project_sbb.m

data = importdata('Users/Desktop/sp18/project/normed_data.csv');
n = 569;
d = 26;
X = data(:,1:d);
Y = data(:,27);
w = normrnd(0,1,[d,1]);
L = max(eig(X'*X));
I = eye(d);

max_it = 4*10^2;
grad_norm = zeros(max_it + 1, 1);
alpha = 1/L;
w_prev = zeros(d,1);
grad_prev = zeros(d,1);
H_k = eye(d);
t = cputime;
times = zeros(max_it + 1, 1);
ite = 1;
while(ite<=max_it)
    grad_w = zeros(d,1);
    sum = 0;
    for i=1:n
        z = exp(-Y(i)*X(i,:)*w);
        grad_w = grad_w+ (-Y(i)*X(i,:)*z)'/(1+z);
    end
    grad_norm(ite) = log10(norm(grad_w/n));
    s = w - w_prev;
    y = grad_w - grad_prev;
    alpha = (y'*s)/(y'*y);
    H_k = alpha*I;
    grad_prev = grad_w;
    w_prev = w;
    w =  w - H_k*grad_w;
    times(ite) = cputime-t;
    ite = ite +1;
end

figure;
plot_length = max_it;
plot_vec = 1:1:plot_length;
plot(plot_vec, grad_norm(1:plot_length), 'b-');
plot(times(1:plot_length), grad_norm(1:plot_length), 'b-');
xlabel('iteration');
xlabel('cputime');
ylabel('Log Gradient Norm');
title('SBB');