Please Fill Parts Clearvars Clc Addpath Generation Addpath Basicblocks Addpath Algorith Q43779728
Please fill the parts with “@”:
clearvars
clc
addpath(‘../Generation’)
addpath(‘../Basic_blocks’)
addpath(‘../Algorithms’)
% Loading scenarios
% ===========================
scenario=2;
[data_class set_up]=scenarios_classification(scenario);
% Definition of the problem
%===================================
loss_logistic_L2 = @(N,U,x,y,lambda)(1/N*sum(log(1+exp(-diag(y)*(U*x))))+lambda/2*x’*x);
grad_logistic_L2 = @(N,U,x,y,lambda)(1/N*(sum((diag(-y)*U)./kron(1+exp(diag(y)*(U*x)),ones(1,length(x)))))’+lambda*x);
hess_logistic_L2 = @calculation_Hessian_logistic;
grad_logistic_proximal = @(N,U,x,y,ro,a)(1/N*(sum((diag(-y)*U)./kron(1+exp(diag(y)*(U*x)),ones(1,length(x)))))’+ro*(x-a));
% Solution of the empirical risk using CVX
%=========================================
x_L2_cvx=solver_cvx(set_up,@(N,A,x,y,lambda)loss_logistic_L2(N,A,x,y,lambda));
loss_opt=loss_logistic_L2(set_up.Niter_train,set_up.Utrain(:,1:set_up.M+1),x_L2_cvx,set_up.ytrain(:,1),set_up.Lambda);
% Gradient descent
out_gd =grad_FOM(set_up,@(N,A,x,y,lambda)grad_logistic_L2(N,A,x,y,lambda));
loss_grad=eval_loss(out_gd,set_up,@(N,A,x,y,lambda)loss_logistic_L2(N,A,x,y,lambda));
% Newton algorithm
out_hess =grad_SOM(set_up,@(N,A,x,y,lambda)grad_logistic_L2(N,A,x,y,lambda),@(N,A,x,y,lambda)hess_logistic_L2(N,A,x,y,lambda));
loss_hess=eval_loss(out_hess,set_up,@(N,A,x,y,lambda)loss_logistic_L2(N,A,x,y,lambda));
% BFGS algorithm
out_BFGS =BFGS(set_up,@(N,A,x,y,lambda)grad_logistic_L2(N,A,x,y,lambda));
loss_BFGS=eval_loss(out_BFGS,set_up,@(N,A,x,y,lambda)loss_logistic_L2(N,A,x,y,lambda));
% Plot of learning curves
figure(1)
plot(1:set_up.Niter_train,10*log10(sum((loss_grad-loss_opt*ones(1,set_up.Niter_train)).^2,1)),’b’,’LineWidth’,3),
hold
plot(1:set_up.Niter_train,10*log10(sum((loss_hess-loss_opt*ones(1,set_up.Niter_train)).^2,1)),’r’,’LineWidth’,3),
plot(1:set_up.Niter_train,10*log10(sum((loss_BFGS-loss_opt*ones(1,set_up.Niter_train)).^2,1)),’g’,’LineWidth’,3),
hold off
legend(‘Gradient’,’Hess’,’BFGS’),grid
xlabel(‘Iterations’)
ylabel(‘MSE’)
title(‘Logistic-L2. Different implementations’)
% Let’s make a zoom
% Plot of learning curves
figure(2)
show=30;
plot(1:show,10*log10(sum((loss_grad(1,show)-loss_opt*ones(1,show)).^2,1)),’b’,’LineWidth’,3),
hold
plot(1:show,10*log10(sum((loss_hess(1:show)-loss_opt*ones(1,show)).^2,1)),’r’,’LineWidth’,3),
plot(1:show,10*log10((loss_BFGS(1:show)-loss_opt*ones(1,show)).^2),’g’,’LineWidth’,3),
hold off
grid
xlabel(‘Iterations’)
ylabel(‘MSE’)
title(‘Logistic Algorithm (Zoom)’)
legend(‘Gradient’,’Newton’,’BFGS’)
Expert Answer
Answer to Please fill the parts with “@”: clearvars clc addpath(‘../Generation’) addpath(‘../Basic_blocks’) addpath(‘../Algorithms…
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