From 8aee1501dc45afa0d33b83aa2ee5839f32f5d8ab Mon Sep 17 00:00:00 2001
From: Pat Alt <55311242+pat-alt@users.noreply.github.com>
Date: Wed, 17 May 2023 19:24:47 +0200
Subject: [PATCH] ufff

---
 artifacts/results/gmsc_benchmark.csv          | 2760 ++++++++---------
 artifacts/results/gmsc_model_performance.csv  |    8 +-
 artifacts/results/gmsc_model_performance.jls  |  Bin 361 -> 361 bytes
 artifacts/results/gmsc_models.jls             |  Bin 3678034 -> 1470034 bytes
 .../results/images/circles_generated_JEM.png  |  Bin 192521 -> 192409 bytes
 .../results/images/circles_generated_MLP.png  |  Bin 183197 -> 183191 bytes
 artifacts/results/images/gmsc_benchmark.png   |  Bin 507092 -> 469107 bytes
 .../results/images/mnist_eccco_all_digits.png |  Bin 205947 -> 464115 bytes
 .../results/images/moons_generated_JEM.png    |  Bin 232176 -> 232181 bytes
 .../results/images/moons_generated_MLP.png    |  Bin 187081 -> 187118 bytes
 artifacts/results/mnist_architectures.jls     |  Bin 33211 -> 33211 bytes
 artifacts/results/mnist_vae.jls               |  Bin 1003682 -> 1003682 bytes
 artifacts/results/mnist_vae_weak.jls          |  Bin 105130 -> 105130 bytes
 notebooks/circles.qmd                         |   16 +-
 notebooks/gmsc.qmd                            |   19 +-
 notebooks/linearly_separable.qmd              |   16 +-
 notebooks/mnist.qmd                           |   31 +-
 notebooks/moons.qmd                           |   16 +-
 notebooks/tables.Rmd                          |   55 +-
 paper/contents/table_all_valid.tex            |    2 +-
 paper/contents/table_ebm_params.tex           |   17 +
 paper/contents/table_params.tex               |   19 +
 paper/paper.pdf                               |  Bin 1363535 -> 1930156 bytes
 paper/paper.tex                               |   51 +-
 24 files changed, 1606 insertions(+), 1404 deletions(-)
 create mode 100644 paper/contents/table_ebm_params.tex
 create mode 100644 paper/contents/table_params.tex

diff --git a/artifacts/results/gmsc_benchmark.csv b/artifacts/results/gmsc_benchmark.csv
index aa40c331..6b2a2040 100644
--- a/artifacts/results/gmsc_benchmark.csv
+++ b/artifacts/results/gmsc_benchmark.csv
@@ -1,1921 +1,1921 @@
 sample,variable,value,dataname,generator,model,target,factual
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 10,validity,1.0,GMSC,ECCCo,JEM Ensemble,1,0
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diff --git a/artifacts/results/gmsc_model_performance.csv b/artifacts/results/gmsc_model_performance.csv
index bbcf6e19..0011835c 100644
--- a/artifacts/results/gmsc_model_performance.csv
+++ b/artifacts/results/gmsc_model_performance.csv
@@ -1,5 +1,5 @@
 acc,precision,f1score,mod_name
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-0.74192,0.7440655651535738,0.7413515594246411,JEM
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+0.741,0.746854398924903,0.73945523005902,MLP
+0.732,0.7377867790550845,0.7303595072420607,MLP Ensemble
+0.72,0.7544599896365386,0.7101881293057764,JEM
diff --git a/artifacts/results/gmsc_model_performance.jls b/artifacts/results/gmsc_model_performance.jls
index 2c18063d847e4a768a7f612f39e810ee95a4cc0b..d6088129d9ce90e35ac2cd03638a9b211efac9ca 100644
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diff --git a/artifacts/results/images/moons_generated_JEM.png b/artifacts/results/images/moons_generated_JEM.png
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diff --git a/artifacts/results/images/moons_generated_MLP.png b/artifacts/results/images/moons_generated_MLP.png
index 8e7078fce81b1ca81c92ab9b331063c078b5697f..8d970ec4af0fa1d1ee25ba3d74f199bbddb1f8b9 100644
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diff --git a/artifacts/results/mnist_architectures.jls b/artifacts/results/mnist_architectures.jls
index 166c2de99758134ab6d45178a62742dc11b65871..42d72be1de103a6e64215bcec3773b7664de7a96 100644
GIT binary patch
delta 59
zcmdnp%(T0iX@fc=i-EGS;bd(_Ss4RS2IU9Jj0_MU@5jjEo0ysB!pN*_Y_K_nF@llN
KVDnz4e{}$jd=1S2

