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mcb131hw4.m
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mcb131hw4.m
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%% PROBLEM 2
N = 2;
P_set = [10 50];
test_acc = nan(2,10,size(P_set,2));
train_acc = nan(2,10,size(P_set,2));
figure;
for P = P_set
for epoch = 1:10
X_train = randn(P,2);
Y_train = sign(X_train(:,1));
X_test = randn(1000,2);
Y_test = sign(X_test(:,1));
SVMStruct_linear = fitcsvm(X_train,Y_train,'KernelFunction','linear');
Y_trainhat = predict(SVMStruct_linear,X_train);
train_acc(1,epoch,P==P_set) = nanmean(Y_train==Y_trainhat);
Y_testhat = predict(SVMStruct_linear,X_test);
test_acc(1,epoch,P==P_set) = nanmean(Y_test==Y_testhat);
SVMStruct_arccos = fitcsvm(X_train,Y_train,'KernelFunction','rbf');
Y_trainhat = predict(SVMStruct_arccos,X_train);
train_acc(2,epoch,P==P_set) = nanmean(Y_train==Y_trainhat);
Y_testhat = predict(SVMStruct_arccos,X_test);
test_acc(2,epoch,P==P_set) = nanmean(Y_test==Y_testhat);
end
subplot(1,2,1)
hold on
plot(find(P==P_set),nanmean(train_acc(1,:,P==P_set)),'ok','MarkerFaceColor','k')
plot(find(P==P_set)+.1,nanmean(train_acc(2,:,P==P_set)),'ob','MarkerFaceColor','b')
plot(find(P==P_set)*ones(1,10),train_acc(1,:,P==P_set),'ok')
plot(find(P==P_set)*ones(1,10)+.1,train_acc(2,:,P==P_set),'ob')
xlim([0 3])
ylim([.3 1])
plot([0 3],[.5 .5],':k')
set(gca,'xtick',[1 2],'xticklabel',P_set)
xlabel('P')
ylabel('training accuracy')
axis square
subplot(1,2,2)
hold on
plot(find(P==P_set),nanmean(test_acc(1,:,P==P_set)),'ok','MarkerFaceColor','k')
plot(find(P==P_set)+.1,nanmean(test_acc(2,:,P==P_set)),'ob','MarkerFaceColor','b')
plot(find(P==P_set)*ones(1,10),test_acc(1,:,P==P_set),'ok')
plot(find(P==P_set)*ones(1,10)+.1,test_acc(2,:,P==P_set),'ob')
xlim([0 3])
ylim([.3 1])
plot([0 3],[.5 .5],':k')
set(gca,'xtick',[1 2],'xticklabel',P_set)
xlabel('P')
ylabel('testing accuracy')
legend('linear kernel','our kernel','location','southeast')
axis square
end
%% PROBLEM 3
close all
nr = 2;
nc = 2;
sig_y = 4.5;
sig_yx = 2;
sig_x = 1;
w1 = [-2.5:.02:2.5];
w2 = [-2.5:.02:2.5];
E = abs(sig_y - 2*w1'*w2*sig_yx + ((w1'*w2).^2)*sig_x);
y = sig_yx./(sig_x*w2);
figure('position',[0 500 600 600]);
subplot(nr,nc,1)
hold on
imagesc('XData',w1,'YData',w2,'CData',E)
plot(w1,0,'.r','MarkerSize',10)
plot(0,w2,'.r','MarkerSize',10)
plot(w1,y,'.m','MarkerSize',10)
plot(y,w2,'.m','MarkerSize',10)
xlabel('w1')
ylabel('w2')
axis square
ylim([min(w1) max(w1)])
xlim([min(w1) max(w1)])
subplot(nr,nc,2)
hold on
mesh(w1,w2,E);
zlabel('abs error')
xlabel('w1')
ylabel('w2')
view(-15,60)
axis square
%% 3f
n_steps = 1000;
dt = .01;
tau = 1;
cmap = parula(4);
init = [.001 .001;2.1 -2;2 -2];
w1 = nan(n_steps,size(init,1));
w2 = nan(n_steps,size(init,1));
E = nan(n_steps,size(init,1));
for traj = 1:size(init,1)
w1(1,traj) = init(traj,1);
w2(1,traj) = init(traj,2);
for t = 1:n_steps
dEdw1 = -2*w2(t,traj)*sig_yx+2*(w2(t,traj)^2)*w1(t,traj)*sig_x;
dEdw2 = -2*w1(t,traj)*sig_yx+2*(w1(t,traj)^2)*w2(t,traj)*sig_x;
w1(t+1,traj) = w1(t,traj) - (1/tau)*dEdw1*dt;
w2(t+1,traj) = w2(t,traj) - (1/tau)*dEdw2*dt;
E(t,traj) = abs(sig_y - 2*w1(t,traj)'*w2(t,traj)*sig_yx + ...
((w1(t,traj)'*w2(t,traj)).^2)*sig_x);
end
subplot(nr,nc,3)
hold on
plot(w1(:,traj),w2(:,traj),'.','color',cmap(traj,:),'lineWidth',5)
xlabel('w1')
ylabel('w2')
axis square
subplot(nr,nc,4)
hold on
plot(E(:,traj),'color',cmap(traj,:),'lineWidth',2)
xlabel('iteration')
ylabel('absolute error')
ylim([0 10])
axis square
legend(['w = ' num2str(init(1,1)) ' ; ' num2str(init(1,2)) ],...
['w = ' num2str(init(2,1)) ' ; ' num2str(init(2,2)) ],...
['w = ' num2str(init(3,1)) ' ; ' num2str(init(3,2)) ])
end
w_grid = [0:.02:2.5];
E = abs(sig_y - 2*w_grid.*w_grid*sig_yx + ...
((w_grid.*w_grid).^2)*sig_x);
figure('position',[600 300 900 400]);
subplot(1,3,1)
hold on
plot(w_grid,E,'lineWidth',2)
plot(0,E(1),'or')
plot(w_grid(E==min(E)),min(E),'ok')
legend('error','fixed pt:saddle point','fixed pt:min','location','northwest')
xlabel('w')
ylabel('abs error')
axis square
ylim([0 20])
xlim([0 2.5])
D_set = 2:20;
w_grid = [0:.02:2.5];
E = nan(size(w_grid,2),size(init,1),max(D_set));
dmap = parula(max(D_set)+1);
for traj = 1:3
for D = 2:max(D_set)
E(:,traj,D) = abs(sig_y - 2*w_grid.^D*sig_yx + ...
((w_grid.^D).^2)*sig_x);
subplot(1,3,2)
hold on
plot(w_grid,squeeze(E(:,traj,D)),'color',dmap(D,:),'lineWidth',2)
xlabel('w')
end
end
legend('D = 2',' = 3',' = 4',' = 5',' = 6',' = 7',' = 8',...
' = 9',' ...','location','northwest');
ylim([0 20])
xlim([0 2.5])
axis square
init= [.5;1;1.1];
dEdw = nan(size(D_set,2),size(init,1));
for traj = 1:size(init,1)
w = init(traj);
dEdw(:,traj) = -2*w.^(D_set-1)*sig_yx+2*w.^(2*D_set-1)*sig_x;
end
subplot(1,3,3)
plot(D_set,dEdw,'lineWidth',2)
legend(['w = ' num2str(init(1))],['w = ' num2str(init(2)) ],...
['w = ' num2str(init(3)) ],'location','northwest')
xlabel('D')
ylabel('gradient of E w.r.t w')
ylim([-5 20])
xlim([2 20])
axis square
%%