From 01841664aed45456f4a70be18c1db99cba6907ab Mon Sep 17 00:00:00 2001
From: pat-alt <altmeyerpat@gmail.com>
Date: Mon, 24 Apr 2023 08:50:01 +0200
Subject: [PATCH] MNIST complete run (examples)

---
 artifacts/results/mnist_classifier.jls | Bin 0 -> 102146 bytes
 artifacts/results/mnist_vae.jls        | Bin 0 -> 1003702 bytes
 artifacts/results/mnist_vae_weak.jls   | Bin 0 -> 199710 bytes
 notebooks/dev_mnist.qmd                | 365 +++++++++++++++++++++++++
 notebooks/mnist.qmd                    | 221 ++++++++++++---
 paper/paper.pdf                        | Bin 303848 -> 304533 bytes
 paper/paper.tex                        |   6 +-
 www/eccco_mnist.png                    | Bin 20647 -> 20076 bytes
 www/surrogate_gone_wrong.png           | Bin 13405 -> 15129 bytes
 www/you_may_not_like_it.png            | Bin 13519 -> 12796 bytes
 10 files changed, 544 insertions(+), 48 deletions(-)
 create mode 100644 artifacts/results/mnist_classifier.jls
 create mode 100644 artifacts/results/mnist_vae.jls
 create mode 100644 artifacts/results/mnist_vae_weak.jls
 create mode 100644 notebooks/dev_mnist.qmd

