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.
sedumi will be called several times to refine the solution.
Original size: 656 variables, 401 equality constraints
200 exponentials add 1600 variables, 1000 equality constraints
-----------------------------------------------------------------
Cones | Errors |
Mov/Act | Centering Exp cone Poly cone | Status
--------+---------------------------------+---------
200/200 | 5.361e+00 2.242e+00 1.198e-09 | Solved
200/200 | 4.227e-01 1.259e-02 1.428e-09 | Solved
200/200 | 4.361e-02 1.353e-04 1.858e-09 | Solved
117/164 | 1.943e-03 1.780e-07 1.938e-09 | Solved
1/112 | 8.779e-04 1.938e-09 1.938e-09 | Solved
0/111 | 1.143e-06 1.939e-09 1.937e-09 | Solved
-----------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +2.10331e+14