int
QP_Solver::check_inactive ()
{
// final check
fprintf (stdout, "\nChecking optimality of inactive variables ");
fflush (stdout);
// make dummy classifier
try {
Model *tmp_model = new Model (param);
tmp_model->b = -lambda_eq;
for (int i = 0; i < l; i++) {
if (! is_lower_bound (i)) tmp_model->add (alpha[i] * y[i], (feature_node *) x[i]);
}
int react_num = 0;
for (int k= l-1; k >= active_size; k--) {
double lambda_up = 1 - y[k] * tmp_model->classify (x[k]);
G[k] = y[k] * tmp_model->b - lambda_up;
// Oops!, must be added to the active example.
if ( (! is_lower_bound (k) && lambda_up < -eps) ||
(! is_upper_bound (k) && lambda_up > eps) ) {
swap_index (k, active_size);
active_size++;
++k;
++react_num;
}
}
delete tmp_model;
fprintf (stdout, " re-activated: %d\n", react_num);
return react_num;
}
catch (...) {
fprintf (stderr, "QP_Solver::check_inactive(): Out of memory\n");
exit (EXIT_FAILURE);
return 0;
}
}
void
QP_Solver::learn_sub()
{
fprintf (stdout, "%6d examples, cache size: %d\n",
active_size, q_matrix->size);
while(++iter) {
/////////////////////////////////////////////////////////
// Select Working set
double Gmax1 = -INF;
int i = -1;
double Gmax2 = -INF;
int j = -1;
for (int k = 0; k < active_size; k++) {
if (y[k] > 0) {
if (!is_upper_bound (k)) {
if (-G[k] > Gmax1) {
Gmax1 = -G[k];
i = k;
}
}
if (!is_lower_bound (k)) {
if (G[k] > Gmax2) {
Gmax2 = G[k];
j = k;
}
}
} else {
if (!is_upper_bound (k)) {
if (-G[k] > Gmax2) {
Gmax2 = -G[k];
j = k;
}
}
if (!is_lower_bound (k)) {
if (G[k] > Gmax1) {
Gmax1 = G[k];
i = k;
}
}
}
}
/////////////////////////////////////////////////////////
//
// Solving QP sub problems
//
double old_alpha_i = alpha[i];
double old_alpha_j = alpha[j];
double *Q_i = q_matrix->getQ (i, active_size);
double *Q_j = q_matrix->getQ (j, active_size);
if (y[i] * y[j] < 0) {
double L = _max (0.0, alpha[j] - alpha[i]);
double H = _min (C, C + alpha[j] - alpha[i]);
alpha[j] += (-G[i] - G[j]) / (Q_i[i] + Q_j[j] + 2 * Q_i[j]);
if (alpha[j] >= H) alpha[j] = H;
else if (alpha[j] <= L) alpha[j] = L;
alpha[i] += (alpha[j] - old_alpha_j);
} else {
double L = _max (0.0, alpha[i] + alpha[j] - C);
double H = _min (C, alpha[i] + alpha[j]);
alpha[j] += (G[i] - G[j]) / (Q_i[i] + Q_j[j] - 2 * Q_i[j]);
if (alpha[j] >= H) alpha[j] = H;
else if (alpha[j] <= L) alpha[j] = L;
alpha[i] -= (alpha[j] - old_alpha_j);
}
/////////////////////////////////////////////////////////
//
// update status
//
status[i] = alpha2status (alpha[i]);
status[j] = alpha2status (alpha[j]);
double delta_alpha_i = alpha[i] - old_alpha_i;
double delta_alpha_j = alpha[j] - old_alpha_j;
/////////////////////////////////////////////////////////
//
// Update O and Calculate \lambda^eq for shrinking, Calculate lambda^eq,
// (c.f. Advances in Kernel Method pp.175)