diff --git a/artifacts/results/mnist_classifier.jls b/artifacts/results/mnist_classifier.jls
new file mode 100644
index 0000000000000000000000000000000000000000..1a66ab701028818f831939d432d2e82f2efaecae
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diff --git a/artifacts/results/mnist_vae_weak.jls b/artifacts/results/mnist_vae_weak.jls
new file mode 100644
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diff --git a/notebooks/dev_mnist.qmd b/notebooks/dev_mnist.qmd
new file mode 100644
index 00000000..9b2b2f6d
--- /dev/null
+++ b/notebooks/dev_mnist.qmd
@@ -0,0 +1,365 @@
+```{julia}
+include("notebooks/setup.jl")
+eval(setup_notebooks)
+```
+
+# MNIST
+
+```{julia}
+function pre_process(x; noise::Float32=0.03f0)
+    ϵ = Float32.(randn(size(x)) * noise)
+    x = @.(2 * x - 1) .+ ϵ
+    return x
+end
+```
+
+```{julia}
+# Data:
+n_obs = 1000
+counterfactual_data = load_mnist(n_obs)
+counterfactual_data.X = pre_process.(counterfactual_data.X)
+X, y = CounterfactualExplanations.DataPreprocessing.unpack_data(counterfactual_data)
+X = table(permutedims(X))
+labels = counterfactual_data.output_encoder.labels
+input_dim, n_obs = size(counterfactual_data.X)
+n_digits = Int(sqrt(input_dim))
+output_dim = length(unique(labels))
+```
+
+First, let's create a couple of image classifier architectures:
+
+```{julia}
+# Model parameters:
+epochs = 100
+batch_size = minimum([Int(round(n_obs/10)), 128])
+n_hidden = 128
+activation = Flux.relu
+builder = MLJFlux.@builder Flux.Chain(
+
+    Dense(n_in, n_hidden, activation),
+    # Dense(n_hidden, n_hidden, activation),
+    # Dense(n_hidden, n_hidden, activation),
+    
+    # Dense(n_in, n_hidden),
+    # BatchNorm(n_hidden, activation),
+    # Dense(n_hidden, n_hidden),
+    # BatchNorm(n_hidden, activation),
+
+    Dense(n_hidden, n_out),
+)
+# builder = MLJFlux.Short(n_hidden=n_hidden, dropout=0.1, σ=activation)
+# builder = MLJFlux.MLP(
+#     hidden=(
+#         n_hidden,
+#         n_hidden,
+#         n_hidden,
+#     ), 
+#     σ=activation
+# )
+α = [1.0,1.0,5e-3]
+
+# Simple MLP:
+mlp = NeuralNetworkClassifier(
+    builder=builder, 
+    epochs=epochs,
+    batch_size=batch_size,
+    finaliser=x -> x,
+    loss=Flux.Losses.logitcrossentropy,
+)
+
+# Deep Ensemble:
+mlp_ens = EnsembleModel(model=mlp, n=5)
+
+# Joint Energy Model:
+𝒟x = Uniform(-1,1)
+𝒟y = Categorical(ones(output_dim) ./ output_dim)
+sampler = ConditionalSampler(
+    𝒟x, 𝒟y, 
+    input_size=(input_dim,), 
+    batch_size=1
+)
+jem = JointEnergyClassifier(
+    sampler;
+    builder=builder,
+    batch_size=batch_size,
+    finaliser=x -> x,
+    loss=Flux.Losses.logitcrossentropy,
+    jem_training_params=(
+        α=α,verbosity=10,
+        # use_gen_loss=false,
+        # use_reg_loss=false,
+    ),
+    sampling_steps=20,
+    epochs=epochs,
+)
+
+# Deep Ensemble of Joint Energy Models:
+jem_ens = EnsembleModel(model=jem, n=5)
+```
+
+```{julia}
+cov = .95
+conf_model = conformal_model(jem_ens; method=:adaptive_inductive, coverage=cov)
+mach = machine(conf_model, X, labels)
+fit!(mach)
+M = ECCCo.ConformalModel(mach.model, mach.fitresult)
+```
+
+```{julia}
+if mach.model.model isa JointEnergyClassifier
+    sampler = mach.model.model.jem.sampler
+else
+    K = length(counterfactual_data.y_levels)
+    input_size = size(selectdim(counterfactual_data.X, ndims(counterfactual_data.X), 1))
+    𝒟x = Uniform(extrema(counterfactual_data.X)...)
+    𝒟y = Categorical(ones(K) ./ K)
