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roc2.jl
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roc2.jl
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### A Pluto.jl notebook ###
# v0.16.1
using Markdown
using InteractiveUtils
# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error).
macro bind(def, element)
quote
local el = $(esc(element))
global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : missing
el
end
end
# ╔═╡ 756852b6-2d38-11ec-20f0-9d0de7093de7
using ADNLPModels, JSOSolvers, NLPModels, Logging, LinearAlgebra, Plots, PlutoUI, Random
# ╔═╡ a96a7ab6-3990-46a2-9f2a-2f63d4813c13
begin
Random.seed!(3)
n = 100
X = 2 * rand(n, 2) .- 1
y = [X[i,2] - 2 * (X[i,1] - 0.3)^2 + 0.2 > randn() * 0.5 ? 0 : 1 for i = 1:n]
sigmoid(t) = t ≥ 0 ? 1 / (1 + exp(-t)) : exp(t) / (1 + exp(t))
model(β, x) = sigmoid.([ones(size(x,1)) x x.^2 x[:,1] .* x[:,2]] * β)
loss(ŷ, y) = -sum(
y[i] == 1 ? log(ŷ[i] + 1e-8) : log(1 - ŷ[i] + 1e-8)
for i = 1:n
)
likelihood(β) = loss(model(β, X), y)
neg_args = (3,:pink,:square,stroke(1,:red))
pos_args = (3,:lightblue,:circle,stroke(1,:blue))
function plot_data!(plt)
I = findall(y .== 0)
scatter!(plt, X[I,1], X[I,2], m=neg_args)
I = findall(y .== 1)
scatter!(plt, X[I,1], X[I,2], m=pos_args)
end
function plot_model!(plt, β, τ)
f = (x₁, x₂) -> model(β, [x₁ x₂])[1]
xg = range(-1, 1, length=50)
yg = range(-1, 1, length=50)
contourf!(plt, xg, yg, f, levels=50, lw=0, c=[:pink,:white,:lightblue], clims=(0,1))
contour!(plt, xg, yg, f, levels=11, c=:gray, l=:dash)
contour!(plt, xg, yg, f, levels=[τ], c=:black, lw=2)
end
nothing
end
# ╔═╡ 397e420e-be52-4d30-b857-e1732c2ca013
md"""
β = [
$(@bind slβ₀ Slider(-3:0.1:3, show_value=true, default=0.0)),
$(@bind slβ₁ Slider(-3:0.1:3, show_value=true, default=1.0)),
$(@bind slβ₂ Slider(-3:0.1:3, show_value=true, default=1.0)),
$(@bind slβ₃ Slider(-3:0.1:3, show_value=true, default=0.0)),
$(@bind slβ₄ Slider(-3:0.1:3, show_value=true, default=0.0)),
$(@bind slβ₅ Slider(-3:0.1:3, show_value=true, default=0.0))
]
τ = $(@bind slτ Slider(0.1:0.1:0.9, show_value=true, default=0.5))
"""
# ╔═╡ 8e38801f-556c-498d-8fcb-7f33eef6e1a2
let
β = [slβ₀; slβ₁; slβ₂; slβ₃; slβ₄; slβ₅]
ĥ = model(β, X)
τr = [sort(ĥ); 1.0]
TPR = [1.0]
FPR = [1.0]
for (i,τ) in enumerate(τr)
ŷ = [ĥᵢ ≤ τ ? 0 : 1 for ĥᵢ in ĥ]
M = [
sum((y .== 1) .& (ŷ .== 1)) sum((y .== 1) .& (ŷ .== 0));
sum((y .== 0) .& (ŷ .== 1)) sum((y .== 0) .& (ŷ .== 0))
]
push!(TPR, TPR[end])
push!(TPR, M[1,1] / sum(M[1,:]))
push!(FPR, FPR[end])
push!(FPR, M[2,1] / sum(M[2,:]))
end
τr = [0.0; τr]
μ = (-log((1 - slτ) / slτ) - β[1]) / β[2]
ŷ = [ĥᵢ ≤ slτ ? 0 : 1 for ĥᵢ in ĥ]
plt = plot(layout=grid(2, 2), size=(800,600), leg=false)
plot!(plt[1,1], leg=false)
plot_model!(plt[1,1], β, slτ)
plot_data!(plt[1,1])
title!(plt[1,1], "fit")
M = [
sum((y .== 1) .& (ŷ .== 1)) sum((y .== 1) .& (ŷ .== 0));
sum((y .== 0) .& (ŷ .== 1)) sum((y .== 0) .& (ŷ .== 0))
]
tpr = M[1,1] / sum(M[1,:])
plot!(plt[1,2], sort([τr[2:end]; τr]), TPR, c=:black, lw=2, leg=false)