// lambda_eq = 1/|FREE| \sum_{i \in FREE} y_i - \sum_{l} y_i \alpha_i k(x_i,x_j) (11.29)
//
lambda_eq = 0.0;
int size_A = 0;
for (int k = 0; k < active_size; k++) {
G[k] += Q_i[k] * delta_alpha_i + Q_j[k] * delta_alpha_j;
if (is_free (k)) {
lambda_eq -= G[k] * y[k];
size_A++;
}
}
/////////////////////////////////////////////////////////
//
// Select example for shrinking,
// (c.f. 11.5 Efficient Implementation in Advances in Kernel Method pp. 175)
//
lambda_eq = size_A ? (lambda_eq / size_A) : 0.0;
double kkt_violation = 0.0;
for (int k = 0; k < active_size; k++) {
double lambda_up = -(G[k] + y[k] * lambda_eq); // lambda_lo = -lambda_up
// termination criteria (11.32,11.33,11.34)
if (! is_lower_bound (k) && lambda_up < -kkt_violation) kkt_violation = -lambda_up;
if (! is_upper_bound (k) && lambda_up > kkt_violation) kkt_violation = lambda_up;
// "If the estimate (11.30) or (11.31) was positive (or above some threshold) at
// each of the last h iterations, it is likely that this will be true at the optimal solution"
// lambda^up (11.30) lambda^low = lambda^up * status[k]
if (lambda_up * status[k] > shrink_eps) {
if (shrink_iter[k]++ > shrink_size) {
active_size--;
swap_index (k, active_size); // remove this data from working set
q_matrix->swap_index(k, active_size);
q_matrix->update(active_size);
k--;
}
} else {
// reset iter, if current data dose not satisfy the condition (11.30), (11.31)
shrink_iter[k] = 0;
}
}
/////////////////////////////////////////////////////////
//
// Check terminal criteria, show information of iteration
//
if (kkt_violation < eps) break;
if ((iter % 50) == 0) { fprintf (stdout, "."); fflush (stdout); };
if ((iter % 1000) == 0) {
fprintf (stdout, " %6d %6d %5d %1.4f %5.1f%% %5.1f%%\n",
iter, active_size, q_matrix->size, kkt_violation,
100.0 * (q_matrix->hit - hit_old)/2000,
100.0 * q_matrix->hit/(q_matrix->hit + q_matrix->miss));
fflush (stdout);
// save old hit rate
hit_old = q_matrix->hit;
// This shrink eps rule is delivered from svm_light.
shrink_eps = shrink_eps * 0.7 + kkt_violation * 0.3;
}
}
}
void Solver::do_shrinking()
{
int i,j,k;
if(select_working_set(i,j)!=0) return;
double Gm1 = -y[j]*G[j];
double Gm2 = y[i]*G[i];
// shrink
for(k=0;k<active_size;k++)
{
if(is_lower_bound(k))
{
if(y[k]==+1)
{
if(-G[k] >= Gm1) continue;
}
else if(-G[k] >= Gm2) continue;
}
else if(is_upper_bound(k))
{
if(y[k]==+1)
{
if(G[k] >= Gm2) continue;
}
else if(G[k] >= Gm1) continue;
}
else continue;
--active_size;
swap_index(k,active_size);
--k; // look at the newcomer
}
// unshrink, check all variables again before final iterations
if(unshrinked || -(Gm1 + Gm2) > eps*10) return;
unshrinked = true;
reconstruct_gradient();
for(k=l-1;k>=active_size;k--)
{
if(is_lower_bound(k))
{
if(y[k]==+1)
{
if(-G[k] < Gm1) continue;
}
