $\pm$ 1.8 & 39.6 $\pm$ 0.8 & 47.6 \\
GroupDRO & 41.2 $\pm$ 0.7 & 38.6 $\pm$ 2.1 & 56.7 $\pm$ 0.9 & 36.4 $\pm$ 2.1 & 43.2 \\
Mixup & 59.6 $\pm$ 2.0 & 42.2 $\pm$ 1.4 & 55.9 $\pm$ 0.8 & 33.9 $\pm$ 1.4 & 47.9 \\
MLDG & 54.2 $\pm$ 3.0 & 44.3 $\pm$ 1.1 & 55.6 $\pm$ 0.3 & 36.9 $\pm$ 2.2 & 47.7 \\
CORAL & 51.6 $\pm$ 2.4 & 42.2 $\pm$ 1.0 & 57.0 $\pm$ 1.0 & 39.8 $\pm$ 2.9 & 47.6 \\
MMD & 41.9 $\pm$ 3.0 & 34.8 $\pm$ 1.0 & 57.0 $\pm$ 1.9 & 35.2 $\pm$ 1.8 & 42.2 \\
DANN & 51.1 $\pm$ 3.5 & 40.6 $\pm$ 0.6 & 57.4 $\pm$ 0.5 & 37.7 $\pm$ 1.8 & 46.7 \\
CDANN & 47.0 $\pm$ 1.9 & 41.3 $\pm$ 4.8 & 54.9 $\pm$ 1.7 & 39.8 $\pm$ 2.3 & 45.8 \\
MTL & 49.3 $\pm$ 1.2 & 39.6 $\pm$ 6.3 & 55.6 $\pm$ 1.1 & 37.8 $\pm$ 0.8 & 45.6 \\
SagNet & 53.0 $\pm$ 2.9 & 43.0 $\pm$ 2.5 & 57.9 $\pm$ 0.6 & 40.4 $\pm$ 1.3 & 48.6 \\
ARM & 49.3 $\pm$ 0.7 & 38.3 $\pm$ 2.4 & 55.8 $\pm$ 0.8 & 38.7 $\pm$ 1.3 & 45.5 \\
VREx & 48.2 $\pm$ 4.3 & 41.7 $\pm$ 1.3 & 56.8 $\pm$ 0.8 & 38.7 $\pm$ 3.1 & 46.4 \\
RSC & 50.2 $\pm$ 2.2 & 39.2 $\pm$ 1.4 & 56.3 $\pm$ 1.4 & 40.8 $\pm$ 0.6 & 46.6 \\
\bottomrule
\end{tabular}}
\end{center}
\subsubsection{DomainNet}
\begin{center}
\adjustbox{max width=\textwidth}{%
\begin{tabular}{lccccccc}
\toprule
\textbf{Algorithm} & \textbf{clip} & \textbf{info} & \textbf{paint} & \textbf{quick} & \textbf{real} & \textbf{sketch} & \textbf{Avg} \\
\midrule
ERM & 58.1 $\pm$ 0.3 & 18.8 $\pm$ 0.3 & 46.7 $\pm$ 0.3 & 12.2 $\pm$ 0.4 & 59.6 $\pm$ 0.1 & 49.8 $\pm$ 0.4 & 40.9 \\
IRM & 48.5 $\pm$ 2.8 & 15.0 $\pm$ 1.5 & 38.3 $\pm$ 4.3 & 10.9 $\pm$ 0.5 & 48.2 $\pm$ 5.2 & 42.3 $\pm$ 3.1 & 33.9 \\
GroupDRO & 47.2 $\pm$ 0.5 & 17.5 $\pm$ 0.4 & 33.8 $\pm$ 0.5 & 9.3 $\pm$ 0.3 & 51.6 $\pm$ 0.4 & 40.1 $\pm$ 0.6 & 33.3 \\
Mixup & 55.7 $\pm$ 0.3 & 18.5 $\pm$ 0.5 & 44.3 $\pm$ 0.5 & 12.5 $\pm$ 0.4 & 55.8 $\pm$ 0.3 & 48.2 $\pm$ 0.5 & 39.2 \\
MLDG & 59.1 $\pm$ 0.2 & 19.1 $\pm$ 0.3 & 45.8 $\pm$ 0.7 & 13.4 $\pm$ 0.3 & 59.6 $\pm$ 0.2 & 50.2 $\pm$ 0.4 & 41.2 \\
CORAL & 59.2 $\pm$ 0.1 & 19.7 $\pm$ 0.2 & 46.6 $\pm$ 0.3 & 13.4 $\pm$ 0.4 & 59.8 $\pm$ 0.2 & 50.1 $\pm$ 0.6 & 41.5 \\
MMD & 32.1 $\pm$ 13.3 & 11.0 $\pm$ 4.6 & 26.8 $\pm$ 11.3 & 8.7 $\pm$ 2.1 & 32.7 $\pm$ 13.8 & 28.9 $\pm$ 11.9 & 23.4 \\
DANN & 53.1 $\pm$ 0.2 & 18.3 $\pm$ 0.1 & 44.2 $\pm$ 0.7 & 11.8 $\pm$ 0.1 & 55.5 $\pm$ 0.4 & 46.8 $\pm$ 0.6 & 38.3 \\
CDANN & 54.6 $\pm$ 0.4 & 17.3 $\pm$ 0.1 & 43.7 $\pm$ 0.9 & 12.1 $\pm$ 0.7 & 56.2 $\pm$ 0.4 & 45.9 $\pm$ 0.5 & 38.3 \\
MTL & 57.9 $\pm$ 0.5 & 18.5 $\pm$ 0.4 & 46.0 $\pm$ 0.1 & 12.5 $\pm$ 0.1 & 59.5 $\pm$ 0.3 & 49.2 $\pm$ 0.1 & 40.6 \\
SagNet & 57.7 $\pm$ 0.3 & 19.0 $\pm$ 0.2 & 45.3 $\pm$ 0.3 & 12.7 $\pm$ 0.5 & 58.1 $\pm$ 0.5 & 48.8 $\pm$ 0.2 & 40.3 \\
ARM & 49.7 $\pm$ 0.3 & 16.3 $\pm$ 0.5 & 40.9 $\pm$ 1.1 & 9.4 $\pm$ 0.1 & 53.4 $\pm$ 0.4 & 43.5 $\pm$ 0.4 & 35.5 \\
VREx & 47.3 $\pm$ 3.5 & 16.0 $\pm$ 1.5 & 35.8 $\pm$ 4.6 & 10.9 $\pm$ 0.3 & 49.6 $\pm$ 4.9 & 42.0 $\pm$ 3.0 & 33.6 \\
RSC & 55.0 $\pm$ 1.2 & 18.3 $\pm$ 0.5 & 44.4 $\pm$ 0.6 & 12.2 $\pm$ 0.2 & 55.7 $\pm$ 0.7 & 47.8 $\pm$ 0.9 & 38.9 \\
\bottomrule
\end{tabular}}
\end{center}
\subsubsection{Averages}
\begin{center}
\adjustbox{max width=\textwidth}{%
\begin{tabular}{lcccccccc}
\toprule
\textbf{Algorithm} & \textbf{ColoredMNIST} & \textbf{RotatedMNIST} & \textbf{VLCS} & \textbf{PACS} & \textbf{OfficeHome} & \textbf{TerraIncognita} & \textbf{DomainNet} & \textbf{Avg} \\
\midrule
ERM & 51.5 $\pm$ 0.1 & 98.0 $\pm$ 0.0 & 77.5 $\pm$ 0.4 & 85.5 $\pm$ 0.2 & 66.5 $\pm$ 0.3 & 46.1 $\pm$ 1.8 & 40.9 $\pm$ 0.1 & 66.6 \\
IRM & 52.0 $\pm$ 0.1 & 97.7 $\pm$ 0.1 & 78.5 $\pm$ 0.5 & 83.5 $\pm$ 0.8 & 64.3 $\pm$ 2.2 & 47.6 $\pm$ 0.8 & 33.9 $\pm$ 2.8 & 65.4 \\
GroupDRO & 52.1 $\pm$ 0.0 & 98.0 $\pm$ 0.0 & 76.7 $\pm$ 0.6 & 84.4 $\pm$ 0.8 & 66.0 $\pm$ 0.7 & 43.2 $\pm$ 1.1 & 33.3 $\pm$ 0.2 & 64.8 \\
Mixup & 52.1 $\pm$ 0.2 & 98.0 $\pm$ 0.1 & 77.4 $\pm$ 0.6 & 84.6 $\pm$ 0.6 & 68.1 $\pm$ 0.3 & 47.9 $\pm$ 0.8 & 39.2 $\pm$ 0.1 & 66.7 \\
