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regressao-logistica2.jl
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regressao-logistica2.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)
# model(β, x) = sigmoid.([
# ones(size(x,1)) x x.^2 x[:,1] .* x[:,2] x.^3 x[:,1].^2 .* x[:,2] x[:,1] .* x[:,2].^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
let
plt = plot(leg=false)
plot_data!(plt)
end
end
# ╔═╡ ca9260b1-99cb-459b-9b7e-6245532185a0
md"""
$$h_β(x) = \sigma(\beta_0 + \beta_1 x_1 + \beta_2 x_2 + \beta_3 x_1^2 + \beta_4 x_2^2 + \beta_5 x_1 x_2)$$
"""
# ╔═╡ 397e420e-be52-4d30-b857-e1732c2ca013
md"""
β = [
$(@bind slβ₀ Slider(-3:0.1:3, show_value=true)),
$(@bind slβ₁ Slider(-3:0.1:3, show_value=true)),
$(@bind slβ₂ Slider(-3:0.1:3, show_value=true)),
$(@bind slβ₃ Slider(-3:0.1:3, show_value=true)),
$(@bind slβ₄ Slider(-3:0.1:3, show_value=true)),
$(@bind slβ₅ Slider(-3:0.1:3, show_value=true))
]
τ = $(@bind slτ Slider(0.1:0.1:0.9, show_value=true, default=0.5))
"""
# ╔═╡ 7c426875-c4f6-4839-af69-b4c67ab009bb
let
β = [slβ₀; slβ₁; slβ₂; slβ₃; slβ₄; slβ₅]
plt = plot(leg=false)
plot_model!(plt, β, slτ)
plot_data!(plt)
end
# ╔═╡ 68e0f8f7-f8a0-4608-b5f0-6177ec41d037
let
σ(t) = t ≥ 0 ? 1 / (1 + exp(-t)) : exp(t) / (1 + exp(t))
Random.seed!(0)
nlp = ADNLPModel(likelihood, randn(6))
β = copy(nlp.meta.x0)
anim = Animation()
evals = 0
ks = 1:50
Ls = Float64[obj(nlp, β)]
∇Ls = Float64[norm(grad(nlp, β))]
ŷ = round.(Int, model(β, X))
Accs = Float64[sum(ŷ .== y) / n]
α = 0.05
for k = ks
Hβ = hess(nlp, β) + 1e-8 * LinearAlgebra.I
if minimum(eigen(Hβ).values) < 0
error(string(eigen(Hβ).values))
end
β -= α * (Hβ \ grad(nlp, β))
I = findall(y .== 0)
plt = plot(layout=grid(2,2), size=(800,600), leg=false)
plot_model!(plt[1,1], β, 0.5)
plot_data!(plt[1,1])
title!(plt[1,1], "Fit")
push!(Ls, obj(nlp, β))
plot!(plt[1,2], 0:k, Ls, xlims=(0,ks[end]), ylims=(5,Ls[1]), leg=false)
title!(plt[1,2], "ℓ(β)")
push!(∇Ls, norm(grad(nlp, β)))
plot!(plt[2,1], 0:k, ∇Ls, xlims=(0,ks[end]), ylims=(1e-8,∇Ls[1]), yaxis=:log, leg=false)
title!(plt[2,1], "‖∇ℓ(β)‖")
ŷ = round.(Int, model(β, X))
push!(Accs, sum(ŷ .== y) / n)
plot!(plt[2,2], 0:k, Accs, xlims=(0,ks[end]), ylims=(0, 1), leg=false)
title!(plt[2,2], "Acurácia")
frame(anim)
end
gif(anim, fps=10)
end
# ╔═╡ e2a201c9-337b-4e68-b221-407f686a0149
let
Random.seed!(0)
nlp = ADNLPModel(likelihood, randn(6))
output = with_logger(NullLogger()) do
lbfgs(nlp)
end
β = output.solution
plt = plot(leg=false)
plot_model!(plt, β, 0.5)
plot_data!(plt)
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
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deps = ["ForwardDiff", "LinearAlgebra", "NLPModels", "Requires", "SparseArrays"]
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[[Base64]]
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[[Bzip2_jll]]
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git-tree-sha1 = "19a35467a82e236ff51bc17a3a44b69ef35185a2"
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[[Cairo_jll]]
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git-tree-sha1 = "f2202b55d816427cd385a9a4f3ffb226bee80f99"
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[[ChainRulesCore]]
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[[ColorTypes]]
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version = "0.11.0"
[[Colors]]
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git-tree-sha1 = "417b0ed7b8b838aa6ca0a87aadf1bb9eb111ce40"
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[[CommonSubexpressions]]
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[[Compat]]
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git-tree-sha1 = "31d0151f5716b655421d9d75b7fa74cc4e744df2"
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[[DataStructures]]
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[[Dates]]
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[[DiffRules]]
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