delta 59
zcmdnp%(T0iX@fc=i>0!O!DMYlSs6=F2IU9Jj0_MU@5jjEo0ysB!pN*_Y`HmwF@llN
Ka`RrMe{}$nNe%G;

diff --git a/artifacts/results/mnist_vae.jls b/artifacts/results/mnist_vae.jls
index 6bd916f99fd0f8046def3082ec0ddda04f70474c..12bead8bc75c668cf76bbee75526f88785b60288 100644
GIT binary patch
delta 99
zcmZ3q(00*6+lCg#7N!>F7M3lnUNY^4LR>)14a7V^%)7l%h|m1w_P{TEjEvhI75R5E
vZugR5eXqTJ#cjTo677~AtU$~L#Oy%KvE9;x)8f?jps##D6~C1DSLgx&oFF3Q

delta 99
zcmZ3q(00*6+lCg#7N!>F7M3lnUNYOQUvR$HZojO<1;pGy%mc){+b`?zS)6M3l3@j6
wHXvpPVvg-zGMwfow`+-Tt(4f__>_~8aXa^SzW3VOo1Ss*WZeEsiGPJI06w-Q82|tP

diff --git a/artifacts/results/mnist_vae_weak.jls b/artifacts/results/mnist_vae_weak.jls
index 43582e6b78a04ca0144dd911bc4b377335c883cd..c81a673624b1d36493bfe580eda7e0ee3a03de7c 100644
GIT binary patch
delta 60
zcmZ3rm2K5lwhdlg(-qkn4W}ovF_usE>MEapgN@O1b7uGYs>uht45v!~dE0->Gp?(e
Q{IRQIdk{P03JFGE0N<Av&;S4c

delta 59
zcmV-B0L1^QwFauS2Czzslk$ppmth70F_(&g0e7>qi?4c@k_G`ulY5GHlWB`dlS+y)
Rw*i6ys2I1}1_7^n0Zk#188QF>

diff --git a/notebooks/circles.qmd b/notebooks/circles.qmd
index a71667d1..6b6aa0cc 100644
--- a/notebooks/circles.qmd
+++ b/notebooks/circles.qmd
@@ -7,7 +7,7 @@ eval(setup_notebooks)
 
 ```{julia}
 # Hyper:
-_retrain = true
+_retrain = false
 
 # Data:
 test_size = 0.2
@@ -239,6 +239,20 @@ generator_dict = Dict(
 )
 ```
 
+```{julia}
+generator_params = DataFrame(
+    Dict(
+        :λ1 => λ₁,
+        :λ2 => λ₂,
+        :λ3 => λ₃,
+        :opt => string(typeof(opt)),
+        :eta => opt.eta,
+        :dataname => "Circles",
+    )
+)
+CSV.write(joinpath(params_path, "generator/circles.csv"), generator_params)
+```
+
 ### POC
 
 ```{julia}
diff --git a/notebooks/gmsc.qmd b/notebooks/gmsc.qmd
index 17a7646a..b469a56a 100644
--- a/notebooks/gmsc.qmd
+++ b/notebooks/gmsc.qmd
@@ -7,12 +7,11 @@ eval(setup_notebooks)
 
