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diff --git a/paper/paper.tex b/paper/paper.tex
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--- a/paper/paper.tex
+++ b/paper/paper.tex
@@ -31,10 +31,11 @@
\usepackage{microtype} % microtypography
\usepackage{xcolor} % colors
\usepackage{amsmath}
+\usepackage{graphicx}
% Bibliography
\bibliographystyle{plainnat}
-\setcitestyle{authoryear, round, comma}
+\setcitestyle{numbers,square,comma}
\title{Conformal Counterfactual Explanations}
@@ -118,26 +119,24 @@ Most state-of-the-art approaches to generating Counterfactual Explanations (CE)
where $\text{yloss}$ denotes the primary loss function already introduced above and $\text{cost}$ is either a single penalty or a collection of penalties that are used to impose constraints through regularization. Following the convention in \citet{altmeyer2023endogenous} we use $\mathbf{s}^\prime=\{ s_k\}_K$ to denote the vector $K$-dimensional array of counterfactual states. This is to explicitly account for the fact that we can generate multiple counterfactuals, as with DiCE \citep{mothilal2020explaining}, and may choose to traverse a latent representation $\mathcal{Z}$ of the feature space $\mathcal{X}$, as we will discuss further below.
-Solutions to Equation~\ref{eq:general} are considered valid as soon as the predicted label matches the target label. A stripped-down counterfactual explanation is therefore little different from an adversarial example. In, for example, generic counterfactual search as in \citet{wachter2017counterfactual} has been applied to MNIST data.
+Solutions to Equation~\ref{eq:general} are considered valid as soon as the predicted label matches the target label. A stripped-down counterfactual explanation is therefore little different from an adversarial example. In Figure~\ref{fig:adv}, for example, generic counterfactual search as in \citet{wachter2017counterfactual} has been applied to MNIST data.
+
+To properly serve both AI practitioners and individuals affected by AI decision-making systems, Counterfactual Explanations should have certain desirable properties, sometimes referred to as \textit{desiderata}. Besides diversity, which we already introduced above, some of the most prominent desiderata include sparsity, proximity \citep{wachter2017counterfactual}, actionability~\citep{ustun2019actionable}, plausibility \citep{joshi2019realistic,poyiadzi2020face,schut2021generating}, robustness \citep{upadhyay2021robust,pawelczyk2022probabilistically,altmeyer2023endogenous} and causality~\citep{karimi2021algorithmic}. Researchers have come up with various ways to meet these desiderata, which have been surveyed in~\citep{verma2020counterfactual} and~\citep{karimi2020survey}.
\begin{figure}
\centering
- \fbox{\rule[-.5cm]{0cm}{4cm} \rule[-.5cm]{4cm}{0cm}}
- \caption{Sample figure caption.}
+ \begin{minipage}[t]{0.45\textwidth}
+ \centering
+ \includegraphics[width=\textwidth]{www/you_may_not_like_it.png}
+ \caption{You may not like it, but this is what stripped-down counterfactuals look like. Counterfactuals for turning an 8 (eight) into a 3 (three) using different methodologies. Left: Using the generic approach proposed in \citet{wachter2017counterfactual}. Center: Using REVISE \citep{joshi2019realistic} with a well-specified surrogate. Right: Using REVISE \citep{joshi2019realistic} with a poorly specified surrogate.}\label{fig:adv}
+ \end{minipage}\hfill
+ \begin{minipage}[t]{0.45\textwidth}
+ \centering
+ \includegraphics[width=\textwidth]{www/mnist_9to4_latent.png}
+ \caption{Using surrogates introduces a dependency. Counterfactuals for turning a 9 (nine) into a 4 (four) using REVISE: original image (left); counterfactual using a well-specified surrogate (center); and counterfactual using a poorly specified surrogate (right).}\label{fig:vae}
+ \end{minipage}
\end{figure}
-To properly serve both AI practitioners and individuals affected by AI decision-making systems, Counterfactual Explanations should have certain desirable properties, sometimes referred to as \textit{desiderata}. Besides diversity, which we already introduced above, some of the most prominent desiderata include sparsity, proximity \citep{wachter2017counterfactual}, actionability~\citep{ustun2019actionable}, plausibility \citep{joshi2019realistic,poyiadzi2020face,schut2021generating}, robustness \citep{upadhyay2021robust,pawelczyk2022probabilistically,altmeyer2023endogenous} and causality~\citep{karimi2021algorithmic}. Researchers have come up with various ways to meet these desiderata, which have been surveyed in~\citep{verma2020counterfactual} and~\citep{karimi2020survey}.
-
-
-\section*{References}
-
-
-References follow the acknowledgments. Use unnumbered first-level heading for
-the references. Any choice of citation style is acceptable as long as you are
-consistent. It is permissible to reduce the font size to \verb+small+ (9 point)
-when listing the references.
-Note that the Reference section does not count towards the page limit.
-
\medskip
\bibliography{../bib}
@@ -499,6 +498,14 @@ More information about this disclosure can be found at: \url{https://neurips.cc/
Do {\bf not} include this section in the anonymized submission, only in the final paper. You can use the \texttt{ack} environment provided in the style file to autmoatically hide this section in the anonymized submission.
\end{ack}
+\section*{References}
+
+
+References follow the acknowledgments. Use unnumbered first-level heading for
+the references. Any choice of citation style is acceptable as long as you are
+consistent. It is permissible to reduce the font size to \verb+small+ (9 point)
+when listing the references.
+Note that the Reference section does not count towards the page limit.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section*{Checklist}
diff --git a/notebooks/www/you_may_not_like_it.png b/paper/www/you_may_not_like_it.png
similarity index 100%
rename from notebooks/www/you_may_not_like_it.png
rename to paper/www/you_may_not_like_it.png