scatter!(plt[1,2], [slτ], [tpr], m=(:green,5,stroke(0)))
title!(plt[1,2], "Razão de verdadeiros positivos")
fpr = M[2,1] / sum(M[2,:])
plot!(plt[2,1], sort([τr[2:end]; τr]), FPR, c=:black, lw=2, leg=false)
scatter!(plt[2,1], [slτ], [fpr], m=(:green,5,stroke(0)))
title!(plt[2,1], "Razão de falsos positivos")
plot!(plt[2,2], FPR, TPR, c=:black, lw=2, m=(2,:black), leg=false)
xlabel!(plt[2,2], "Razão de falsos positivos")
ylabel!(plt[2,2], "Razão de verdadeiros positivos")
scatter!(plt[2,2], [fpr], [tpr], m=(:green,5,stroke(0)))
plot!(plt[2,2], [0, 1], [0, 1], c=:black, l=:dot)
end
# ╔═╡ ca8b041b-5dbd-493c-9ad0-39f37cfab622
let
nlp = ADNLPModel(likelihood, randn(6))
output = with_logger(NullLogger()) do
lbfgs(nlp)
end
β = output.solution
ĥ = model(β, X)
τr = [sort(ĥ); 1.0]
TPR = [1.0]
FPR = [1.0]
for (i,τ) in enumerate(τr)
ŷ = [ĥᵢ ≤ τ ? 0 : 1 for ĥᵢ in ĥ]
M = [
sum((y .== 1) .& (ŷ .== 1)) sum((y .== 1) .& (ŷ .== 0));
sum((y .== 0) .& (ŷ .== 1)) sum((y .== 0) .& (ŷ .== 0))
]
push!(TPR, TPR[end])
push!(TPR, M[1,1] / sum(M[1,:]))
push!(FPR, FPR[end])
push!(FPR, M[2,1] / sum(M[2,:]))
end
τr = [0.0; τr]
μ = (-log((1 - slτ) / slτ) - β[1]) / β[2]
ŷ = [ĥᵢ ≤ slτ ? 0 : 1 for ĥᵢ in ĥ]
plt = plot(layout=grid(2, 2), size=(800,600), leg=false)
plot!(plt[1,1], leg=false)
plot_model!(plt[1,1], β, slτ)
plot_data!(plt[1,1])
title!(plt[1,1], "fit ótimo")
M = [
sum((y .== 1) .& (ŷ .== 1)) sum((y .== 1) .& (ŷ .== 0));
sum((y .== 0) .& (ŷ .== 1)) sum((y .== 0) .& (ŷ .== 0))
]
tpr = M[1,1] / sum(M[1,:])
plot!(plt[1,2], sort([τr[2:end]; τr]), TPR, c=:black, lw=2, leg=false)
scatter!(plt[1,2], [slτ], [tpr], m=(:green,5,stroke(0)))
title!(plt[1,2], "Razão de verdadeiros positivos")
fpr = M[2,1] / sum(M[2,:])
plot!(plt[2,1], sort([τr[2:end]; τr]), FPR, c=:black, lw=2, leg=false)
scatter!(plt[2,1], [slτ], [fpr], m=(:green,5,stroke(0)))
title!(plt[2,1], "Razão de falsos positivos")
plot!(plt[2,2], FPR, TPR, c=:black, lw=2, m=(2,:black), leg=false)
xlabel!(plt[2,2], "Razão de falsos positivos")
ylabel!(plt[2,2], "Razão de verdadeiros positivos")
scatter!(plt[2,2], [fpr], [tpr], m=(:green,5,stroke(0)))
plot!(plt[2,2], [0, 1], [0, 1], c=:black, l=:dot)
end
# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
ADNLPModels = "54578032-b7ea-4c30-94aa-7cbd1cce6c9a"
JSOSolvers = "10dff2fc-5484-5881-a0e0-c90441020f8a"
LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
Logging = "56ddb016-857b-54e1-b83d-db4d58db5568"
NLPModels = "a4795742-8479-5a88-8948-cc11e1c8c1a6"
Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
[compat]
ADNLPModels = "~0.3.0"
JSOSolvers = "~0.7.2"
NLPModels = "~0.17.2"
Plots = "~1.22.6"
PlutoUI = "~0.7.16"
"""
# ╔═╡ 00000000-0000-0000-0000-000000000002
PLUTO_MANIFEST_TOML_CONTENTS = """
# This file is machine-generated - editing it directly is not advised
[[ADNLPModels]]
deps = ["ForwardDiff", "LinearAlgebra", "NLPModels", "Requires", "SparseArrays"]
git-tree-sha1 = "132e452a4edb241d42438f0ed3f0879e4ed7ca61"