 ```{julia}
 # Hyper:
-_retrain = false
+_retrain = true
 
 # Data:
 test_size = 0.2
-n_obs = Int(50000 / (1.0 - test_size))
-counterfactual_data, test_data = train_test_split(load_gmsc(n_obs); test_size=test_size)
+counterfactual_data, test_data = train_test_split(load_gmsc(); test_size=test_size)
 X, y = CounterfactualExplanations.DataPreprocessing.unpack_data(counterfactual_data)
 X = table(permutedims(X))
 labels = counterfactual_data.output_encoder.labels
@@ -160,6 +159,20 @@ generator_dict = Dict(
 )
 ```
 
+```{julia}
+generator_params = DataFrame(
+    Dict(
+        :λ1 => λ₁,
+        :λ2 => λ₂,
+        :λ3 => λ₃,
+        :opt => string(typeof(opt)),
+        :eta => opt.eta,
+        :dataname => "GMSC",
+    )
+)
+CSV.write(joinpath(params_path, "generator/gmsc.csv"), generator_params)
+```
+
 ```{julia}
 # Measures:
 measures = [
diff --git a/notebooks/linearly_separable.qmd b/notebooks/linearly_separable.qmd
index 97c2fab5..c81c9b1d 100644
--- a/notebooks/linearly_separable.qmd
+++ b/notebooks/linearly_separable.qmd
@@ -7,7 +7,7 @@ eval(setup_notebooks)
 
 ```{julia}
 # Hyper:
-_retrain = true
+_retrain = false
 
 # Data:
 test_size = 0.2
@@ -242,6 +242,20 @@ generator_dict = Dict(
 )
 ```
 
+```{julia}
+generator_params = DataFrame(
+    Dict(
+        :λ1 => λ₁,
+        :λ2 => λ₂,
+        :λ3 => λ₃,
+        :opt => string(typeof(opt)),
+        :eta => opt.eta,
+        :dataname => "Linearly Separable",
+    )
+)
+CSV.write(joinpath(params_path, "generator/linearly_separable.csv"), generator_params)
+```
+
 ### POC
 
 ```{julia}
diff --git a/notebooks/mnist.qmd b/notebooks/mnist.qmd
index e721f849..78de409a 100644
--- a/notebooks/mnist.qmd
+++ b/notebooks/mnist.qmd
@@ -445,6 +445,7 @@ function plot_mnist(
     rng::Union{Int,AbstractRNG}=Random.GLOBAL_RNG,
     _plot_title::Bool=true,
     show_factual::Bool=false,
+    img_height::Int=180,
     kwargs...,
 )
     Random.seed!(rng)
@@ -468,14 +469,14 @@ function plot_mnist(
     _x = CounterfactualExplanations.counterfactual(ce)
     plt = Plots.plot(
         convert2image(MNIST, reshape(_x,28,28)),
-        axis=nothing, 
+        axis=([], false),
         size=(img_height, img_height),
         title=_title
     )
     if show_factual
         plt_factual = Plots.plot(
             convert2image(MNIST, reshape(x,28,28)),
-            axis=nothing, 
+            axis=([], false),
             size=(img_height, img_height),
             title="Factual"
         )
@@ -487,19 +488,19 @@ end
 ```
 
 ```{julia}
-_regen_all_digits = false
+_regen_all_digits = true
 if _regen_all_digits
-    function plot_all_digits(rng=123;verbose=true,kwargs...)
+    function plot_all_digits(rng=123;verbose=true,img_height=180,kwargs...)
         plts = []
         for i in 0:9
             for j in 0:9
                 @info "Generating counterfactual for $(i) -> $(j)"
-                plt = plot_mnist(i,j;kwargs...,rng=rng)
+                plt = plot_mnist(i,j;kwargs...,rng=rng, img_height=img_height)
                 !verbose || display(plt)
                 plts = [plts..., plt]
             end
         end
-        plt = Plots.plot(plts...; size=(img_height*10,img_height*10), layout=(10,10))
+        plt = Plots.plot(plts...; size=(img_height*10,img_height*10), layout=(10,10), dpi=300)
         return plt
     end
     plt = plot_all_digits(generator=eccco_generator)
@@ -514,13 +515,27 @@ end
 
 # Benchmark generators:
 generator_dict = Dict(
-    "Wachter" => WachterGenerator(λ=Λ[1]),
-    "REVISE" => REVISEGenerator(λ=Λ[1]),
+    "Wachter" => WachterGenerator(λ=Λ[1], opt=eccco_generator.opt),
+    "REVISE" => REVISEGenerator(λ=Λ[1], opt=eccco_generator.opt),
     "Schut" => greedy_generator,
     "ECCCo" => eccco_generator,
 )
 ```
 