+    sampler = ConditionalSampler(𝒟x, 𝒟y; input_size=input_size)
+end
+opt = ImproperSGLD()
+f(x) = logits(M, x)
+
+n_iter = 200
+_w = 1500
+plts = []
+neach = 10
+for i in 1:10
+    x = sampler(f, opt; niter=n_iter, n_samples=neach, y=i)
+    plts_i = []
+    for j in 1:size(x, 2)
+        xj = x[:,j]
+        xj = reshape(xj, (n_digits, n_digits))
+        plts_i = [plts_i..., Plots.heatmap(rotl90(xj), axis=nothing, cb=false)]
+    end
+    plt = Plots.plot(plts_i..., size=(_w,0.10*_w), layout=(1,10))
+    plts = [plts..., plt]
+end
+plt = Plots.plot(plts..., size=(_w,_w), layout=(10,1))
+display(plt)
+
+```
+
+```{julia}
+test_data = load_mnist_test()
+test_data.X = pre_process.(test_data.X)
+f1 = CounterfactualExplanations.Models.model_evaluation(M, test_data)
+println("F1 score (test): $(round(f1,digits=3))")
+```
+
+```{julia}
+Random.seed!(1234)
+
+# Set up search:
+factual_label = 9
+x = reshape(counterfactual_data.X[:,rand(findall(predict_label(M, counterfactual_data).==factual_label))],input_dim,1)
+target = 7
+factual = predict_label(M, counterfactual_data, x)[1]
+γ = 0.9
+T = 100
+
+η=1.0
+
+# Generate counterfactual using generic generator:
+generator = GenericGenerator(opt=Flux.Optimise.Adam(0.01),)
+ce_wachter = generate_counterfactual(
+    x, target, counterfactual_data, M, generator; 
+    decision_threshold=γ, max_iter=T,
+    initialization=:identity,
+    converge_when=:generator_conditions,
+)
+
+generator = GreedyGenerator(η=η)
+ce_jsma = generate_counterfactual(
+    x, target, counterfactual_data, M, generator; 
+    decision_threshold=γ, max_iter=T,
+    initialization=:identity,
+    converge_when=:generator_conditions,
+)
+
+# ECCCo:
+λ=[0.1,0.1,0.1]
+temp=0.1
+
+# Generate counterfactual using ECCCo generator:
+generator = ECCCoGenerator(
+    λ=λ, 
+    temp=temp, 
+    opt=Flux.Optimise.Adam(0.01),
+)
+ce_conformal = generate_counterfactual(
+    x, target, counterfactual_data, M, generator; 
+    decision_threshold=γ, max_iter=T,
+    initialization=:identity,
+    converge_when=:generator_conditions,
+)
+
+# Generate counterfactual using ECCCo generator:
+generator = ECCCoGenerator(
+    λ=λ, 
+    temp=temp, 
+    opt=CounterfactualExplanations.Generators.JSMADescent(η=η),
+)
+ce_conformal_jsma = generate_counterfactual(
+    x, target, counterfactual_data, M, generator; 
+    decision_threshold=γ, max_iter=T,
+    initialization=:identity,
+    converge_when=:generator_conditions,
+)
+
+# Plot:
+p1 = Plots.plot(
+    convert2image(MNIST, reshape(x,28,28)),
+    axis=nothing, 
+    size=(img_height, img_height),
+    title="Factual"
+)
+plts = [p1]
+
+ces = [ce_wachter, ce_conformal, ce_jsma, ce_conformal_jsma]
+_names = ["Wachter", "ECCCo", "JSMA", "ECCCo-JSMA"]
+for x in zip(ces, _names)
+    ce, _name = (x[1],x[2])
+    x = CounterfactualExplanations.counterfactual(ce)
+    _phat = target_probs(ce)
+    _title = "$_name (p̂=$(round(_phat[1]; digits=3)))"
+    plt = Plots.plot(
+        convert2image(MNIST, reshape(x,28,28)),
+        axis=nothing, 
+        size=(img_height, img_height),
+        title=_title
+    )
+    plts = [plts..., plt]
+end
+plt = Plots.plot(plts...; size=(img_height*length(plts),img_height), layout=(1,length(plts)))
+display(plt)
+savefig(plt, joinpath(www_path, "eccco_mnist.png"))
+```
+
+```{julia}
+# Random.seed!(1234)
+
+# Set up search:
+factual_label = 8
+x = reshape(counterfactual_data.X[:,rand(findall(predict_label(M, counterfactual_data).==factual_label))],input_dim,1)
+target = 3