MLDG & 51.5 $\pm$ 0.1 & 97.9 $\pm$ 0.0 & 77.2 $\pm$ 0.4 & 84.9 $\pm$ 1.0 & 66.8 $\pm$ 0.6 & 47.7 $\pm$ 0.9 & 41.2 $\pm$ 0.1 & 66.7 \\
CORAL & 51.5 $\pm$ 0.1 & 98.0 $\pm$ 0.1 & 78.8 $\pm$ 0.6 & 86.2 $\pm$ 0.3 & 68.7 $\pm$ 0.3 & 47.6 $\pm$ 1.0 & 41.5 $\pm$ 0.1 & 67.5 \\
MMD & 51.5 $\pm$ 0.2 & 97.9 $\pm$ 0.0 & 77.5 $\pm$ 0.9 & 84.6 $\pm$ 0.5 & 66.3 $\pm$ 0.1 & 42.2 $\pm$ 1.6 & 23.4 $\pm$ 9.5 & 63.3 \\
DANN & 51.5 $\pm$ 0.3 & 97.8 $\pm$ 0.1 & 78.6 $\pm$ 0.4 & 83.6 $\pm$ 0.4 & 65.9 $\pm$ 0.6 & 46.7 $\pm$ 0.5 & 38.3 $\pm$ 0.1 & 66.1 \\
CDANN & 51.7 $\pm$ 0.1 & 97.9 $\pm$ 0.1 & 77.5 $\pm$ 0.1 & 82.6 $\pm$ 0.9 & 65.8 $\pm$ 1.3 & 45.8 $\pm$ 1.6 & 38.3 $\pm$ 0.3 & 65.6 \\
MTL & 51.4 $\pm$ 0.1 & 97.9 $\pm$ 0.0 & 77.2 $\pm$ 0.4 & 84.6 $\pm$ 0.5 & 66.4 $\pm$ 0.5 & 45.6 $\pm$ 1.2 & 40.6 $\pm$ 0.1 & 66.2 \\
SagNet & 51.7 $\pm$ 0.0 & 98.0 $\pm$ 0.0 & 77.8 $\pm$ 0.5 & 86.3 $\pm$ 0.2 & 68.1 $\pm$ 0.1 & 48.6 $\pm$ 1.0 & 40.3 $\pm$ 0.1 & 67.2 \\
ARM & 56.2 $\pm$ 0.2 & 98.2 $\pm$ 0.1 & 77.6 $\pm$ 0.3 & 85.1 $\pm$ 0.4 & 64.8 $\pm$ 0.3 & 45.5 $\pm$ 0.3 & 35.5 $\pm$ 0.2 & 66.1 \\
VREx & 51.8 $\pm$ 0.1 & 97.9 $\pm$ 0.1 & 78.3 $\pm$ 0.2 & 84.9 $\pm$ 0.6 & 66.4 $\pm$ 0.6 & 46.4 $\pm$ 0.6 & 33.6 $\pm$ 2.9 & 65.6 \\
RSC & 51.7 $\pm$ 0.2 & 97.6 $\pm$ 0.1 & 77.1 $\pm$ 0.5 & 85.2 $\pm$ 0.9 & 65.5 $\pm$ 0.9 & 46.6 $\pm$ 1.0 & 38.9 $\pm$ 0.5 & 66.1 \\
\bottomrule
\end{tabular}}
\end{center}
\subsection{Model selection: leave-one-domain-out cross-validation}
\subsubsection{ColoredMNIST}
\begin{center}
\adjustbox{max width=\textwidth}{%
\begin{tabular}{lcccc}
\toprule
\textbf{Algorithm} & \textbf{+90\%} & \textbf{+80\%} & \textbf{-90\%} & \textbf{Avg} \\
\midrule
ERM & 50.0 $\pm$ 0.2 & 50.1 $\pm$ 0.2 & 10.0 $\pm$ 0.0 & 36.7 \\
IRM & 46.7 $\pm$ 2.4 & 51.2 $\pm$ 0.3 & 23.1 $\pm$ 10.7 & 40.3 \\
GroupDRO & 50.1 $\pm$ 0.5 & 50.0 $\pm$ 0.5 & 10.2 $\pm$ 0.1 & 36.8 \\
Mixup & 36.6 $\pm$ 10.9 & 53.4 $\pm$ 5.9 & 10.2 $\pm$ 0.1 & 33.4 \\
MLDG & 50.1 $\pm$ 0.6 & 50.1 $\pm$ 0.3 & 10.0 $\pm$ 0.1 & 36.7 \\
CORAL & 49.5 $\pm$ 0.0 & 59.5 $\pm$ 8.2 & 10.2 $\pm$ 0.1 & 39.7 \\
MMD & 50.3 $\pm$ 0.2 & 50.0 $\pm$ 0.4 & 9.9 $\pm$ 0.2 & 36.8 \\
DANN & 49.9 $\pm$ 0.1 & 62.1 $\pm$ 7.0 & 10.0 $\pm$ 0.1 & 40.7 \\
CDANN & 63.2 $\pm$ 10.1 & 44.4 $\pm$ 4.5 & 9.9 $\pm$ 0.2 & 39.1 \\
MTL & 44.3 $\pm$ 4.9 & 50.7 $\pm$ 0.0 & 10.1 $\pm$ 0.1 & 35.0 \\
SagNet & 49.9 $\pm$ 0.4 & 49.7 $\pm$ 0.3 & 10.0 $\pm$ 0.1 & 36.5 \\
ARM & 50.0 $\pm$ 0.3 & 50.1 $\pm$ 0.3 & 10.2 $\pm$ 0.0 & 36.8 \\
VREx & 50.2 $\pm$ 0.4 & 50.5 $\pm$ 0.5 & 10.1 $\pm$ 0.0 & 36.9 \\
RSC & 49.6 $\pm$ 0.3 & 49.7 $\pm$ 0.4 & 10.1 $\pm$ 0.0 & 36.5 \\
\bottomrule
\end{tabular}}
\end{center}
\subsubsection{RotatedMNIST}
\begin{center}
\adjustbox{max width=\textwidth}{%
\begin{tabular}{lccccccc}
\toprule
\textbf{Algorithm} & \textbf{0} & \textbf{15} & \textbf{30} & \textbf{45} & \textbf{60} & \textbf{75} & \textbf{Avg} \\
\midrule
ERM & 95.3 $\pm$ 0.2 & 98.9 $\pm$ 0.1 & 98.9 $\pm$ 0.1 & 98.8 $\pm$ 0.1 & 98.5 $\pm$ 0.1 & 96.2 $\pm$ 0.2 & 97.7 \\
IRM & 94.5 $\pm$ 0.5 & 98.2 $\pm$ 0.2 & 98.7 $\pm$ 0.1 & 96.6 $\pm$ 1.5 & 98.4 $\pm$ 0.1 & 95.8 $\pm$ 0.1 & 97.0 \\
GroupDRO & 95.7 $\pm$ 0.3 & 98.7 $\pm$ 0.1 & 98.9 $\pm$ 0.1 & 98.6 $\pm$ 0.2 & 98.6 $\pm$ 0.2 & 95.3 $\pm$ 0.9 & 97.6 \\
Mixup & 94.8 $\pm$ 0.4 & 98.8 $\pm$ 0.0 & 98.9 $\pm$ 0.1 & 99.0 $\pm$ 0.1 & 98.9 $\pm$ 0.0 & 96.4 $\pm$ 0.3 & 97.8 \\
MLDG & 94.3 $\pm$ 0.4 & 98.8 $\pm$ 0.1 & 99.0 $\pm$ 0.1 & 98.8 $\pm$ 0.1 & 98.8 $\pm$ 0.1 & 96.0 $\pm$ 0.3 & 97.6 \\
CORAL & 95.7 $\pm$ 0.5 & 98.5 $\pm$ 0.2 & 98.9 $\pm$ 0.2 & 98.6 $\pm$ 0.2 & 98.8 $\pm$ 0.1 & 96.3 $\pm$ 0.2 & 97.8 \\
MMD & 95.8 $\pm$ 0.2 & 98.7 $\pm$ 0.1 & 99.0 $\pm$ 0.0 & 98.8 $\pm$ 0.1 & 98.7 $\pm$ 0.1 & 96.1 $\pm$ 0.2 & 97.8 \\
DANN & 95.1 $\pm$ 0.5 & 98.3 $\pm$ 0.5 & 98.5 $\pm$ 0.1 & 99.0 $\pm$ 0.1 & 98.6 $\pm$ 0.1 & 96.1 $\pm$ 0.3 & 97.6 \\
CDANN & 94.3 $\pm$ 0.5 & 98.4 $\pm$ 0.3 & 98.9 $\pm$ 0.1 & 98.7 $\pm$ 0.1 & 98.9 $\pm$ 0.1 & 95.7 $\pm$ 0.4 & 97.5 \\
