Figure 7.1: Logistic regression (GP version)
randn('state',0);
rand('state',0);
a = 1;
b = -5;
m = 100;
u = 10*rand(m,1);
y = (rand(m,1) < exp(a*u+b)./(1+exp(a*u+b)));
ind_false = find( y == 0 );
ind_true = find( y == 1 );
X = [u(ind_true); u(ind_false)];
X = [X ones(size(u,1),1)];
[m,n] = size(X);
q = length(ind_true);
cvx_begin gp
variables z(n) t(q) s(m)
minimize( prod(t)*prod(s) )
subject to
for k = 1:q
prod( z.^(X(k,:)') ) <= t(k);
end
for k = 1:m
1 + prod( z.^(-X(k,:)') ) <= s(k);
end
cvx_end
theta = log(z);
aml = -theta(1);
bml = -theta(2);
us = linspace(-1,11,1000)';
ps = exp(aml*us + bml)./(1+exp(aml*us+bml));
plot(us,ps,'-', u(ind_true),y(ind_true),'o', ...
u(ind_false),y(ind_false),'o');
axis([-1, 11,-0.1,1.1]);
Successive approximation method to be employed.
SDPT3 will be called several times to refine the solution.
Original size: 653 variables, 255 equality constraints
For improved efficiency, SDPT3 is solving the dual problem.
Approximation size: 2254 variables, 1255 equality constraints
-----------------------------------------------------------------
Target Conic Solver
Precision Error Status
---------------------------
1.221e-04 2.481e+00 Solved
1.221e-04 2.933e-03 Solved
1.221e-04 0.000e+00 Solved
1.490e-08 7.324e-07 Solved
1.490e-08 0.000e+00 Solved
-----------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +2.10331e+14