+factual = predict_label(M, counterfactual_data, x)[1]
+γ = 0.5
+T = 100
+
+# Generate counterfactual using generic generator:
+generator = GenericGenerator(opt=Flux.Optimise.Adam(),)
+ce_wachter = generate_counterfactual(
+    x, target, counterfactual_data, M, generator; 
+    decision_threshold=γ, max_iter=T,
+    initialization=:identity,
+)
+
+generator = GreedyGenerator(η=1.0)
+ce_jsma = generate_counterfactual(
+    x, target, counterfactual_data, M, generator; 
+    decision_threshold=γ, max_iter=T,
+    initialization=:identity,
+)
+
+# ECCCo:
+λ=[0.0,1.0]
+temp=0.5
+
+# Generate counterfactual using CCE generator:
+generator = CCEGenerator(
+    λ=λ, 
+    temp=temp, 
+    opt=Flux.Optimise.Adam(),
+)
+ce_conformal = generate_counterfactual(
+    x, target, counterfactual_data, M, generator; 
+    decision_threshold=γ, max_iter=T,
+    initialization=:identity,
+    converge_when=:generator_conditions,
+)
+
+# Generate counterfactual using CCE generator:
+generator = CCEGenerator(
+    λ=λ, 
+    temp=temp, 
+    opt=CounterfactualExplanations.Generators.JSMADescent(η=1.0),
+)
+ce_conformal_jsma = generate_counterfactual(
+    x, target, counterfactual_data, M, generator; 
+    decision_threshold=γ, max_iter=T,
+    initialization=:identity,
+    converge_when=:generator_conditions,
+)
+
+# Plot:
+p1 = Plots.plot(
+    convert2image(MNIST, reshape(x,28,28)),
+    axis=nothing, 
+    size=(img_height, img_height),
+    title="Factual"
+)
+plts = [p1]
+
+ces = [ce_wachter, ce_conformal, ce_jsma, ce_conformal_jsma]
+_names = ["Wachter", "CCE", "JSMA", "CCE-JSMA"]
+for x in zip(ces, _names)
+    ce, _name = (x[1],x[2])
+    x = CounterfactualExplanations.counterfactual(ce)
+    _phat = target_probs(ce)
+    _title = "$_name (p̂=$(round(_phat[1]; digits=3)))"
+    plt = Plots.plot(
+        convert2image(MNIST, reshape(x,28,28)),
+        axis=nothing, 
+        size=(img_height, img_height),
+        title=_title
+    )
+    plts = [plts..., plt]
+end
+plt = Plots.plot(plts...; size=(img_height*length(plts),img_height), layout=(1,length(plts)))
+display(plt)
+savefig(plt, joinpath(www_path, "cce_mnist.png"))
+```
+
+```{julia}
+if M.model.model isa JointEnergyModels.JointEnergyClassifier
+    jem = M.model.model.jem
+    n_iter = 200
+    _w = 1500
+    plts = []
+    neach = 10
+    for i in 1:10
+        x = jem.sampler(jem.chain, jem.sampling_rule; niter=n_iter, n_samples=neach, y=i)
+        plts_i = []
+        for j in 1:size(x, 2)
+            xj = x[:,j]
+            xj = reshape(xj, (n_digits, n_digits))
+            plts_i = [plts_i..., Plots.heatmap(rotl90(xj), axis=nothing, cb=false)]
+        end
+        plt = Plots.plot(plts_i..., size=(_w,0.10*_w), layout=(1,10))
+        plts = [plts..., plt]
+    end
+    plt = Plots.plot(plts..., size=(_w,_w), layout=(10,1))
+    display(plt)
+end
+```
+
+## Benchmark
+
+```{julia}
+# Benchmark generators:
+generators = Dict(
+    :wachter => GenericGenerator(opt=opt, λ=l2_λ),
+    :revise => REVISEGenerator(opt=opt, λ=l2_λ),
+    :greedy => GreedyGenerator(),
+)
+
+# Conformal Models: 
+
+
+# Measures:
+measures = [
+    CounterfactualExplanations.distance,
+    ECCCo.distance_from_energy,
+    ECCCo.distance_from_targets,
+    CounterfactualExplanations.validity,
+]
+```
\ No newline at end of file
diff --git a/notebooks/mnist.qmd b/notebooks/mnist.qmd
index b4efbc52..3ca0ba0d 100644
--- a/notebooks/mnist.qmd
+++ b/notebooks/mnist.qmd
@@ -5,6 +5,129 @@ eval(setup_notebooks)
 