MTL & 95.5 $\pm$ 0.3 & 98.6 $\pm$ 0.3 & 98.8 $\pm$ 0.1 & 99.0 $\pm$ 0.1 & 99.0 $\pm$ 0.1 & 95.6 $\pm$ 0.3 & 97.8 \\
SagNet & 94.0 $\pm$ 1.6 & 98.7 $\pm$ 0.2 & 98.9 $\pm$ 0.1 & 99.1 $\pm$ 0.0 & 98.8 $\pm$ 0.1 & 74.2 $\pm$ 16.5 & 94.0 \\
ARM & 95.8 $\pm$ 0.1 & 99.0 $\pm$ 0.1 & 99.0 $\pm$ 0.0 & 98.9 $\pm$ 0.1 & 98.8 $\pm$ 0.1 & 96.9 $\pm$ 0.3 & 98.1 \\
VREx & 95.8 $\pm$ 0.2 & 98.7 $\pm$ 0.0 & 98.5 $\pm$ 0.1 & 98.9 $\pm$ 0.1 & 74.0 $\pm$ 20.1 & 95.5 $\pm$ 0.5 & 93.6 \\
RSC & 94.6 $\pm$ 0.0 & 98.4 $\pm$ 0.2 & 99.0 $\pm$ 0.1 & 98.9 $\pm$ 0.0 & 98.8 $\pm$ 0.1 & 95.9 $\pm$ 0.4 & 97.6 \\
\bottomrule
\end{tabular}}
\end{center}
\subsubsection{VLCS}
\begin{center}
\adjustbox{max width=\textwidth}{%
\begin{tabular}{lccccc}
\toprule
\textbf{Algorithm} & \textbf{C} & \textbf{L} & \textbf{S} & \textbf{V} & \textbf{Avg} \\
\midrule
ERM & 98.0 $\pm$ 0.4 & 62.6 $\pm$ 0.9 & 70.8 $\pm$ 1.9 & 77.5 $\pm$ 1.9 & 77.2 \\
IRM & 98.6 $\pm$ 0.3 & 66.0 $\pm$ 1.1 & 69.3 $\pm$ 0.9 & 71.5 $\pm$ 1.9 & 76.3 \\
GroupDRO & 98.1 $\pm$ 0.3 & 66.4 $\pm$ 0.9 & 71.0 $\pm$ 0.3 & 76.1 $\pm$ 1.4 & 77.9 \\
Mixup & 98.4 $\pm$ 0.3 & 63.4 $\pm$ 0.7 & 72.9 $\pm$ 0.8 & 76.1 $\pm$ 1.2 & 77.7 \\
MLDG & 98.5 $\pm$ 0.3 & 61.7 $\pm$ 1.2 & 73.6 $\pm$ 1.8 & 75.0 $\pm$ 0.8 & 77.2 \\
CORAL & 96.9 $\pm$ 0.9 & 65.7 $\pm$ 1.2 & 73.3 $\pm$ 0.7 & 78.7 $\pm$ 0.8 & 78.7 \\
MMD & 98.3 $\pm$ 0.1 & 65.6 $\pm$ 0.7 & 69.7 $\pm$ 1.0 & 75.7 $\pm$ 0.9 & 77.3 \\
DANN & 97.3 $\pm$ 1.3 & 63.7 $\pm$ 1.3 & 72.6 $\pm$ 1.4 & 74.2 $\pm$ 1.7 & 76.9 \\
CDANN & 97.6 $\pm$ 0.6 & 63.4 $\pm$ 0.8 & 70.5 $\pm$ 1.4 & 78.6 $\pm$ 0.5 & 77.5 \\
MTL & 97.6 $\pm$ 0.6 & 60.6 $\pm$ 1.3 & 71.0 $\pm$ 1.2 & 77.2 $\pm$ 0.7 & 76.6 \\
SagNet & 97.3 $\pm$ 0.4 & 61.6 $\pm$ 0.8 & 73.4 $\pm$ 1.9 & 77.6 $\pm$ 0.4 & 77.5 \\
ARM & 97.2 $\pm$ 0.5 & 62.7 $\pm$ 1.5 & 70.6 $\pm$ 0.6 & 75.8 $\pm$ 0.9 & 76.6 \\
VREx & 96.9 $\pm$ 0.3 & 64.8 $\pm$ 2.0 & 69.7 $\pm$ 1.8 & 75.5 $\pm$ 1.7 & 76.7 \\
RSC & 97.5 $\pm$ 0.6 & 63.1 $\pm$ 1.2 & 73.0 $\pm$ 1.3 & 76.2 $\pm$ 0.5 & 77.5 \\
\bottomrule
\end{tabular}}
\end{center}
\subsubsection{PACS}
\begin{center}
\adjustbox{max width=\textwidth}{%
\begin{tabular}{lccccc}
\toprule
\textbf{Algorithm} & \textbf{A} & \textbf{C} & \textbf{P} & \textbf{S} & \textbf{Avg} \\
\midrule
ERM & 83.2 $\pm$ 1.3 & 76.8 $\pm$ 1.7 & 97.2 $\pm$ 0.3 & 74.8 $\pm$ 1.3 & 83.0 \\
IRM & 81.7 $\pm$ 2.4 & 77.0 $\pm$ 1.3 & 96.3 $\pm$ 0.2 & 71.1 $\pm$ 2.2 & 81.5 \\
GroupDRO & 84.4 $\pm$ 0.7 & 77.3 $\pm$ 0.8 & 96.8 $\pm$ 0.8 & 75.6 $\pm$ 1.4 & 83.5 \\
Mixup & 85.2 $\pm$ 1.9 & 77.0 $\pm$ 1.7 & 96.8 $\pm$ 0.8 & 73.9 $\pm$ 1.6 & 83.2 \\
MLDG & 81.4 $\pm$ 3.6 & 77.9 $\pm$ 2.3 & 96.2 $\pm$ 0.3 & 76.1 $\pm$ 2.1 & 82.9 \\
CORAL & 80.5 $\pm$ 2.8 & 74.5 $\pm$ 0.4 & 96.8 $\pm$ 0.3 & 78.6 $\pm$ 1.4 & 82.6 \\
MMD & 84.9 $\pm$ 1.7 & 75.1 $\pm$ 2.0 & 96.1 $\pm$ 0.9 & 76.5 $\pm$ 1.5 & 83.2 \\
DANN & 84.3 $\pm$ 2.8 & 72.4 $\pm$ 2.8 & 96.5 $\pm$ 0.8 & 70.8 $\pm$ 1.3 & 81.0 \\
CDANN & 78.3 $\pm$ 2.8 & 73.8 $\pm$ 1.6 & 96.4 $\pm$ 0.5 & 66.8 $\pm$ 5.5 & 78.8 \\
MTL & 85.6 $\pm$ 1.5 & 78.9 $\pm$ 0.6 & 97.1 $\pm$ 0.3 & 73.1 $\pm$ 2.7 & 83.7 \\
SagNet & 81.1 $\pm$ 1.9 & 75.4 $\pm$ 1.3 & 95.7 $\pm$ 0.9 & 77.2 $\pm$ 0.6 & 82.3 \\
ARM & 85.9 $\pm$ 0.3 & 73.3 $\pm$ 1.9 & 95.6 $\pm$ 0.4 & 72.1 $\pm$ 2.4 & 81.7 \\
VREx & 81.6 $\pm$ 4.0 & 74.1 $\pm$ 0.3 & 96.9 $\pm$ 0.4 & 72.8 $\pm$ 2.1 & 81.3 \\
RSC & 83.7 $\pm$ 1.7 & 82.9 $\pm$ 1.1 & 95.6 $\pm$ 0.7 & 68.1 $\pm$ 1.5 & 82.6 \\
\bottomrule
\end{tabular}}
\end{center}
\subsubsection{OfficeHome}
\begin{center}
\adjustbox{max width=\textwidth}{%
\begin{tabular}{lccccc}
\toprule
\textbf{Algorithm} & \textbf{A} & \textbf{C} & \textbf{P} & \textbf{R} & \textbf{Avg} \\
\midrule
ERM & 61.1 $\pm$ 0.9 & 50.7 $\pm$ 0.6 & 74.6 $\pm$ 0.3 & 76.4 $\pm$ 0.6 & 65.7 \\
IRM & 58.2 $\pm$ 1.2 & 51.6 $\pm$ 1.2 & 73.3 $\pm$ 2.2 & 74.1 $\pm$ 1.7 & 64.3 \\
GroupDRO & 59.9 $\pm$ 0.4 & 51.0 $\pm$ 0.4 & 73.7 $\pm$ 0.3 & 76.0 $\pm$ 0.2 & 65.2 \\
