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OLS_ML_2.jl
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#Calculate the gradient | |
function grad_OLS!(G, beta_hat, X, y) | |
G[:] = transpose(X)*(X*beta_hat - y) | |
end | |
#Gradient descent way | |
function OLS_gd(X::Array, y::Vector; epochs::Int64=1000, r::Float64=1e-5, beta_hat = zeros(size(X,2)), verbose::Bool=false) | |
grad_n = zeros(size(X,2)) | |
for epoch=1:epochs | |
grad_OLS!(grad_n, beta_hat, X, y) | |
beta_hat -= r*grad_n | |
if verbose==true | |
if mod(epoch, round(Int, epochs/10))==1 | |
println("MSE: $(mse(beta_hat, X, y))") | |
end | |
end | |
end | |
return beta_hat | |
end | |
beta_hat_gd_1 = OLS_gd(X,y, epochs=1); | |
plot(beta, zeros(size(X,2)), seriestype=:scatter, label="GD (0 iter.)") | |
plot!(beta, beta, seriestype=:line, label="45° line", legend = :outertopleft) | |
xlabel!(L"True value $\beta$") | |
ylabel!(L"Estimated value $\hat{\beta}$ (GD)") | |
# refinement loop | |
anim = @animate for i=1:50 | |
if mod(i, 5) == 0 | |
beta_hat_gd = OLS_gd(X,y, epochs=i); | |
plot!(beta, beta_hat_gd, seriestype=:scatter, label="GD ($(i) iter.)") | |
plot!(beta, beta, seriestype=:line, label=:none, legend = :outertopleft) | |
xlabel!(L"True value $\beta$") | |
ylabel!(L"Estimated value $\hat{\beta}$ (GD)") | |
end | |
end | |
gif(anim,joinpath(dirname(@__FILE__),"convergence_GD_OLS.gif"),fps=5) |
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