 # MNIST
 
+## Anecdotal Evidence
+
+### Examples in Introduction
+
+#### Wachter and JSMA
+
+```{julia}
+# Data:
+counterfactual_data = load_mnist()
+X, y = CounterfactualExplanations.DataPreprocessing.unpack_data(counterfactual_data)
+input_dim, n_obs = size(counterfactual_data.X)
+M = load_mnist_mlp()
+
+# Target:
+factual_label = 8
+x = reshape(X[:,rand(findall(predict_label(M, counterfactual_data).==factual_label))],input_dim,1)
+target = 3
+factual = predict_label(M, counterfactual_data, x)[1]
+γ = 0.9
+T = 50
+```
+
+```{julia}
+# Search:
+opt = Flux.Optimise.Adam(0.01)
+generator = GenericGenerator(opt=opt)
+ce_wachter = generate_counterfactual(
+    x, target, counterfactual_data, M, generator; 
+    decision_threshold=γ, max_iter=T,
+    initialization=:identity,
+)
+generator = GreedyGenerator(η=1.0)
+ce_jsma = generate_counterfactual(
+    x, target, counterfactual_data, M, generator; 
+    decision_threshold=γ, max_iter=T,
+    initialization=:identity,
+)
+```
+
+```{julia}
+p1 = Plots.plot(
+    convert2image(MNIST, reshape(x,28,28)),
+    axis=nothing, 
+    size=(img_height, img_height),
+    title="Factual"
+)
+plts = [p1]
+
+ces = zip([ce_wachter,ce_jsma])
+counterfactuals = reduce((x,y)->cat(x,y,dims=3),map(ce -> CounterfactualExplanations.counterfactual(ce[1]), ces))
+phat = reduce((x,y) -> cat(x,y,dims=3), map(ce -> target_probs(ce[1]), ces))
+for x in zip(eachslice(counterfactuals; dims=3), eachslice(phat; dims=3), ["Wachter","JSMA"])
+    ce, _phat, _name = (x[1],x[2],x[3])
+    _title = "$(_name) (p=$(round(_phat[1]; digits=2)))"
+    plt = Plots.plot(
+        convert2image(MNIST, reshape(ce,28,28)),
+        axis=nothing, 
+        size=(img_height, img_height),
+        title=_title
+    )
+    plts = [plts..., plt]
+end
+plt = Plots.plot(plts...; size=(img_height*length(plts),img_height), layout=(1,length(plts)))
+display(plt)
+savefig(plt, joinpath(www_path, "you_may_not_like_it.png"))
+```
+
+#### REVISE
+
+```{julia}
+using CounterfactualExplanations.Models: load_mnist_vae
+vae = load_mnist_vae()
+vae_weak = load_mnist_vae(;strong=false)
+Serialization.serialize(joinpath(output_path,"mnist_classifier.jls"), M)
+Serialization.serialize(joinpath(output_path,"mnist_vae.jls"), vae)
+Serialization.serialize(joinpath(output_path,"mnist_vae_weak.jls"), vae_weak)
+```
+
+```{julia}
+# Define generator:
+generator = REVISEGenerator(
+  opt = opt,
+  λ=0.01
+)
+# Generate recourse:
+counterfactual_data.generative_model = vae # assign generative model
+ce_strong = generate_counterfactual(
+    x, target, counterfactual_data, M, generator; 
+    decision_threshold=γ, max_iter=T,
+    initialization=:identity,
+)
+counterfactual_data = deepcopy(counterfactual_data)
+counterfactual_data.generative_model = vae_weak
+ce_weak = generate_counterfactual(
+    x, target, counterfactual_data, M, generator;
+    decision_threshold=γ, max_iter=T,
+    initialization=:identity,
+)
+```
+
+```{julia}
+ces = zip([ce_strong,ce_weak])
+counterfactuals = reduce((x,y)->cat(x,y,dims=3),map(ce -> CounterfactualExplanations.counterfactual(ce[1]), ces))
+phat = reduce((x,y) -> cat(x,y,dims=3), map(ce -> target_probs(ce[1]), ces))
+plts = [p1]
+for x in zip(eachslice(counterfactuals; dims=3), eachslice(phat; dims=3), ["Strong VAE","Weak VAE"])
+    ce, _phat, _name = (x[1],x[2],x[3])
+    _title = "$(_name) (p=$(round(_phat[1]; digits=2)))"
+    plt = Plots.plot(
+        convert2image(MNIST, reshape(ce,28,28)),
+        axis=nothing, 
+        size=(img_height, img_height),
+        title=_title
+    )
+    plts = [plts..., plt]
+end
+plt = Plots.plot(plts...; size=(img_height*length(plts),img_height), layout=(1,length(plts)))
+display(plt)
+savefig(plt, joinpath(www_path, "surrogate_gone_wrong.png"))
+```
+
+### ECCo
+
 ```{julia}
 function pre_process(x; noise::Float32=0.03f0)
     ϵ = Float32.(randn(size(x)) * noise)
@@ -15,8 +138,6 @@ end
 
 ```{julia}
 # Data:
-n_obs = 1000
-counterfactual_data = load_mnist(n_obs)
 counterfactual_data.X = pre_process.(counterfactual_data.X)
 X, y = CounterfactualExplanations.DataPreprocessing.unpack_data(counterfactual_data)
 X = table(permutedims(X))
@@ -35,74 +156,84 @@ batch_size = minimum([Int(round(n_obs/10)), 128])
 n_hidden = 128
 activation = Flux.relu
 builder = MLJFlux.@builder Flux.Chain(
-
     Dense(n_in, n_hidden, activation),
-    # Dense(n_hidden, n_hidden, activation),
-    # Dense(n_hidden, n_hidden, activation),
-    
-    # Dense(n_in, n_hidden),
-    # BatchNorm(n_hidden, activation),
-    # Dense(n_hidden, n_hidden),
-    # BatchNorm(n_hidden, activation),
-
     Dense(n_hidden, n_out),
 )
-# builder = MLJFlux.Short(n_hidden=n_hidden, dropout=0.1, σ=activation)
-# builder = MLJFlux.MLP(
-#     hidden=(
-#         n_hidden,
-#         n_hidden,
-#         n_hidden,
-#     ), 
-#     σ=activation
-# )
-α = [1.0,1.0,5e-3]
+n_ens = 5                                   # number of models in ensemble
+_loss = Flux.Losses.logitcrossentropy       # loss function
+_finaliser = x -> x                         # finaliser function
+```
 