Mixup & 61.4 $\pm$ 0.5 & 53.0 $\pm$ 0.3 & 75.8 $\pm$ 0.2 & 77.7 $\pm$ 0.3 & 67.0 \\
MLDG & 60.5 $\pm$ 1.4 & 51.9 $\pm$ 0.2 & 74.4 $\pm$ 0.6 & 77.6 $\pm$ 0.4 & 66.1 \\
CORAL & 64.5 $\pm$ 0.8 & 54.8 $\pm$ 0.2 & 76.6 $\pm$ 0.3 & 78.1 $\pm$ 0.2 & 68.5 \\
MMD & 60.8 $\pm$ 0.7 & 53.7 $\pm$ 0.5 & 50.2 $\pm$ 19.9 & 76.0 $\pm$ 0.7 & 60.2 \\
DANN & 60.2 $\pm$ 1.3 & 52.2 $\pm$ 0.9 & 71.3 $\pm$ 2.0 & 76.0 $\pm$ 0.6 & 64.9 \\
CDANN & 58.7 $\pm$ 2.9 & 49.0 $\pm$ 2.1 & 73.6 $\pm$ 1.0 & 76.0 $\pm$ 1.1 & 64.3 \\
MTL & 59.1 $\pm$ 0.3 & 52.1 $\pm$ 1.2 & 74.7 $\pm$ 0.4 & 77.0 $\pm$ 0.6 & 65.7 \\
SagNet & 63.0 $\pm$ 0.8 & 54.0 $\pm$ 0.3 & 76.6 $\pm$ 0.3 & 76.8 $\pm$ 0.4 & 67.6 \\
ARM & 58.7 $\pm$ 0.8 & 49.8 $\pm$ 1.1 & 73.1 $\pm$ 0.5 & 75.9 $\pm$ 0.1 & 64.4 \\
VREx & 57.6 $\pm$ 3.4 & 51.3 $\pm$ 1.3 & 74.9 $\pm$ 0.2 & 75.8 $\pm$ 0.7 & 64.9 \\
RSC & 61.6 $\pm$ 1.0 & 51.1 $\pm$ 0.8 & 74.8 $\pm$ 1.1 & 75.7 $\pm$ 0.9 & 65.8 \\
\bottomrule
\end{tabular}}
\end{center}
\subsubsection{TerraIncognita}
\begin{center}
\adjustbox{max width=\textwidth}{%
\begin{tabular}{lccccc}
\toprule
\textbf{Algorithm} & \textbf{L100} & \textbf{L38} & \textbf{L43} & \textbf{L46} & \textbf{Avg} \\
\midrule
ERM & 34.4 $\pm$ 5.6 & 38.1 $\pm$ 4.0 & 55.7 $\pm$ 1.0 & 37.4 $\pm$ 1.1 & 41.4 \\
IRM & 46.7 $\pm$ 1.8 & 40.9 $\pm$ 2.1 & 52.2 $\pm$ 3.3 & 24.9 $\pm$ 10.0 & 41.2 \\
GroupDRO & 45.2 $\pm$ 6.2 & 40.1 $\pm$ 2.0 & 55.8 $\pm$ 1.4 & 38.3 $\pm$ 4.2 & 44.9 \\
Mixup & 59.7 $\pm$ 1.5 & 41.3 $\pm$ 2.1 & 55.9 $\pm$ 0.8 & 37.9 $\pm$ 1.5 & 48.7 \\
MLDG & 51.0 $\pm$ 1.9 & 39.2 $\pm$ 0.2 & 56.2 $\pm$ 1.1 & 38.3 $\pm$ 2.4 & 46.2 \\
CORAL & 52.4 $\pm$ 7.2 & 39.7 $\pm$ 1.5 & 56.1 $\pm$ 0.9 & 37.1 $\pm$ 2.2 & 46.3 \\
MMD & 49.1 $\pm$ 2.2 & 42.0 $\pm$ 1.6 & 55.3 $\pm$ 1.9 & 39.5 $\pm$ 2.0 & 46.5 \\
DANN & 46.9 $\pm$ 3.9 & 38.8 $\pm$ 1.1 & 55.5 $\pm$ 1.4 & 36.2 $\pm$ 1.1 & 44.4 \\
CDANN & 43.9 $\pm$ 7.3 & 32.5 $\pm$ 4.4 & 41.0 $\pm$ 7.8 & 42.4 $\pm$ 1.8 & 39.9 \\
MTL & 42.8 $\pm$ 4.6 & 43.9 $\pm$ 1.1 & 55.5 $\pm$ 0.8 & 37.5 $\pm$ 1.9 & 44.9 \\
SagNet & 48.1 $\pm$ 2.4 & 47.1 $\pm$ 0.8 & 54.4 $\pm$ 1.1 & 39.1 $\pm$ 1.8 & 47.2 \\
ARM & 48.9 $\pm$ 5.3 & 34.4 $\pm$ 3.5 & 51.9 $\pm$ 0.8 & 35.4 $\pm$ 2.3 & 42.6 \\
VREx & 46.4 $\pm$ 1.4 & 25.5 $\pm$ 5.8 & 39.6 $\pm$ 12.8 & 37.8 $\pm$ 3.6 & 37.3 \\
RSC & 40.0 $\pm$ 1.3 & 32.1 $\pm$ 2.5 & 53.9 $\pm$ 0.5 & 34.2 $\pm$ 0.2 & 40.0 \\
\bottomrule
\end{tabular}}
\end{center}
\subsubsection{DomainNet}
\begin{center}
\adjustbox{max width=\textwidth}{%
\begin{tabular}{lccccccc}
\toprule
\textbf{Algorithm} & \textbf{clip} & \textbf{info} & \textbf{paint} & \textbf{quick} & \textbf{real} & \textbf{sketch} & \textbf{Avg} \\
\midrule
ERM & 58.1 $\pm$ 0.3 & 17.8 $\pm$ 0.3 & 47.0 $\pm$ 0.3 & 12.2 $\pm$ 0.4 & 59.2 $\pm$ 0.7 & 49.5 $\pm$ 0.6 & 40.6 \\
IRM & 47.5 $\pm$ 2.7 & 15.0 $\pm$ 1.5 & 37.3 $\pm$ 5.1 & 10.9 $\pm$ 0.5 & 48.0 $\pm$ 5.4 & 42.3 $\pm$ 3.1 & 33.5 \\
GroupDRO & 47.2 $\pm$ 0.5 & 17.0 $\pm$ 0.6 & 33.8 $\pm$ 0.5 & 9.2 $\pm$ 0.4 & 51.6 $\pm$ 0.4 & 39.2 $\pm$ 1.2 & 33.0 \\
Mixup & 54.4 $\pm$ 0.6 & 18.0 $\pm$ 0.4 & 44.5 $\pm$ 0.5 & 11.5 $\pm$ 0.2 & 55.8 $\pm$ 1.1 & 46.9 $\pm$ 0.2 & 38.5 \\
MLDG & 58.3 $\pm$ 0.7 & 19.3 $\pm$ 0.2 & 45.8 $\pm$ 0.7 & 13.2 $\pm$ 0.3 & 59.4 $\pm$ 0.2 & 49.8 $\pm$ 0.3 & 41.0 \\
CORAL & 59.2 $\pm$ 0.1 & 19.5 $\pm$ 0.3 & 46.2 $\pm$ 0.1 & 13.4 $\pm$ 0.4 & 59.1 $\pm$ 0.5 & 49.5 $\pm$ 0.8 & 41.1 \\
MMD & 32.2 $\pm$ 13.3 & 11.0 $\pm$ 4.6 & 26.8 $\pm$ 11.3 & 8.7 $\pm$ 2.1 & 32.7 $\pm$ 13.8 & 28.9 $\pm$ 11.9 & 23.4 \\
DANN & 52.7 $\pm$ 0.1 & 18.0 $\pm$ 0.3 & 44.2 $\pm$ 0.7 & 11.8 $\pm$ 0.1 & 55.5 $\pm$ 0.4 & 46.8 $\pm$ 0.6 & 38.2 \\
CDANN & 53.1 $\pm$ 0.9 & 17.3 $\pm$ 0.1 & 43.7 $\pm$ 0.9 & 11.6 $\pm$ 0.6 & 56.2 $\pm$ 0.4 & 45.9 $\pm$ 0.5 & 38.0 \\
MTL & 57.3 $\pm$ 0.3 & 19.3 $\pm$ 0.2 & 45.7 $\pm$ 0.4 & 12.5 $\pm$ 0.1 & 59.3 $\pm$ 0.2 & 49.2 $\pm$ 0.1 & 40.6 \\
SagNet & 56.2 $\pm$ 0.3 & 18.9 $\pm$ 0.2 & 46.2 $\pm$ 0.5 & 12.6 $\pm$ 0.6 & 58.2 $\pm$ 0.6 & 49.1 $\pm$ 0.2 & 40.2 \\
