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| 20 | +\newlabel{intro}{{I}{1}{Introduction}{section.1}{}} |
| 21 | +\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Dynamics in Algorithmic Recourse: (a) we have a simple linear classifier trained for binary classification where samples from the negative class ($y=0$) are marked in blue and samples of the positive class ($y=1$) are marked in orange; (b) the implementation of AR for a random subset of individuals leads to a noticable domain shift; (c) as the classifier is retrained we observe a corresponding model shift; (d) as this process is repeated, the decision boundary moves away from the target class.}}{2}{figure.1}\protected@file@percent } |
| 22 | +\newlabel{fig:poc}{{1}{2}{Dynamics in Algorithmic Recourse: (a) we have a simple linear classifier trained for binary classification where samples from the negative class ($y=0$) are marked in blue and samples of the positive class ($y=1$) are marked in orange; (b) the implementation of AR for a random subset of individuals leads to a noticable domain shift; (c) as the classifier is retrained we observe a corresponding model shift; (d) as this process is repeated, the decision boundary moves away from the target class}{figure.1}{}} |
| 23 | +\newlabel{exm:consumer}{{I.1}{2}{Consumer Credit}{example.1.1}{}} |
| 24 | +\newlabel{exm:student}{{I.2}{2}{Student Admission}{example.1.2}{}} |
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| 46 | +\newlabel{prp:costs}{{IV.2}{5}{Costs}{proposition.4.2}{}} |
| 47 | +\newlabel{prp:het}{{IV.3}{5}{Heterogeneity}{proposition.4.3}{}} |
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| 67 | +\newlabel{tab:architecture}{{I}{7}{Neural network architectures and training parameters}{table.1}{}} |
| 68 | +\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Synthetic classification datasets used in our experiments. Samples from the negative class ($y=0$) are marked in blue while samples of the positive class ($y=1$) are marked in orange.}}{7}{figure.2}\protected@file@percent } |
| 69 | +\newlabel{fig:synthetic-data}{{2}{7}{Synthetic classification datasets used in our experiments. Samples from the negative class ($y=0$) are marked in blue while samples of the positive class ($y=1$) are marked in orange}{figure.2}{}} |
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| 80 | +\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces Results for synthetic data with overlapping classes. The shown model MMD (PP MMD) was computed over a mesh grid of 1,000 points. Error bars indicate the standard deviation across folds.}}{9}{figure.3}\protected@file@percent } |
| 81 | +\newlabel{fig:syn}{{3}{9}{Results for synthetic data with overlapping classes. The shown model MMD (PP MMD) was computed over a mesh grid of 1,000 points. Error bars indicate the standard deviation across folds}{figure.3}{}} |
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| 83 | +\newlabel{fig:real}{{4}{9}{Results for deep ensemble using real-world datasets. The shown model MMD (PP MMD) was computed over actual samples, rather than a mesh grid. Error bars indicate the standard deviation across folds}{figure.4}{}} |
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| 85 | +\newlabel{mitigate}{{VII}{9}{Mitigation Strategies and Experiments}{section.7}{}} |
| 86 | +\newlabel{prp:mitigate}{{VII.1}{9}{Mitigation Strategies}{proposition.7.1}{}} |
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| 95 | +\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces Illustrative example demonstrating the properties of the various mitigation strategies. Samples from the negative class ($y=0$) are marked in blue while samples of the positive class ($y=1$) are marked in orange.}}{10}{figure.5}\protected@file@percent } |
| 96 | +\newlabel{fig:mitigation}{{5}{10}{Illustrative example demonstrating the properties of the various mitigation strategies. Samples from the negative class ($y=0$) are marked in blue while samples of the positive class ($y=1$) are marked in orange}{figure.5}{}} |
| 97 | +\@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces The differences in counterfactual outcomes when using the various mitigation strategies compared to the baseline approach, that is Wachter with $\gamma =0.5$. Results for synthetic data with overlapping classes. The shown model MMD (PP MMD) was computed over a mesh grid of points. Error bars indicate the standard deviation across folds.}}{11}{figure.6}\protected@file@percent } |
| 98 | +\newlabel{fig:mitigate-results}{{6}{11}{The differences in counterfactual outcomes when using the various mitigation strategies compared to the baseline approach, that is Wachter with $\gamma =0.5$. Results for synthetic data with overlapping classes. The shown model MMD (PP MMD) was computed over a mesh grid of points. Error bars indicate the standard deviation across folds}{figure.6}{}} |
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| 102 | +\newlabel{fig:mitigate-real-world-results}{{8}{11}{The differences in counterfactual outcomes when using the various mitigation strategies compared to the baseline approach, that is Wachter with $\gamma =0.5$. Results for deep ensemble using real-world datasets. The shown model MMD (PP MMD) was computed over actual samples, rather than a mesh grid. Error bars indicate the standard deviation across folds}{figure.8}{}} |
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