else if(-G[k] < Gm2) continue;
}
else if(is_upper_bound(k))
{
if(y[k]==+1)
{
if(G[k] < Gm2) continue;
}
else if(G[k] < Gm1) continue;
}
else continue;
swap_index(k,active_size);
active_size++;
++k; // look at the newcomer
}
}
void Solver_NU::do_shrinking()
{
double Gmax1 = -INF; // max { -grad(f)_i * d | y_i = +1, d = +1 }
double Gmax2 = -INF; // max { -grad(f)_i * d | y_i = +1, d = -1 }
double Gmax3 = -INF; // max { -grad(f)_i * d | y_i = -1, d = +1 }
double Gmax4 = -INF; // max { -grad(f)_i * d | y_i = -1, d = -1 }
int k;
for(k=0;k<active_size;k++)
{
if(!is_upper_bound(k))
{
if(y[k]==+1)
{
if(-G[k] > Gmax1) Gmax1 = -G[k];
}
else if(-G[k] > Gmax3) Gmax3 = -G[k];
}
if(!is_lower_bound(k))
{
if(y[k]==+1)
{
if(G[k] > Gmax2) Gmax2 = G[k];
}
else if(G[k] > Gmax4) Gmax4 = G[k];
}
}
double Gm1 = -Gmax2;
double Gm2 = -Gmax1;
double Gm3 = -Gmax4;
double Gm4 = -Gmax3;
for(k=0;k<active_size;k++)
{
if(is_lower_bound(k))
{
if(y[k]==+1)
{
if(-G[k] >= Gm1) continue;
}
else if(-G[k] >= Gm3) continue;
}
else if(is_upper_bound(k))
{
if(y[k]==+1)
{
if(G[k] >= Gm2) continue;
}
else if(G[k] >= Gm4) continue;
}
else continue;
--active_size;
swap_index(k,active_size);
--k; // look at the newcomer
}
// unshrink, check all variables again before final iterations
if(unshrinked || max(-(Gm1+Gm2),-(Gm3+Gm4)) > eps*10) return;
unshrinked = true;
reconstruct_gradient();
for(k=l-1;k>=active_size;k--)
{
if(is_lower_bound(k))
{
if(y[k]==+1)
{
if(-G[k] < Gm1) continue;
}
else if(-G[k] < Gm3) continue;
}
else if(is_upper_bound(k))
{
if(y[k]==+1)
{
if(G[k] < Gm2) continue;
}
else if(G[k] < Gm4) continue;
}
else continue;
swap_index(k,active_size);
active_size++;
++k; // look at the newcomer
}
}
void Solver<TQ>::do_shrinking()
{
float Gmax1 = -INF; // max { -y_i * grad(f)_i | i in I_up(\alpha) }
float Gmax2 = -INF; // max { y_i * grad(f)_i | i in I_low(\alpha) }
// find maximal violating pair first
for(int i=0;i<active_size;i++)
{
if(y[i]==+1)
{
if(!is_upper_bound(i))
{
if(-G[i] >= Gmax1)
Gmax1 = -G[i];
}
if(!is_lower_bound(i))
{
if(G[i] >= Gmax2)
Gmax2 = G[i];
}
}
else
{
if(!is_upper_bound(i))
{
if(-G[i] >= Gmax2)
Gmax2 = -G[i];
}
if(!is_lower_bound(i))
{
if(G[i] >= Gmax1)
Gmax1 = G[i];
}
}
}
// shrink
for(int i=0;i<active_size;i++)
if (be_shrunken(i, Gmax1, Gmax2))
{
active_size--;
while (active_size > i)
{
if (!be_shrunken(active_size, Gmax1, Gmax2))
{
swap_index(i,active_size);
break;
}
active_size--;
}
}
// unshrink, check all variables again before final iterations
if(unshrinked || Gmax1 + Gmax2 > eps*10) return;
unshrinked = true;
reconstruct_gradient();
for(int i=l-1;i>=active_size;i--)
if (!be_shrunken(i, Gmax1, Gmax2))
{
while (active_size < i)
{
if (be_shrunken(active_size, Gmax1, Gmax2))
{
swap_index(i,active_size);
break;
}
active_size++;
}
active_size++;
}
}