ARM & 49.0 $\pm$ 0.7 & 15.8 $\pm$ 0.3 & 40.8 $\pm$ 1.1 & 9.4 $\pm$ 0.2 & 53.0 $\pm$ 0.4 & 43.4 $\pm$ 0.3 & 35.2 \\
VREx & 46.5 $\pm$ 4.1 & 15.6 $\pm$ 1.8 & 35.8 $\pm$ 4.6 & 10.9 $\pm$ 0.3 & 49.6 $\pm$ 4.9 & 42.0 $\pm$ 3.0 & 33.4 \\
RSC & 55.0 $\pm$ 1.2 & 18.3 $\pm$ 0.5 & 44.4 $\pm$ 0.6 & 12.2 $\pm$ 0.2 & 55.7 $\pm$ 0.7 & 47.8 $\pm$ 0.9 & 38.9 \\
\bottomrule
\end{tabular}}
\end{center}
\subsubsection{Averages}
\begin{center}
\adjustbox{max width=\textwidth}{%
\begin{tabular}{lcccccccc}
\toprule
\textbf{Algorithm} & \textbf{ColoredMNIST} & \textbf{RotatedMNIST} & \textbf{VLCS} & \textbf{PACS} & \textbf{OfficeHome} & \textbf{TerraIncognita} & \textbf{DomainNet} & \textbf{Avg} \\
\midrule
ERM & 36.7 $\pm$ 0.1 & 97.7 $\pm$ 0.0 & 77.2 $\pm$ 0.4 & 83.0 $\pm$ 0.7 & 65.7 $\pm$ 0.5 & 41.4 $\pm$ 1.4 & 40.6 $\pm$ 0.2 & 63.2 \\
IRM & 40.3 $\pm$ 4.2 & 97.0 $\pm$ 0.2 & 76.3 $\pm$ 0.6 & 81.5 $\pm$ 0.8 & 64.3 $\pm$ 1.5 & 41.2 $\pm$ 3.6 & 33.5 $\pm$ 3.0 & 62.0 \\
GroupDRO & 36.8 $\pm$ 0.1 & 97.6 $\pm$ 0.1 & 77.9 $\pm$ 0.5 & 83.5 $\pm$ 0.2 & 65.2 $\pm$ 0.2 & 44.9 $\pm$ 1.4 & 33.0 $\pm$ 0.3 & 62.7 \\
Mixup & 33.4 $\pm$ 4.7 & 97.8 $\pm$ 0.0 & 77.7 $\pm$ 0.6 & 83.2 $\pm$ 0.4 & 67.0 $\pm$ 0.2 & 48.7 $\pm$ 0.4 & 38.5 $\pm$ 0.3 & 63.8 \\
MLDG & 36.7 $\pm$ 0.2 & 97.6 $\pm$ 0.0 & 77.2 $\pm$ 0.9 & 82.9 $\pm$ 1.7 & 66.1 $\pm$ 0.5 & 46.2 $\pm$ 0.9 & 41.0 $\pm$ 0.2 & 64.0 \\
CORAL & 39.7 $\pm$ 2.8 & 97.8 $\pm$ 0.1 & 78.7 $\pm$ 0.4 & 82.6 $\pm$ 0.5 & 68.5 $\pm$ 0.2 & 46.3 $\pm$ 1.7 & 41.1 $\pm$ 0.1 & 65.0 \\
MMD & 36.8 $\pm$ 0.1 & 97.8 $\pm$ 0.1 & 77.3 $\pm$ 0.5 & 83.2 $\pm$ 0.2 & 60.2 $\pm$ 5.2 & 46.5 $\pm$ 1.5 & 23.4 $\pm$ 9.5 & 60.7 \\
DANN & 40.7 $\pm$ 2.3 & 97.6 $\pm$ 0.2 & 76.9 $\pm$ 0.4 & 81.0 $\pm$ 1.1 & 64.9 $\pm$ 1.2 & 44.4 $\pm$ 1.1 & 38.2 $\pm$ 0.2 & 63.4 \\
CDANN & 39.1 $\pm$ 4.4 & 97.5 $\pm$ 0.2 & 77.5 $\pm$ 0.2 & 78.8 $\pm$ 2.2 & 64.3 $\pm$ 1.7 & 39.9 $\pm$ 3.2 & 38.0 $\pm$ 0.1 & 62.2 \\
MTL & 35.0 $\pm$ 1.7 & 97.8 $\pm$ 0.1 & 76.6 $\pm$ 0.5 & 83.7 $\pm$ 0.4 & 65.7 $\pm$ 0.5 & 44.9 $\pm$ 1.2 & 40.6 $\pm$ 0.1 & 63.5 \\
SagNet & 36.5 $\pm$ 0.1 & 94.0 $\pm$ 3.0 & 77.5 $\pm$ 0.3 & 82.3 $\pm$ 0.1 & 67.6 $\pm$ 0.3 & 47.2 $\pm$ 0.9 & 40.2 $\pm$ 0.2 & 63.6 \\
ARM & 36.8 $\pm$ 0.0 & 98.1 $\pm$ 0.1 & 76.6 $\pm$ 0.5 & 81.7 $\pm$ 0.2 & 64.4 $\pm$ 0.2 & 42.6 $\pm$ 2.7 & 35.2 $\pm$ 0.1 & 62.2 \\
VREx & 36.9 $\pm$ 0.3 & 93.6 $\pm$ 3.4 & 76.7 $\pm$ 1.0 & 81.3 $\pm$ 0.9 & 64.9 $\pm$ 1.3 & 37.3 $\pm$ 3.0 & 33.4 $\pm$ 3.1 & 60.6 \\
RSC & 36.5 $\pm$ 0.2 & 97.6 $\pm$ 0.1 & 77.5 $\pm$ 0.5 & 82.6 $\pm$ 0.7 & 65.8 $\pm$ 0.7 & 40.0 $\pm$ 0.8 & 38.9 $\pm$ 0.5 & 62.7 \\
\bottomrule
\end{tabular}}
\end{center}
\subsection{Model selection: test-domain validation set (oracle)}
\subsubsection{ColoredMNIST}
\begin{center}
\adjustbox{max width=\textwidth}{%
\begin{tabular}{lcccc}
\toprule
\textbf{Algorithm} & \textbf{+90\%} & \textbf{+80\%} & \textbf{-90\%} & \textbf{Avg} \\
\midrule
ERM & 71.8 $\pm$ 0.4 & 72.9 $\pm$ 0.1 & 28.7 $\pm$ 0.5 & 57.8 \\
IRM & 72.0 $\pm$ 0.1 & 72.5 $\pm$ 0.3 & 58.5 $\pm$ 3.3 & 67.7 \\
GroupDRO & 73.5 $\pm$ 0.3 & 73.0 $\pm$ 0.3 & 36.8 $\pm$ 2.8 & 61.1 \\
Mixup & 72.5 $\pm$ 0.2 & 73.9 $\pm$ 0.4 & 28.6 $\pm$ 0.2 & 58.4 \\
MLDG & 71.9 $\pm$ 0.3 & 73.5 $\pm$ 0.2 & 29.1 $\pm$ 0.9 & 58.2 \\
CORAL & 71.1 $\pm$ 0.2 & 73.4 $\pm$ 0.2 & 31.1 $\pm$ 1.6 & 58.6 \\
MMD & 69.0 $\pm$ 2.3 & 70.4 $\pm$ 1.6 & 50.6 $\pm$ 0.2 & 63.3 \\
DANN & 72.4 $\pm$ 0.5 & 73.9 $\pm$ 0.5 & 24.9 $\pm$ 2.7 & 57.0 \\
CDANN & 71.8 $\pm$ 0.5 & 72.9 $\pm$ 0.1 & 33.8 $\pm$ 6.4 & 59.5 \\
MTL & 71.2 $\pm$ 0.2 & 73.5 $\pm$ 0.2 & 28.0 $\pm$ 0.6 & 57.6 \\
SagNet & 72.1 $\pm$ 0.3 & 73.2 $\pm$ 0.3 & 29.4 $\pm$ 0.5 & 58.2 \\
ARM & 84.9 $\pm$ 0.9 & 76.8 $\pm$ 0.6 & 27.9 $\pm$ 2.1 & 63.2 \\
VREx & 72.8 $\pm$ 0.3 & 73.0 $\pm$ 0.3 & 55.2 $\pm$ 4.0 & 67.0 \\
RSC & 72.0 $\pm$ 0.1 & 73.2 $\pm$ 0.1 & 30.2 $\pm$ 1.6 & 58.5 \\
\bottomrule
\end{tabular}}
\end{center}
\subsubsection{RotatedMNIST}
\begin{center}
