diff --git a/paper/paper.pdf b/paper/paper.pdf index 5fde1fdb46b2fca30789821d61249c4fd56ab2ec..3c38aed66327ec9e907742399e995a88f2ccd3b8 100644 Binary files a/paper/paper.pdf and b/paper/paper.pdf differ diff --git a/paper/paper.tex b/paper/paper.tex index 54dedfd2130ac174c7b4d0ada1ce8ab27c066dba..bf8001ced75a889406b9ba1c34ef407415bf2542 100644 --- a/paper/paper.tex +++ b/paper/paper.tex @@ -164,7 +164,7 @@ The word \textit{fidelity} stems from the Latin word `fidelis', which means `fai \begin{definition}[Conformal Counterfactuals] \label{def:conformal} - Let $\mathcal{X}_{\theta}|y=t = p_{\theta}(x|y=t)$ denote the conditional distribution of $x$ in the target class $t$, where $theta$ denotes the parameters of model $M$. Then for $x^{\prime}$ to be considered a conformal counterfactual, we need: $x^{\prime} \sim \mathcal{X}_{\theta}|y=t$. + Let $\mathcal{X}_{\theta}|t = p_{\theta}(x|y=t)$ denote the conditional distribution of $x$ in the target class $t$, where $theta$ denotes the parameters of model $M$. Then for $x^{\prime}$ to be considered a conformal counterfactual, we need: $x^{\prime} \sim \mathcal{X}_{\theta}|t$. \end{definition} In words, conformal counterfactuals conform with what the predictive model has learned about the input data $x$. Since this definition works with distributional properties, it explicitly accounts for the multiplicity of explanations we discussed earlier. Except for the posterior conditional distribution $p_{\theta}(x|y=t)$, we already have access to all the ingredients in Definition~\ref{def:conformal}. @@ -173,6 +173,9 @@ How can we quantify $p_{\theta}(x|y=t)$? After all, the predictive model $M$ was Fortunately, recent work by \citet{grathwohl2020your} on Energy Based Models (EBM) has pointed out that there is a generative model hidden within every discriminative model. \citet{schut2021generating} were the first to notice and leverage this in the context of CE. +\subsection{Conformal Training meets Counterfactual Explanations} + +\section{Experiments} \medskip