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OLS_ML_1
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using LinearAlgebra | |
using Distributions | |
using Plots | |
using Distributions | |
using Random | |
using LaTeXStrings | |
n_points=10000 | |
dim_input=100 #dim of input, without the intercept | |
dim_output=1 | |
# Normal noise | |
d = Normal() | |
# True parameters | |
beta = rand(d, dim_input + 1); | |
# Noise | |
e = rand(d, n_points); | |
# Input data: | |
X = rand(d, (n_points,dim_input)); | |
# Add the intercept: | |
X = hcat(ones(n_points),X); | |
#Linear Model | |
y = X*beta .+ e; | |
#OLS way | |
function OLS_direct(X::Array, y::Vector) | |
inv(transpose(X)*X)*transpose(X)*y | |
end | |
@time beta_hat = OLS_direct(X, y); | |
plot(beta, beta_hat, seriestype=:scatter, label="OLS (Direct)") | |
plot!(beta, beta, seriestype=:line, label="45° line") | |
xlabel!(L"True value $\beta$") | |
ylabel!(L"Estimated value $\hat{\beta}$ (Direct)") | |
savefig("OLS_direct.png") |
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