\adjustbox{max width=\textwidth}{%
\begin{tabular}{lccccccc}
\toprule
\textbf{Algorithm} & \textbf{0} & \textbf{15} & \textbf{30} & \textbf{45} & \textbf{60} & \textbf{75} & \textbf{Avg} \\
\midrule
ERM & 95.3 $\pm$ 0.2 & 98.7 $\pm$ 0.1 & 98.9 $\pm$ 0.1 & 98.7 $\pm$ 0.2 & 98.9 $\pm$ 0.0 & 96.2 $\pm$ 0.2 & 97.8 \\
IRM & 94.9 $\pm$ 0.6 & 98.7 $\pm$ 0.2 & 98.6 $\pm$ 0.1 & 98.6 $\pm$ 0.2 & 98.7 $\pm$ 0.1 & 95.2 $\pm$ 0.3 & 97.5 \\
GroupDRO & 95.9 $\pm$ 0.1 & 99.0 $\pm$ 0.1 & 98.9 $\pm$ 0.1 & 98.8 $\pm$ 0.1 & 98.6 $\pm$ 0.1 & 96.3 $\pm$ 0.4 & 97.9 \\
Mixup & 95.8 $\pm$ 0.3 & 98.7 $\pm$ 0.0 & 99.0 $\pm$ 0.1 & 98.8 $\pm$ 0.1 & 98.8 $\pm$ 0.1 & 96.6 $\pm$ 0.2 & 98.0 \\
MLDG & 95.7 $\pm$ 0.2 & 98.9 $\pm$ 0.1 & 98.8 $\pm$ 0.1 & 98.9 $\pm$ 0.1 & 98.6 $\pm$ 0.1 & 95.8 $\pm$ 0.4 & 97.8 \\
CORAL & 96.2 $\pm$ 0.2 & 98.8 $\pm$ 0.1 & 98.8 $\pm$ 0.1 & 98.8 $\pm$ 0.1 & 98.9 $\pm$ 0.1 & 96.4 $\pm$ 0.2 & 98.0 \\
MMD & 96.1 $\pm$ 0.2 & 98.9 $\pm$ 0.0 & 99.0 $\pm$ 0.0 & 98.8 $\pm$ 0.0 & 98.9 $\pm$ 0.0 & 96.4 $\pm$ 0.2 & 98.0 \\
DANN & 95.9 $\pm$ 0.1 & 98.9 $\pm$ 0.1 & 98.6 $\pm$ 0.2 & 98.7 $\pm$ 0.1 & 98.9 $\pm$ 0.0 & 96.3 $\pm$ 0.3 & 97.9 \\
CDANN & 95.9 $\pm$ 0.2 & 98.8 $\pm$ 0.0 & 98.7 $\pm$ 0.1 & 98.9 $\pm$ 0.1 & 98.8 $\pm$ 0.1 & 96.1 $\pm$ 0.3 & 97.9 \\
MTL & 96.1 $\pm$ 0.2 & 98.9 $\pm$ 0.0 & 99.0 $\pm$ 0.0 & 98.7 $\pm$ 0.1 & 99.0 $\pm$ 0.0 & 95.8 $\pm$ 0.3 & 97.9 \\
SagNet & 95.9 $\pm$ 0.1 & 99.0 $\pm$ 0.1 & 98.9 $\pm$ 0.1 & 98.6 $\pm$ 0.1 & 98.8 $\pm$ 0.1 & 96.3 $\pm$ 0.1 & 97.9 \\
ARM & 95.9 $\pm$ 0.4 & 99.0 $\pm$ 0.1 & 98.8 $\pm$ 0.1 & 98.9 $\pm$ 0.1 & 99.1 $\pm$ 0.1 & 96.7 $\pm$ 0.2 & 98.1 \\
VREx & 95.5 $\pm$ 0.2 & 99.0 $\pm$ 0.0 & 98.7 $\pm$ 0.2 & 98.8 $\pm$ 0.1 & 98.8 $\pm$ 0.0 & 96.4 $\pm$ 0.0 & 97.9 \\
RSC & 95.4 $\pm$ 0.1 & 98.6 $\pm$ 0.1 & 98.6 $\pm$ 0.1 & 98.9 $\pm$ 0.0 & 98.8 $\pm$ 0.1 & 95.4 $\pm$ 0.3 & 97.6 \\
\bottomrule
\end{tabular}}
\end{center}
\subsubsection{VLCS}
\begin{center}
\adjustbox{max width=\textwidth}{%
\begin{tabular}{lccccc}
\toprule
\textbf{Algorithm} & \textbf{C} & \textbf{L} & \textbf{S} & \textbf{V} & \textbf{Avg} \\
\midrule
ERM & 97.6 $\pm$ 0.3 & 67.9 $\pm$ 0.7 & 70.9 $\pm$ 0.2 & 74.0 $\pm$ 0.6 & 77.6 \\
IRM & 97.3 $\pm$ 0.2 & 66.7 $\pm$ 0.1 & 71.0 $\pm$ 2.3 & 72.8 $\pm$ 0.4 & 76.9 \\
GroupDRO & 97.7 $\pm$ 0.2 & 65.9 $\pm$ 0.2 & 72.8 $\pm$ 0.8 & 73.4 $\pm$ 1.3 & 77.4 \\
Mixup & 97.8 $\pm$ 0.4 & 67.2 $\pm$ 0.4 & 71.5 $\pm$ 0.2 & 75.7 $\pm$ 0.6 & 78.1 \\
MLDG & 97.1 $\pm$ 0.5 & 66.6 $\pm$ 0.5 & 71.5 $\pm$ 0.1 & 75.0 $\pm$ 0.9 & 77.5 \\
CORAL & 97.3 $\pm$ 0.2 & 67.5 $\pm$ 0.6 & 71.6 $\pm$ 0.6 & 74.5 $\pm$ 0.0 & 77.7 \\
MMD & 98.8 $\pm$ 0.0 & 66.4 $\pm$ 0.4 & 70.8 $\pm$ 0.5 & 75.6 $\pm$ 0.4 & 77.9 \\
DANN & 99.0 $\pm$ 0.2 & 66.3 $\pm$ 1.2 & 73.4 $\pm$ 1.4 & 80.1 $\pm$ 0.5 & 79.7 \\
CDANN & 98.2 $\pm$ 0.1 & 68.8 $\pm$ 0.5 & 74.3 $\pm$ 0.6 & 78.1 $\pm$ 0.5 & 79.9 \\
MTL & 97.9 $\pm$ 0.7 & 66.1 $\pm$ 0.7 & 72.0 $\pm$ 0.4 & 74.9 $\pm$ 1.1 & 77.7 \\
SagNet & 97.4 $\pm$ 0.3 & 66.4 $\pm$ 0.4 & 71.6 $\pm$ 0.1 & 75.0 $\pm$ 0.8 & 77.6 \\
ARM & 97.6 $\pm$ 0.6 & 66.5 $\pm$ 0.3 & 72.7 $\pm$ 0.6 & 74.4 $\pm$ 0.7 & 77.8 \\
VREx & 98.4 $\pm$ 0.2 & 66.4 $\pm$ 0.7 & 72.8 $\pm$ 0.1 & 75.0 $\pm$ 1.4 & 78.1 \\
RSC & 98.0 $\pm$ 0.4 & 67.2 $\pm$ 0.3 & 70.3 $\pm$ 1.3 & 75.6 $\pm$ 0.4 & 77.8 \\
\bottomrule
\end{tabular}}
\end{center}
\subsubsection{PACS}
\begin{center}
\adjustbox{max width=\textwidth}{%
\begin{tabular}{lccccc}
\toprule
\textbf{Algorithm} & \textbf{A} & \textbf{C} & \textbf{P} & \textbf{S} & \textbf{Avg} \\
\midrule
ERM & 86.5 $\pm$ 1.0 & 81.3 $\pm$ 0.6 & 96.2 $\pm$ 0.3 & 82.7 $\pm$ 1.1 & 86.7 \\
IRM & 84.2 $\pm$ 0.9 & 79.7 $\pm$ 1.5 & 95.9 $\pm$ 0.4 & 78.3 $\pm$ 2.1 & 84.5 \\
GroupDRO & 87.5 $\pm$ 0.5 & 82.9 $\pm$ 0.6 & 97.1 $\pm$ 0.3 & 81.1 $\pm$ 1.2 & 87.1 \\
Mixup & 87.5 $\pm$ 0.4 & 81.6 $\pm$ 0.7 & 97.4 $\pm$ 0.2 & 80.8 $\pm$ 0.9 & 86.8 \\
MLDG & 87.0 $\pm$ 1.2 & 82.5 $\pm$ 0.9 & 96.7 $\pm$ 0.3 & 81.2 $\pm$ 0.6 & 86.8 \\
