Coursera ML course, exercise 1, ported to Julia

ex1.jl

using LinearAlgebra
using DelimitedFiles
using Plots

gr()

warmup() = I

J(X, y, θ) = sum((X * θ - y) .^ 2) / (2 * length(y))

function ∇J(X, y, θ)
    err = X * θ - y
    (err' * X)' ./ size(X, 1)
end

function gradientdescent(X, y, θ, α, n)
    J_history = zeros(n, 1)
    for i in 1:n
        ∇ = ∇J(X, y, θ)
        θ -= α * ∇
        J_history[i] = J(X, y, θ)
    end
    θ, J_history
end

data = readdlm("ex1data1.txt", ',', Float64, '\n')
X = data[:, 1]
y = data[:, 2]
m = length(y)

p = scatter(X, y)
display(p)

X = [ones(m) X]
θ = zeros(2, 1)

println("J = $(J(X, y, θ))")

iterations = 1500
α = 0.01

θ, _ = gradientdescent(X, y, θ, α, iterations)
println("θ = $θ")
scatter!(p, X[:,2], X * θ)

θ0 = range(-10, 10, length=100)
θ1 = range(-1, 4, length=100)

c = contour(θ0, θ1, (θ0, θ1) -> J(X, y, [θ0, θ1]),
  levels=exp10.(range(-2, 3, length=20)))
scatter!([θ[1]], [θ[2]])
display(c)

plotly()
surface(θ0, θ1, (θ0, θ1) -> J(X, y, [θ0, θ1]))