linear_regression.jl

# linear_regression
# 2021-06-06
# author: jeovazero

Σ = sum

h(t, x) = Σ(t .* x)

j(θ, x, y) = 1 / 2 * Σ([(h(θ, x[i]) - y[i])^2 for i in 1:length(y)])

grad_j(θ, x, y) =
    [Σ([(y[i] - h(θ, x[i])) * x[i][j] for i in 1:length(y)]) for j in 1:length(θ)]

function linear_regression(initial_theta, x, y, learning_rate, threshold)
    local θ = initial_theta
    local grad_θ = grad_j(θ, x, y)
    while j(θ, x, y) > threshold
        θ = [θ[i] + learning_rate * grad_θ[i] for i in 1:length(θ)]
        grad_θ = grad_j(θ, x, y)
    end
    return θ
end

t = [1, 1, 1]
x = [[1, 2, 3], [2, 3, 1], [5, 6, 2]]
y = [14, 11, 23]
e = 0.00001
a = 0.0001
# optimal_answer = [1,2,3]

println("theta: ", linear_regression(t, x, y, a, e))

# output:
#  theta: [1.009970699169594, 1.9910891910904216, 3.0027040755191465]
#