+```{julia}
+generator_params = DataFrame(
+    Dict(
+        :λ1 => Λ[1],
+        :λ2 => Λ[2],
+        :λ3 => Λ[3],
+        :opt => string(typeof(eccco_generator.opt)),
+        :eta => eccco_generator.opt.eta,
+        :dataname => "MNIST",
+    )
+)
+CSV.write(joinpath(params_path, "generator/mnist.csv"), generator_params)
+```
+
 ```{julia}
 # Measures:
 measures = [
diff --git a/notebooks/moons.qmd b/notebooks/moons.qmd
index 97bf10fa..263c6382 100644
--- a/notebooks/moons.qmd
+++ b/notebooks/moons.qmd
@@ -7,7 +7,7 @@ eval(setup_notebooks)
 
 ```{julia}
 # Hyper:
-_retrain = true
+_retrain = false
 
 # Data:
 test_size = 0.2
@@ -239,6 +239,20 @@ generator_dict = Dict(
 )
 ```
 
+```{julia}
+generator_params = DataFrame(
+    Dict(
+        :λ1 => λ₁,
+        :λ2 => λ₂,
+        :λ3 => λ₃,
+        :opt => string(typeof(opt)),
+        :eta => opt.eta,
+        :dataname => "Moons",
+    )
+)
+CSV.write(joinpath(params_path, "generator/moons.csv"), generator_params)
+```
+
 ### POC
 