CORAL & 86.6 $\pm$ 0.8 & 81.8 $\pm$ 0.9 & 97.1 $\pm$ 0.5 & 82.7 $\pm$ 0.6 & 87.1 \\
MMD & 88.1 $\pm$ 0.8 & 82.6 $\pm$ 0.7 & 97.1 $\pm$ 0.5 & 81.2 $\pm$ 1.2 & 87.2 \\
DANN & 87.0 $\pm$ 0.4 & 80.3 $\pm$ 0.6 & 96.8 $\pm$ 0.3 & 76.9 $\pm$ 1.1 & 85.2 \\
CDANN & 87.7 $\pm$ 0.6 & 80.7 $\pm$ 1.2 & 97.3 $\pm$ 0.4 & 77.6 $\pm$ 1.5 & 85.8 \\
MTL & 87.0 $\pm$ 0.2 & 82.7 $\pm$ 0.8 & 96.5 $\pm$ 0.7 & 80.5 $\pm$ 0.8 & 86.7 \\
SagNet & 87.4 $\pm$ 0.5 & 81.2 $\pm$ 1.2 & 96.3 $\pm$ 0.8 & 80.7 $\pm$ 1.1 & 86.4 \\
ARM & 85.0 $\pm$ 1.2 & 81.4 $\pm$ 0.2 & 95.9 $\pm$ 0.3 & 80.9 $\pm$ 0.5 & 85.8 \\
VREx & 87.8 $\pm$ 1.2 & 81.8 $\pm$ 0.7 & 97.4 $\pm$ 0.2 & 82.1 $\pm$ 0.7 & 87.2 \\
RSC & 86.0 $\pm$ 0.7 & 81.8 $\pm$ 0.9 & 96.8 $\pm$ 0.7 & 80.4 $\pm$ 0.5 & 86.2 \\
\bottomrule
\end{tabular}}
\end{center}
\subsubsection{OfficeHome}
\begin{center}
\adjustbox{max width=\textwidth}{%
\begin{tabular}{lccccc}
\toprule
\textbf{Algorithm} & \textbf{A} & \textbf{C} & \textbf{P} & \textbf{R} & \textbf{Avg} \\
\midrule
ERM & 61.7 $\pm$ 0.7 & 53.4 $\pm$ 0.3 & 74.1 $\pm$ 0.4 & 76.2 $\pm$ 0.6 & 66.4 \\
IRM & 56.4 $\pm$ 3.2 & 51.2 $\pm$ 2.3 & 71.7 $\pm$ 2.7 & 72.7 $\pm$ 2.7 & 63.0 \\
GroupDRO & 60.5 $\pm$ 1.6 & 53.1 $\pm$ 0.3 & 75.5 $\pm$ 0.3 & 75.9 $\pm$ 0.7 & 66.2 \\
Mixup & 63.5 $\pm$ 0.2 & 54.6 $\pm$ 0.4 & 76.0 $\pm$ 0.3 & 78.0 $\pm$ 0.7 & 68.0 \\
MLDG & 60.5 $\pm$ 0.7 & 54.2 $\pm$ 0.5 & 75.0 $\pm$ 0.2 & 76.7 $\pm$ 0.5 & 66.6 \\
CORAL & 64.8 $\pm$ 0.8 & 54.1 $\pm$ 0.9 & 76.5 $\pm$ 0.4 & 78.2 $\pm$ 0.4 & 68.4 \\
MMD & 60.4 $\pm$ 1.0 & 53.4 $\pm$ 0.5 & 74.9 $\pm$ 0.1 & 76.1 $\pm$ 0.7 & 66.2 \\
DANN & 60.6 $\pm$ 1.4 & 51.8 $\pm$ 0.7 & 73.4 $\pm$ 0.5 & 75.5 $\pm$ 0.9 & 65.3 \\
CDANN & 57.9 $\pm$ 0.2 & 52.1 $\pm$ 1.2 & 74.9 $\pm$ 0.7 & 76.2 $\pm$ 0.2 & 65.3 \\
MTL & 60.7 $\pm$ 0.8 & 53.5 $\pm$ 1.3 & 75.2 $\pm$ 0.6 & 76.6 $\pm$ 0.6 & 66.5 \\
SagNet & 62.7 $\pm$ 0.5 & 53.6 $\pm$ 0.5 & 76.0 $\pm$ 0.3 & 77.8 $\pm$ 0.1 & 67.5 \\
ARM & 58.8 $\pm$ 0.5 & 51.8 $\pm$ 0.7 & 74.0 $\pm$ 0.1 & 74.4 $\pm$ 0.2 & 64.8 \\
VREx & 59.6 $\pm$ 1.0 & 53.3 $\pm$ 0.3 & 73.2 $\pm$ 0.5 & 76.6 $\pm$ 0.4 & 65.7 \\
RSC & 61.7 $\pm$ 0.8 & 53.0 $\pm$ 0.9 & 74.8 $\pm$ 0.8 & 76.3 $\pm$ 0.5 & 66.5 \\
\bottomrule
\end{tabular}}
\end{center}
\subsubsection{TerraIncognita}
\begin{center}
\adjustbox{max width=\textwidth}{%
\begin{tabular}{lccccc}
\toprule
\textbf{Algorithm} & \textbf{L100} & \textbf{L38} & \textbf{L43} & \textbf{L46} & \textbf{Avg} \\
\midrule
ERM & 59.4 $\pm$ 0.9 & 49.3 $\pm$ 0.6 & 60.1 $\pm$ 1.1 & 43.2 $\pm$ 0.5 & 53.0 \\
IRM & 56.5 $\pm$ 2.5 & 49.8 $\pm$ 1.5 & 57.1 $\pm$ 2.2 & 38.6 $\pm$ 1.0 & 50.5 \\
GroupDRO & 60.4 $\pm$ 1.5 & 48.3 $\pm$ 0.4 & 58.6 $\pm$ 0.8 & 42.2 $\pm$ 0.8 & 52.4 \\
Mixup & 67.6 $\pm$ 1.8 & 51.0 $\pm$ 1.3 & 59.0 $\pm$ 0.0 & 40.0 $\pm$ 1.1 & 54.4 \\
MLDG & 59.2 $\pm$ 0.1 & 49.0 $\pm$ 0.9 & 58.4 $\pm$ 0.9 & 41.4 $\pm$ 1.0 & 52.0 \\
CORAL & 60.4 $\pm$ 0.9 & 47.2 $\pm$ 0.5 & 59.3 $\pm$ 0.4 & 44.4 $\pm$ 0.4 & 52.8 \\
MMD & 60.6 $\pm$ 1.1 & 45.9 $\pm$ 0.3 & 57.8 $\pm$ 0.5 & 43.8 $\pm$ 1.2 & 52.0 \\
DANN & 55.2 $\pm$ 1.9 & 47.0 $\pm$ 0.7 & 57.2 $\pm$ 0.9 & 42.9 $\pm$ 0.9 & 50.6 \\
CDANN & 56.3 $\pm$ 2.0 & 47.1 $\pm$ 0.9 & 57.2 $\pm$ 1.1 & 42.4 $\pm$ 0.8 & 50.8 \\
MTL & 58.4 $\pm$ 2.1 & 48.4 $\pm$ 0.8 & 58.9 $\pm$ 0.6 & 43.0 $\pm$ 1.3 & 52.2 \\
SagNet & 56.4 $\pm$ 1.9 & 50.5 $\pm$ 2.3 & 59.1 $\pm$ 0.5 & 44.1 $\pm$ 0.6 & 52.5 \\
ARM & 60.1 $\pm$ 1.5 & 48.3 $\pm$ 1.6 & 55.3 $\pm$ 0.6 & 40.9 $\pm$ 1.1 & 51.2 \\
VREx & 56.8 $\pm$ 1.7 & 46.5 $\pm$ 0.5 & 58.4 $\pm$ 0.3 & 43.8 $\pm$ 0.3 & 51.4 \\
RSC & 59.9 $\pm$ 1.4 & 46.7 $\pm$ 0.4 & 57.8 $\pm$ 0.5 & 44.3 $\pm$ 0.6 & 52.1 \\
\bottomrule
\end{tabular}}
\end{center}
\subsubsection{DomainNet}
\begin{center}
\adjustbox{max width=\textwidth}{%
\begin{tabular}{lccccccc}
\toprule
\textbf{Algorithm} & \textbf{clip} & \textbf{info} & \textbf{paint} & \textbf{quick} & \textbf{real} & \textbf{sketch} & \textbf{Avg} \\
\midrule
