From 08563833811d97eed13c75a4448b6010fb68f327 Mon Sep 17 00:00:00 2001 From: pat-alt Date: Fri, 8 Jul 2022 15:09:42 +0200 Subject: [PATCH] bleh --- paper/paper.qmd | 3 ++- paper/sections/methodology.qmd | 6 +----- 2 files changed, 3 insertions(+), 6 deletions(-) diff --git a/paper/paper.qmd b/paper/paper.qmd index bfb899e..54b7d74 100755 --- a/paper/paper.qmd +++ b/paper/paper.qmd @@ -1,7 +1,8 @@ --- title: "Endogenous Dynamics in Algorithmic Recourse" author: | - \author{\IEEEauthorblockN{Patrick Altmeyer} + \author{ + \IEEEauthorblockN{Patrick Altmeyer} \IEEEauthorblockA{\textit{EEMCS} \\ \textit{Delft University of Technology}\\ Delft, Netherlands \\ diff --git a/paper/sections/methodology.qmd b/paper/sections/methodology.qmd index 179a6f4..5953a7c 100644 --- a/paper/sections/methodology.qmd +++ b/paper/sections/methodology.qmd @@ -6,13 +6,9 @@ In the following we first set out a generalized framework for gradient-based cou In this work we have chosen to focus on a number of gradient-based counterfactual generators to investigate the endogenous dynamics we introduced in @sec-intro. Gradient-based counterfactual search is well-suited for differentiable black-box models like deep neural networks. We can restate @eq-solution in a more general form that encompasses most gradient-based approaches to counterfactual search: -[AGREE ON NOTATION] - $$ \begin{aligned} -\mathbf{s}^\prime &= \arg \min_{\mathbf{s}^\prime \in \mathcal{S}} \left( {\left\{\ell(M(f(s_k^\prime)),t)\right\}_K}^\mathsf{T} \mathbf{1}_K + \lambda {\left\{h(f(s_k^\prime)) \right\}_K}^\mathsf{T} \mathbf{1}_K \right) \\ -&= \arg \min_{\mathbf{s}^\prime \in \mathcal{S}} \left\{ \left(\ell . ((M\circ f).(\mathbf{s}^\prime),t) + \lambda (h \circ f).(\mathbf{s}^\prime)\right)^\mathsf{T} \mathbf{1}_K \right\} \\ -&= \arg \min_{\mathbf{s}^\prime \in \mathcal{S}} \left\{ \sum_{k=1}^{K} {\ell(M(f(s_k^\prime)),t)}+ \lambda {h(f(s_k^\prime)) } \right\} +\mathbf{s}^\prime &= \arg \min_{\mathbf{s}^\prime \in \mathcal{S}} \left\{ \sum_{k=1}^{K} {\ell(M(f(s_k^\prime)),t)}+ \lambda {h(f(s_k^\prime)) } \right\} \end{aligned} $$ {#eq-general}