 ```{julia}
diff --git a/notebooks/tables.Rmd b/notebooks/tables.Rmd
index 1ffcfe04..421a3be7 100644
--- a/notebooks/tables.Rmd
+++ b/notebooks/tables.Rmd
@@ -277,7 +277,7 @@ col_names <- c(
 )
 algin_cols <- c(rep('l',3),rep('c',ncol(tab_full)-3))
 kbl(
-  tab_full, caption = "All results for all datasets: sample averages +/- one standard deviation over all valid counterfactuals. Best outcomes are highlighted in bold. Asterisks indicate that the given value is more than one (*) or two (**) standard deviations away from the baseline (Wachter). \\label{tab:results-full} \\newline", 
+  tab_full, caption = "All results for all datasets: sample averages +/- one standard deviation over all valid counterfactuals. Best outcomes are highlighted in bold. Asterisks indicate that the given value is more than one (*) or two (**) standard deviations away from the baseline (Wachter). \\label{tab:results-full-valid} \\newline", 
   align = "c", col.names=col_names, booktabs = T, escape=F, 
   format="latex"
 ) %>%
@@ -285,4 +285,57 @@ kbl(
   kable_paper(full_width = F) %>%
   collapse_rows(columns = 1:3, latex_hline = "custom", valign = "top", custom_latex_hline = 1:2) %>%
   save_kable("paper/contents/table_all_valid.tex")
+```
+
+## EBM
+
+```{r}
+files <- list.files("artifacts/params/")
+dt <- lapply(files, function(x) {
+    fread(file.path("artifacts/params/", x))
+})
+dt <- Reduce(function(x,y) {rbind(x,y, fill=TRUE)}, dt)
+setcolorder(
+  dt, 
+  c(
+    "dataname", "n_obs",
+    "n_hidden", "n_layers", "activation", "n_ens",
+    "epochs", "batch_size",
+    "jem_sampling_steps", "sgld_batch_size", "lambda"
+  )
+)
+dt_ebm <- dt[,.(dataname, jem_sampling_steps, sgld_batch_size, lambda)]
+col_names <- c(
+  "Dataset",
+  "SGLD Steps", "Batch Size", "$\\lambda$"
+)
+kbl(
+  dt_ebm, caption = "EBM hyperparemeter choices for our experiments. \\label{tab:ebmparams} \\newline", 
+  align = "r", col.names=col_names, booktabs = T, escape=F, 
+  format="latex"
+) %>%
+  kable_styling(font_size = 8) %>%
+  kable_paper(full_width = F) %>%
+  save_kable("paper/contents/table_ebm_params.tex")
+```
+
+## Experimental setup
+
+```{r}
+dt_exp <- dt[,.(dataname, n_obs, n_hidden, n_layers, activation, n_ens, epochs, batch_size)]
+col_names <- c(
+  "Dataset", "Sample Size",
+  "Hidden Units", "Hidden Layers", "Activation", "Ensemble Size",
+  "Epochs", "Batch Size"
+)
+header <- c(" " = 2, "Network Architecture" = 4, "Training" = 2)
+kbl(
+  dt_exp, caption = "Paremeter choices for our experiments. \\label{tab:params} \\newline", 
+  align = "r", col.names=col_names, booktabs = T, escape=F, 
+  format="latex"
+) %>%
+  kable_styling(latex_options = c("scale_down")) %>%
+  kable_paper(full_width = F) %>%
+  add_header_above(header) %>%
+  save_kable("paper/contents/table_params.tex")
 ```
\ No newline at end of file
diff --git a/paper/contents/table_all_valid.tex b/paper/contents/table_all_valid.tex
index 5d4e466b..ac0dc81b 100644
--- a/paper/contents/table_all_valid.tex
+++ b/paper/contents/table_all_valid.tex
@@ -1,6 +1,6 @@
 \begin{table}
 
-\caption{All results for all datasets: sample averages +/- one standard deviation over all valid counterfactuals. Best outcomes are highlighted in bold. Asterisks indicate that the given value is more than one (*) or two (**) standard deviations away from the baseline (Wachter). \label{tab:results-full} \newline}
+\caption{All results for all datasets: sample averages +/- one standard deviation over all valid counterfactuals. Best outcomes are highlighted in bold. Asterisks indicate that the given value is more than one (*) or two (**) standard deviations away from the baseline (Wachter). \label{tab:results-full-valid} \newline}
 \centering
 \resizebox{\linewidth}{!}{
 \begin{tabular}[t]{ccccccccc}
diff --git a/paper/contents/table_ebm_params.tex b/paper/contents/table_ebm_params.tex
new file mode 100644
index 00000000..2136f26e
--- /dev/null
+++ b/paper/contents/table_ebm_params.tex
@@ -0,0 +1,17 @@
+\begin{table}
+
+\caption{EBM hyperparemeter choices for our experiments. \label{tab:ebmparams} \newline}
+\centering
+\fontsize{8}{10}\selectfont
+\begin{tabular}[t]{rrrr}
+\toprule
+Dataset & SGLD Steps & Batch Size & $\lambda$\\
+\midrule
+Circles & 20 & 100 & 0.01\\
+GMSC & 30 & 10 & 0.10\\
+Linearly Separable & 30 & 50 & 0.10\\
+MNIST & 25 & 10 & 0.01\\
+Moons & 30 & 10 & 0.10\\
+\bottomrule
+\end{tabular}
+\end{table}
diff --git a/paper/contents/table_params.tex b/paper/contents/table_params.tex
new file mode 100644
index 00000000..47ba04a0
--- /dev/null
+++ b/paper/contents/table_params.tex
@@ -0,0 +1,19 @@
+\begin{table}
+