+```{julia}
+# JEM parameters:
+𝒟x = Uniform(-1,1)
+𝒟y = Categorical(ones(output_dim) ./ output_dim)
+sampler = ConditionalSampler(
+    𝒟x, 𝒟y, 
+    input_size=(input_dim,), 
+    batch_size=1
+)
+α = [1.0,1.0,1e-2]      # penalty strengths
+```
+
+```{julia}
 # Simple MLP:
 mlp = NeuralNetworkClassifier(
     builder=builder, 
     epochs=epochs,
     batch_size=batch_size,
-    finaliser=x -> x,
-    loss=Flux.Losses.logitcrossentropy,
+    finaliser=_finaliser,
+    loss=_loss,
 )
 
 # Deep Ensemble:
-mlp_ens = EnsembleModel(model=mlp, n=5)
+mlp_ens = EnsembleModel(model=mlp, n=n_ens)
 
 # Joint Energy Model:
-𝒟x = Uniform(-1,1)
-𝒟y = Categorical(ones(output_dim) ./ output_dim)
-sampler = ConditionalSampler(
-    𝒟x, 𝒟y, 
-    input_size=(input_dim,), 
-    batch_size=1
-)
 jem = JointEnergyClassifier(
     sampler;
     builder=builder,
+    epochs=epochs,
     batch_size=batch_size,
-    finaliser=x -> x,
-    loss=Flux.Losses.logitcrossentropy,
+    finaliser=_finaliser,
+    loss=_loss,
     jem_training_params=(
         α=α,verbosity=10,
-        # use_gen_loss=false,
-        # use_reg_loss=false,
     ),
     sampling_steps=20,
-    epochs=epochs,
 )
 
+# JEM with adversarial training:
+jem_adv = deepcopy(jem)
+# jem_adv.adv_training = true
+
 # Deep Ensemble of Joint Energy Models:
-jem_ens = EnsembleModel(model=jem, n=5)
+jem_ens = EnsembleModel(model=jem, n=n_ens)
+
+# Deep Ensemble of Joint Energy Models with adversarial training:
+# jem_ens_plus = EnsembleModel(model=jem_adv, n=n_ens)
+
+# Dictionary of models:
+models = Dict(
+    "MLP" => mlp,
+    "MLP Ensemble" => mlp_ens,
+    "JEM" => jem,
+    "JEM Ensemble" => jem_ens,
+    # "JEM Ensemble+" => jem_ens_plus,
+)
 ```
 
+
 ```{julia}
-cov = .95
-conf_model = conformal_model(jem_ens; method=:adaptive_inductive, coverage=cov)
-mach = machine(conf_model, X, labels)
-fit!(mach)
-M = ECCCo.ConformalModel(mach.model, mach.fitresult)
+# Train models:
+function _train(model, X=X, y=labels; cov=.95, method=:simple_inductive)
+    conf_model = conformal_model(jem_ens; method=method, coverage=cov)
+    mach = machine(conf_model, X, y)
+    fit!(mach)
+    M = ECCCo.ConformalModel(mach.model, mach.fitresult)
+    return M
+end
+model_dict = Dict(mod_name => _train(mod) for (mod_name, mod) in models)
 ```
 
 ```{julia}
@@ -149,9 +280,9 @@ println("F1 score (test): $(round(f1,digits=3))")
 Random.seed!(1234)
 
 # Set up search:
-factual_label = 4
+factual_label = 9
 x = reshape(counterfactual_data.X[:,rand(findall(predict_label(M, counterfactual_data).==factual_label))],input_dim,1)
-target = 5
+target = 7
 factual = predict_label(M, counterfactual_data, x)[1]
 γ = 0.9
 T = 100
@@ -159,7 +290,7 @@ T = 100
 η=1.0
 
