mata me

paper/body.tex

@@ -7,9 +7,9 @@
 
 \section{Introduction}\label{intro}
 
-Counterfactual Explanations (CE) provide a powerful, flexible and intuitive way to not only explain black-box models but also help affected individuals through the means of Algorithmic Recourse. Instead of opening the Black Box, CE works under the premise of strategically perturbing model inputs to understand model behaviour~\citep{wachter2017counterfactual}. Intuitively speaking, we generate explanations in this context by asking what-if questions of the following nature: `Our credit risk model currently predicts that this individual is not credit-worthy. What if they reduced their monthly expenditures by 10\%?'
+Counterfactual Explanations (CE) provide a powerful, flexible and intuitive way to not only explain black-box models but also help affected individuals through the means of Algorithmic Recourse. Instead of opening the black box, Counterfactual Explanations work under the premise of strategically perturbing model inputs to understand model behaviour~\citep{wachter2017counterfactual}. Intuitively speaking, we generate explanations in this context by asking what-if questions of the following nature: `Our credit risk model currently predicts that this individual is not credit-worthy. What if they reduced their monthly expenditures by 10\%?'
 
-This is typically implemented by defining a target outcome $\mathbf{y}^+ \in \mathcal{Y}$ for some individual $\mathbf{x} \in \mathcal{X}=\mathbb{R}^D$ described by $D$ attributes, for which the model $M_{\theta}:\mathcal{X}\mapsto\mathcal{Y}$ initially predicts a different outcome: $M_{\theta}(\mathbf{x})\ne \mathbf{y}^+$. Counterfactuals are then searched by minimizing a loss function that compares the predicted model output to the target outcome: $\text{yloss}(M_{\theta}(\mathbf{x}),\mathbf{y}^+)$. Since CE work directly with the black-box model, valid counterfactuals always have full local fidelity by construction where fidelity is defined as the degree to which explanations approximate the predictions of a black-box model~\citep{mothilal2020explaining,molnar2020interpretable}. 
+This is typically implemented by defining a target outcome $\mathbf{y}^+ \in \mathcal{Y}$ for some individual $\mathbf{x} \in \mathcal{X}=\mathbb{R}^D$ described by $D$ attributes, for which the model $M_{\theta}:\mathcal{X}\mapsto\mathcal{Y}$ initially predicts a different outcome: $M_{\theta}(\mathbf{x})\ne \mathbf{y}^+$. Counterfactuals are then searched by minimizing a loss function that compares the predicted model output to the target outcome: $\text{yloss}(M_{\theta}(\mathbf{x}),\mathbf{y}^+)$. Since Counterfactual Explanations work directly with the black-box model, valid counterfactuals always have full local fidelity by construction where fidelity is defined as the degree to which explanations approximate the predictions of a black-box model~\citep{mothilal2020explaining,molnar2020interpretable}. 
 
 In situations where full fidelity is a requirement, CE offer a more appropriate solution to Explainable Artificial Intelligence (XAI) than other popular approaches like LIME~\citep{ribeiro2016why} and SHAP~\citep{lundberg2017unified}, which involve local surrogate models. But even full fidelity is not a sufficient condition for ensuring that an explanation faithfully describes the behaviour of a model. That is because multiple very distinct explanations can all lead to the same model prediction, especially when dealing with heavily parameterized models like deep neural networks, which are typically underspecified by the data~\citep{wilson2020case}.
 

results_mpi/params/linearly_separable_generator_params.csv

+dataname,eta,lambda_1,lambda_1_Δ,lambda_2,lambda_2_Δ,lambda_3,lambda_3_Δ,n_individuals,opt
+Linearly Separable,0.01,0.25,0.25,0.75,0.75,0.75,0.75,25,Descent

results_mpi/params/linearly_separable_model_params.csv

+activation,batch_size,dataname,epochs,jem_sampling_steps,lambda,n_ens,n_hidden,n_layers,n_obs,sgld_batch_size
+relu,100,Linearly Separable,100,50,0.1,5,32,3,1000,50

results_mpi/params/linearly_separable_model_performance.csv

+acc,precision,f1score,mod_name,dataname
+0.992,0.992,0.992,JEM Ensemble,Linearly Separable
+0.992,0.992,0.992,MLP,Linearly Separable
+0.992,0.992,0.992,MLP Ensemble,Linearly Separable
+0.988,0.98828125,0.9879982717511322,JEM,Linearly Separable