+\caption{Paremeter choices for our experiments. \label{tab:params} \newline}
+\centering
+\resizebox{\linewidth}{!}{
+\begin{tabular}[t]{rrrrrrrr}
+\toprule
+\multicolumn{2}{c}{ } & \multicolumn{4}{c}{Network Architecture} & \multicolumn{2}{c}{Training} \\
+\cmidrule(l{3pt}r{3pt}){3-6} \cmidrule(l{3pt}r{3pt}){7-8}
+Dataset & Sample Size & Hidden Units & Hidden Layers & Activation & Ensemble Size & Epochs & Batch Size\\
+\midrule
+Circles & 1000 & 32 & 3 & swish & 5 & 100 & 100\\
+GMSC & 50000 & 128 & 2 & swish & 5 & 100 & 250\\
+Linearly Separable & 1000 & 16 & 3 & swish & 5 & 100 & 100\\
+MNIST & 10000 & 128 & 1 & swish & 5 & 100 & 128\\
+Moons & 2500 & 32 & 3 & relu & 5 & 500 & 128\\
+\bottomrule
+\end{tabular}}
+\end{table}
diff --git a/paper/paper.pdf b/paper/paper.pdf
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diff --git a/paper/paper.tex b/paper/paper.tex
index 909827ce..9664fd5e 100644
--- a/paper/paper.tex
+++ b/paper/paper.tex
@@ -361,7 +361,7 @@ As mentioned in the body of the paper, we rely on a biased sampler involving sep
   \end{aligned}
 \end{equation}
 
-Consistent with~\citet{grathwohl2020your}, we have specified $\epsilon=2$ and $\sigma=0.01$ as the default values for all of our experiments. The number of total SGLD steps $J$ varies by dataset. Following best practices, we initialize $\mathbf{x}_0$ randomly in 5\% of all cases and sample from a buffer in all other cases. The buffer itself is randomly initialised and gradually grows to a maximum of 10,000 samples during training as $\hat{\mathbf{x}}_{J}$ is stored in each epoch~\citep{du2020implicit,grathwohl2020your}. 
+Consistent with~\citet{grathwohl2020your}, we have specified $\epsilon=2$ and $\sigma=0.01$ as the default values for all of our experiments. The number of total SGLD steps $J$ varies by dataset (Table~\ref{tab:ebmparams}). Following best practices, we initialize $\mathbf{x}_0$ randomly in 5\% of all cases and sample from a buffer in all other cases. The buffer itself is randomly initialised and gradually grows to a maximum of 10,000 samples during training as $\hat{\mathbf{x}}_{J}$ is stored in each epoch~\citep{du2020implicit,grathwohl2020your}. 
 
 It is important to realise that sampling is done during each training epoch, which makes training Joint Energy Models significantly harder than conventional neural classifiers. In each epoch the generated (batch of) sample(s) $\hat{\mathbf{x}}_{J}$ is used as part of the generative loss component, which compares its energy to that of observed samples $\mathbf{x}$: $L_{\text{gen}}(\theta)=\mu_{\theta}(\mathbf{x})[\mathbf{y}]-\mu_{\theta}(\hat{\mathbf{x}}_{J})[\mathbf{y}]$. Our full training objective can be summarized as follows,
 
@@ -371,9 +371,11 @@ It is important to realise that sampling is done during each training epoch, whi
   \end{aligned}
 \end{equation}
 
-where $L_{\text{reg}}(\theta)$ is a Ridge penalty (L2 norm) that regularises energy magnitudes for both observed and generated samples~\citep{du2020implicit}. We have used varying degrees of regularization depending on the dataset. 
+where $L_{\text{reg}}(\theta)$ is a Ridge penalty (L2 norm) that regularises energy magnitudes for both observed and generated samples~\citep{du2020implicit}. We have used varying degrees of regularization depending on the dataset ($\lambda$ in Table~\ref{tab:ebmparams}). 
 
-Contrary to existing work, we have not typically used the entire minibatch of training data for the generative loss component but found that using a subset of the minibatch was often sufficient in attaining decent generative performance. This has helped to reduce the computational burden for our models, which should make it easier for others to reproduce our findings. Figures~\ref{fig:mnist-gen} and~\ref{fig:moons-gen} show generated samples for our \textit{MNIST} and \textit{Moons} data, to provide a sense of their generative property.
+Contrary to existing work, we have not typically used the entire minibatch of training data for the generative loss component but found that using a subset of the minibatch was often sufficient in attaining decent generative performance (Table~\ref{tab:ebmparams}). This has helped to reduce the computational burden for our models, which should make it easier for others to reproduce our findings. Figures~\ref{fig:mnist-gen} and~\ref{fig:moons-gen} show generated samples for our \textit{MNIST} and \textit{Moons} data, to provide a sense of their generative property.
+
+\import{contents/}{table_ebm_params.tex}
 
 \begin{figure}
   \centering
@@ -386,7 +388,6 @@ Contrary to existing work, we have not typically used the entire minibatch of tr