ERM & 58.6 $\pm$ 0.3 & 19.2 $\pm$ 0.2 & 47.0 $\pm$ 0.3 & 13.2 $\pm$ 0.2 & 59.9 $\pm$ 0.3 & 49.8 $\pm$ 0.4 & 41.3 \\
IRM & 40.4 $\pm$ 6.6 & 12.1 $\pm$ 2.7 & 31.4 $\pm$ 5.7 & 9.8 $\pm$ 1.2 & 37.7 $\pm$ 9.0 & 36.7 $\pm$ 5.3 & 28.0 \\
GroupDRO & 47.2 $\pm$ 0.5 & 17.5 $\pm$ 0.4 & 34.2 $\pm$ 0.3 & 9.2 $\pm$ 0.4 & 51.9 $\pm$ 0.5 & 40.1 $\pm$ 0.6 & 33.4 \\
Mixup & 55.6 $\pm$ 0.1 & 18.7 $\pm$ 0.4 & 45.1 $\pm$ 0.5 & 12.8 $\pm$ 0.3 & 57.6 $\pm$ 0.5 & 48.2 $\pm$ 0.4 & 39.6 \\
MLDG & 59.3 $\pm$ 0.1 & 19.6 $\pm$ 0.2 & 46.8 $\pm$ 0.2 & 13.4 $\pm$ 0.2 & 60.1 $\pm$ 0.4 & 50.4 $\pm$ 0.3 & 41.6 \\
CORAL & 59.2 $\pm$ 0.1 & 19.9 $\pm$ 0.2 & 47.4 $\pm$ 0.2 & 14.0 $\pm$ 0.4 & 59.8 $\pm$ 0.2 & 50.4 $\pm$ 0.4 & 41.8 \\
MMD & 32.2 $\pm$ 13.3 & 11.2 $\pm$ 4.5 & 26.8 $\pm$ 11.3 & 8.8 $\pm$ 2.2 & 32.7 $\pm$ 13.8 & 29.0 $\pm$ 11.8 & 23.5 \\
DANN & 53.1 $\pm$ 0.2 & 18.3 $\pm$ 0.1 & 44.2 $\pm$ 0.7 & 11.9 $\pm$ 0.1 & 55.5 $\pm$ 0.4 & 46.8 $\pm$ 0.6 & 38.3 \\
CDANN & 54.6 $\pm$ 0.4 & 17.3 $\pm$ 0.1 & 44.2 $\pm$ 0.7 & 12.8 $\pm$ 0.2 & 56.2 $\pm$ 0.4 & 45.9 $\pm$ 0.5 & 38.5 \\
MTL & 58.0 $\pm$ 0.4 & 19.2 $\pm$ 0.2 & 46.2 $\pm$ 0.1 & 12.7 $\pm$ 0.2 & 59.9 $\pm$ 0.1 & 49.0 $\pm$ 0.0 & 40.8 \\
SagNet & 57.7 $\pm$ 0.3 & 19.1 $\pm$ 0.1 & 46.3 $\pm$ 0.5 & 13.5 $\pm$ 0.4 & 58.9 $\pm$ 0.4 & 49.5 $\pm$ 0.2 & 40.8 \\
ARM & 49.6 $\pm$ 0.4 & 16.5 $\pm$ 0.3 & 41.5 $\pm$ 0.8 & 10.8 $\pm$ 0.1 & 53.5 $\pm$ 0.3 & 43.9 $\pm$ 0.4 & 36.0 \\
VREx & 43.3 $\pm$ 4.5 & 14.1 $\pm$ 1.8 & 32.5 $\pm$ 5.0 & 9.8 $\pm$ 1.1 & 43.5 $\pm$ 5.6 & 37.7 $\pm$ 4.5 & 30.1 \\
RSC & 55.0 $\pm$ 1.2 & 18.3 $\pm$ 0.5 & 44.4 $\pm$ 0.6 & 12.5 $\pm$ 0.1 & 55.7 $\pm$ 0.7 & 47.8 $\pm$ 0.9 & 38.9 \\
\bottomrule
\end{tabular}}
\end{center}
\subsubsection{Averages}
\begin{center}
\adjustbox{max width=\textwidth}{%
\begin{tabular}{lcccccccc}
\toprule
\textbf{Algorithm} & \textbf{ColoredMNIST} & \textbf{RotatedMNIST} & \textbf{VLCS} & \textbf{PACS} & \textbf{OfficeHome} & \textbf{TerraIncognita} & \textbf{DomainNet} & \textbf{Avg} \\
\midrule
ERM & 57.8 $\pm$ 0.2 & 97.8 $\pm$ 0.1 & 77.6 $\pm$ 0.3 & 86.7 $\pm$ 0.3 & 66.4 $\pm$ 0.5 & 53.0 $\pm$ 0.3 & 41.3 $\pm$ 0.1 & 68.7 \\
IRM & 67.7 $\pm$ 1.2 & 97.5 $\pm$ 0.2 & 76.9 $\pm$ 0.6 & 84.5 $\pm$ 1.1 & 63.0 $\pm$ 2.7 & 50.5 $\pm$ 0.7 & 28.0 $\pm$ 5.1 & 66.9 \\
GroupDRO & 61.1 $\pm$ 0.9 & 97.9 $\pm$ 0.1 & 77.4 $\pm$ 0.5 & 87.1 $\pm$ 0.1 & 66.2 $\pm$ 0.6 & 52.4 $\pm$ 0.1 & 33.4 $\pm$ 0.3 & 67.9 \\
Mixup & 58.4 $\pm$ 0.2 & 98.0 $\pm$ 0.1 & 78.1 $\pm$ 0.3 & 86.8 $\pm$ 0.3 & 68.0 $\pm$ 0.2 & 54.4 $\pm$ 0.3 & 39.6 $\pm$ 0.1 & 69.0 \\
MLDG & 58.2 $\pm$ 0.4 & 97.8 $\pm$ 0.1 & 77.5 $\pm$ 0.1 & 86.8 $\pm$ 0.4 & 66.6 $\pm$ 0.3 & 52.0 $\pm$ 0.1 & 41.6 $\pm$ 0.1 & 68.7 \\
CORAL & 58.6 $\pm$ 0.5 & 98.0 $\pm$ 0.0 & 77.7 $\pm$ 0.2 & 87.1 $\pm$ 0.5 & 68.4 $\pm$ 0.2 & 52.8 $\pm$ 0.2 & 41.8 $\pm$ 0.1 & 69.2 \\
MMD & 63.3 $\pm$ 1.3 & 98.0 $\pm$ 0.1 & 77.9 $\pm$ 0.1 & 87.2 $\pm$ 0.1 & 66.2 $\pm$ 0.3 & 52.0 $\pm$ 0.4 & 23.5 $\pm$ 9.4 & 66.9 \\
DANN & 57.0 $\pm$ 1.0 & 97.9 $\pm$ 0.1 & 79.7 $\pm$ 0.5 & 85.2 $\pm$ 0.2 & 65.3 $\pm$ 0.8 & 50.6 $\pm$ 0.4 & 38.3 $\pm$ 0.1 & 67.7 \\
CDANN & 59.5 $\pm$ 2.0 & 97.9 $\pm$ 0.0 & 79.9 $\pm$ 0.2 & 85.8 $\pm$ 0.8 & 65.3 $\pm$ 0.5 & 50.8 $\pm$ 0.6 & 38.5 $\pm$ 0.2 & 68.2 \\
MTL & 57.6 $\pm$ 0.3 & 97.9 $\pm$ 0.1 & 77.7 $\pm$ 0.5 & 86.7 $\pm$ 0.2 & 66.5 $\pm$ 0.4 & 52.2 $\pm$ 0.4 & 40.8 $\pm$ 0.1 & 68.5 \\
SagNet & 58.2 $\pm$ 0.3 & 97.9 $\pm$ 0.0 & 77.6 $\pm$ 0.1 & 86.4 $\pm$ 0.4 & 67.5 $\pm$ 0.2 & 52.5 $\pm$ 0.4 & 40.8 $\pm$ 0.2 & 68.7 \\
ARM & 63.2 $\pm$ 0.7 & 98.1 $\pm$ 0.1 & 77.8 $\pm$ 0.3 & 85.8 $\pm$ 0.2 & 64.8 $\pm$ 0.4 & 51.2 $\pm$ 0.5 & 36.0 $\pm$ 0.2 & 68.1 \\
VREx & 67.0 $\pm$ 1.3 & 97.9 $\pm$ 0.1 & 78.1 $\pm$ 0.2 & 87.2 $\pm$ 0.6 & 65.7 $\pm$ 0.3 & 51.4 $\pm$ 0.5 & 30.1 $\pm$ 3.7 & 68.2 \\
RSC & 58.5 $\pm$ 0.5 & 97.6 $\pm$ 0.1 & 77.8 $\pm$ 0.6 & 86.2 $\pm$ 0.5 & 66.5 $\pm$ 0.6 & 52.1 $\pm$ 0.2 & 38.9 $\pm$ 0.6 & 68.2 \\
\bottomrule
\end{tabular}}
\end{center}
\end{document}