 # Generate counterfactual using generic generator:
-generator = GenericGenerator()
+generator = GenericGenerator(opt=Flux.Optimise.Adam(0.01),)
 ce_wachter = generate_counterfactual(
     x, target, counterfactual_data, M, generator; 
     decision_threshold=γ, max_iter=T,
diff --git a/paper/paper.pdf b/paper/paper.pdf
index 56e5e6bc610e19203b81094a4d550becf73727cd..d59b8d6eb51bd67c8b0070adfbd3bf6244bdcd2f 100644
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diff --git a/paper/paper.tex b/paper/paper.tex
index 3f271797..f4bd6b8a 100644
--- a/paper/paper.tex
+++ b/paper/paper.tex
@@ -96,7 +96,7 @@
 
 
 \begin{abstract}
-  We propose Conformal Counterfactual Explanations: an effortless and rigorous way to produce plausible and conformal Counterfactual Explanations for Black Box Models using Conformal Prediction. To address the need for plausible explanations, existing work has primarily relied on surrogate models to learn the data-generating process. This effectively reallocates the task of learning realistic representations of the data from the model itself to the surrogate. Consequently, the generated explanations may look plausible to humans but not necessarily conform with the behaviour of the Black Box Model. We formalise this notion through the introduction of new evaluation measures. In order to still address the need for plausibility, we build on a recent approach that works by minimizing predictive model uncertainty. Using differentiable Conformal Prediction, we relax the previous assumption that the Black Box Model can produce predictive uncertainty estimates.
+  We propose Eccoe: an effortless and rigorous way to produce plausible and conformal Counterfactual Explanations for Black Box Models using Conformal Prediction. To address the need for plausible explanations, existing work has primarily relied on surrogate models to learn the data-generating process. This effectively reallocates the task of learning realistic representations of the data from the model itself to the surrogate. Consequently, the generated explanations may look plausible to humans but not necessarily conform with the behaviour of the Black Box Model. We formalise this notion through the introduction of new evaluation measures. In order to still address the need for plausibility, we build on a recent approach that works by minimizing predictive model uncertainty. Using differentiable Conformal Prediction, we relax the previous assumption that the Black Box Model can produce predictive uncertainty estimates.
 \end{abstract}
 
 \section{Introduction}\label{intro}
@@ -266,9 +266,9 @@ The fact that conformal classifiers produce set-valued predictions introduces a
 
 where $\kappa \in \{0,1\}$ is a hyper-parameter and $C_{\theta,\mathbf{y}}(\mathbf{x}_i;\alpha)$ can be interpreted as the probability of label $\mathbf{y}$ being included in the prediction set. Formally, it is defined as $C_{\theta,\mathbf{y}}(\mathbf{x}_i;\alpha):=\sigma\left((s(\mathbf{x}_i,\mathbf{y})-\alpha) T^{-1}\right)$ for $\mathbf{y}\in\mathcal{Y}$ where $\sigma$ is the sigmoid function and $T$ is a hyper-parameter used for temperature scaling \citep{stutz2022learning}.
 
-Penalizing the set size in this way is in principal enough to train efficient conformal classifiers \citep{stutz2022learning}. As we explained above, the set size is also closely linked to predictive uncertainty at the local level. This makes the smooth penalty defined in Equation~\ref{eq:setsize} useful in the context of meeting our objective of generating plausible counterfactuals. In particular, we adapt Equation~\ref{eq:general} to define the baseline objective for Conformal Counterfactual Explanations (ECCCo):
+Penalizing the set size in this way is in principle enough to train efficient conformal classifiers \citep{stutz2022learning}. As we explained above, the set size is also closely linked to predictive uncertainty at the local level. This makes the smooth penalty defined in Equation~\ref{eq:setsize} useful in the context of meeting our objective of generating plausible counterfactuals. In particular, we adapt Equation~\ref{eq:general} to define the objective for our proposed Energy-Constrained Conformal Counterfactual Explanations (Eccoe):
 
-\begin{equation}\label{eq:cce}
+\begin{equation}\label{eq:eccoe}
   \begin{aligned}
     \mathbf{Z}^\prime &= \arg \min_{\mathbf{Z}^\prime \in \mathcal{Z}^M} \left\{  {\text{yloss}(M_{\theta}(f(\mathbf{Z}^\prime)),\mathbf{y}^*)}+ \lambda \Omega(C_{\theta}(f(\mathbf{Z}^\prime);\alpha)) \right\} 
   \end{aligned}
diff --git a/www/eccco_mnist.png b/www/eccco_mnist.png
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