   \includegraphics[width=0.5\textwidth]{../artifacts/results/images/moons_generated_JEM.png}
   \caption{Conditionally generated samples (stars) for our \textit{Moons} data using a JEM.}\label{fig:moons-gen}
 \end{figure}
-
 \subsubsection{Inference: Quantifying Models' Generative Property}
 
 At inference time, we assume no prior knowledge about the model's generative property. This means that we do not tab into the existing buffer of generated samples for our Joint Energy Models, but instead generate conditional samples from scratch. While have relied on the default values $\epsilon=2$ and $\sigma=0.01$ also during inference, the number of total SGLD steps was set to $J=500$ in all cases, so significantly higher than during training. For all of our synthetic datasets and models, we generated 50 conditional samples and then formed subsets containing the $n_{E}=25$ lowest-energy samples. While in practice it would be sufficient to do this once for each model and dataset, we have chosen to perform sampling separately for each individual counterfactual in our experiment to account for stochasticity. To help reduce the computational burden for our real-world datasets we have generated only 10 conditional samples each time and used all of them in our counterfactual search. Using more samples, as we originally did, had no substantial impact on our results.
@@ -438,9 +439,51 @@ The core part of our code base is integrated into a larger ecosystem of \texttt{
 
 \subsection{Experimental Setup}\label{app:setup}
 
+Table~\ref{tab:params} provides an overview of all parameters related to our experiments. The \textit{GMSC} data were randomly undersampled for balancing purposes and all features were standardized. \textit{MNIST} data was also randomly undersampled for reasons outlined below. Pixel values were preprocessed to fall in the range of $[-1,1]$ and a small Gaussian noise component ($\sigma=0.03$) was added to training samples following common practices in the EBM literature. 
+
+\subsubsection{Compute}
+
+To enable others to easily replicate our experiments, we have chosen to work with small neural network architectures and randomly undersampled large datasets where appropriate. All of our experiments could then be run locally on a personal machine. The longest runtimes we experienced for model training and counterfactual benchmarking were on the order of 8-12 hours (\textit{MNIST} data). For the synthetic data, all experiments could be completed in less than an hour. 
+
+We have summarised the system information below:
+
+\textbf{Software}:
+
+\begin{itemize}
+  \item System Version: macOS 13.3.1
+  \item Kernel Version: Darwin 22.4.0
+  \item Boot Volume: Macintosh HD
+  \item Boot Mode: Normal
+\end{itemize}
+
+\textbf{Hardware}:
 
+\begin{itemize}
+  \item Model Name: MacBook Pro
+  \item Model Identifier: MacBookPro16,1
+  \item Processor Name: 8-Core Intel Core i9
+  \item Processor Speed: 2.3 GHz
+  \item Number of Processors: 1
+  \item Total Number of Cores: 8
+  \item L2 Cache (per Core): 256 KB
+  \item L3 Cache: 16 MB
+  \item Hyper-Threading Technology: Enabled
+  \item Memory: 32 GB
+\end{itemize}
+
+\import{contents/}{table_params.tex}
 \subsection{Results}\label{app:results}
 
+Figure~\ref{fig:mnist-eccco} shows examples of counterfactuals for \textit{MNIST} data where the underlying model is our \textit{JEM Ensemble}. Original images are shown on the diagonal and the corresponding counterfactuals are plotted across rows.
+
+\begin{figure}
+  \centering
+  \includegraphics[width=0.75\textwidth]{../artifacts/results/images/mnist_eccco_all_digits.png}
+  \caption{Counterfactuals for \textit{MNIST} data and our \textit{JEM Ensemble}. Original images are shown on the diagonal with the corresponding counterfactuals plotted across rows.}\label{fig:mnist-eccco}
+\end{figure}
+
+Table~\ref{tab:results-full} reports all of the evaluation metrics we have computed. Table~\ref{tab:results-full} reports the same metric for the subset of valid counterfactuals. The `Unfaithfulness' and `Implausibility' metrics have been discussed extensively in the body of the paper. The `Cost' metric relates to the distance between the factual and the counterfactual. The `Redundancy' metric measures sparsity as the percentage of features that remain unperturbed (higher is better). The `Uncertainty' metric is just the average value of the smooth set size penalty (Equation~\ref{eq:setsize}). Finally, `Validity' is the percentage of valid counterfactuals. 
+
 \import{contents/}{table_all.tex}
 
 \import{contents/}{table_all_valid.tex}
-- 
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