uuid = "54578032-b7ea-4c30-94aa-7cbd1cce6c9a"
version = "0.3.0"
[[Adapt]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "84918055d15b3114ede17ac6a7182f68870c16f7"
uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
version = "3.3.1"
[[ArgTools]]
uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f"
[[Artifacts]]
uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"
[[Base64]]
uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"
[[Bzip2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "19a35467a82e236ff51bc17a3a44b69ef35185a2"
uuid = "6e34b625-4abd-537c-b88f-471c36dfa7a0"
version = "1.0.8+0"
[[Cairo_jll]]
deps = ["Artifacts", "Bzip2_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "JLLWrappers", "LZO_jll", "Libdl", "Pixman_jll", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Zlib_jll", "libpng_jll"]
git-tree-sha1 = "f2202b55d816427cd385a9a4f3ffb226bee80f99"
uuid = "83423d85-b0ee-5818-9007-b63ccbeb887a"
version = "1.16.1+0"
[[ChainRulesCore]]
deps = ["Compat", "LinearAlgebra", "SparseArrays"]
git-tree-sha1 = "2f294fae04aa5069a67964a3366e151e09ea7c09"
uuid = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
version = "1.9.0"
[[ColorSchemes]]
deps = ["ColorTypes", "Colors", "FixedPointNumbers", "Random"]
git-tree-sha1 = "a851fec56cb73cfdf43762999ec72eff5b86882a"
uuid = "35d6a980-a343-548e-a6ea-1d62b119f2f4"
version = "3.15.0"
[[ColorTypes]]
deps = ["FixedPointNumbers", "Random"]
git-tree-sha1 = "024fe24d83e4a5bf5fc80501a314ce0d1aa35597"
uuid = "3da002f7-5984-5a60-b8a6-cbb66c0b333f"
version = "0.11.0"
[[Colors]]
deps = ["ColorTypes", "FixedPointNumbers", "Reexport"]
git-tree-sha1 = "417b0ed7b8b838aa6ca0a87aadf1bb9eb111ce40"
uuid = "5ae59095-9a9b-59fe-a467-6f913c188581"
version = "0.12.8"
[[CommonSubexpressions]]
deps = ["MacroTools", "Test"]
git-tree-sha1 = "7b8a93dba8af7e3b42fecabf646260105ac373f7"
uuid = "bbf7d656-a473-5ed7-a52c-81e309532950"
version = "0.3.0"
[[Compat]]
deps = ["Base64", "Dates", "DelimitedFiles", "Distributed", "InteractiveUtils", "LibGit2", "Libdl", "LinearAlgebra", "Markdown", "Mmap", "Pkg", "Printf", "REPL", "Random", "SHA", "Serialization", "SharedArrays", "Sockets", "SparseArrays", "Statistics", "Test", "UUIDs", "Unicode"]
git-tree-sha1 = "31d0151f5716b655421d9d75b7fa74cc4e744df2"
uuid = "34da2185-b29b-5c13-b0c7-acf172513d20"
version = "3.39.0"
[[CompilerSupportLibraries_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"
[[Contour]]
deps = ["StaticArrays"]
git-tree-sha1 = "9f02045d934dc030edad45944ea80dbd1f0ebea7"
uuid = "d38c429a-6771-53c6-b99e-75d170b6e991"
version = "0.5.7"
[[DataAPI]]
git-tree-sha1 = "cc70b17275652eb47bc9e5f81635981f13cea5c8"
uuid = "9a962f9c-6df0-11e9-0e5d-c546b8b5ee8a"
version = "1.9.0"
[[DataStructures]]
deps = ["Compat", "InteractiveUtils", "OrderedCollections"]
git-tree-sha1 = "7d9d316f04214f7efdbb6398d545446e246eff02"
uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
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