int TLogRegFit::MLENewton(const double& ChangeEps, const int& MaxStep, const TStr PlotNm) {
TExeTm ExeTm;
TFltV GradV(Theta.Len()), DeltaLV(Theta.Len());
TFltVV HVV(Theta.Len(), Theta.Len());
int iter = 0;
double MinVal = -1e10, MaxVal = 1e10;
for(iter = 0; iter < MaxStep; iter++) {
Gradient(GradV);
Hessian(HVV);
GetNewtonStep(HVV, GradV, DeltaLV);
double Increment = TLinAlg::DotProduct(GradV, DeltaLV);
if (Increment <= ChangeEps) {
break;
}
double LearnRate = GetStepSizeByLineSearch(DeltaLV, GradV, 0.15, 0.5);//InitLearnRate/double(0.01*(double)iter + 1);
for(int i = 0; i < Theta.Len(); i++) {
double Change = LearnRate * DeltaLV[i];
Theta[i] += Change;
if(Theta[i] < MinVal) {
Theta[i] = MinVal;
}
if(Theta[i] > MaxVal) {
Theta[i] = MaxVal;
}
}
}
if (! PlotNm.Empty()) {
printf("MLE with Newton method completed with %d iterations(%s)\n",iter,ExeTm.GetTmStr());
}
return iter;
}
double
TakeStep(OPTOBJ * opt, const double tol, double *factor,
int *newbound)
{
double norm;
double *direct, *space;
double maxfactor;
int i;
space = opt->space;
direct = opt->space;
space += opt->n;
for (i = 0; i < opt->n; i++) {
opt->onbound[i] = 0;
}
do {
norm = GetNewtonStep(direct, opt->H, opt->dx, opt->n, opt->onbound);
} while (UpdateActiveSet
(opt->x, direct, ((struct scaleinfo *) opt->state)->scale, opt->H,
opt->lb, opt->ub, opt->onbound, opt->n));
/*assert(VectorDotProduct(opt->dx, direct, opt->n));*/
/* Scale step to satisfy trust region */
if ( norm<opt->trust){ scale_vector (direct,opt->n,opt->trust/norm); }
*factor = 1.;
*newbound = 0;
maxfactor =
TrimAtBoundaries(opt->x, direct,
((struct scaleinfo *) opt->state)->scale, opt->n,
opt->lb, opt->ub, opt->onbound);
/*
* Three tier decision criteria. i. If Newton step is valid, accept.
* ii. If not, look at function and gradient at boundary and decide
* whether to accept. iii. Otherwise do line search to find maximum.
*/
if (maxfactor <= 1.0) {
/* Don't accept Newton step -- will hit boundary */
double fbound;
ScaledStep(maxfactor, opt->x, opt->xn, direct, opt->onbound, opt->n);
fbound = opt->f(opt->xn, opt->state); opt->neval++;
if (fbound < opt->fc) {
/*
* Point on boundary is better than current point,
* check grad
*/
double fnearbound;
ScaledStep(maxfactor * (1. - BOUND_TOL), opt->x, opt->xn, direct,
opt->onbound, opt->n);
fnearbound = opt->f(opt->xn, opt->state); opt->neval++;
if (fnearbound > fbound) {
/*
* If point on boundary appears to be
* maximum, keep it
*/
ScaledStep(maxfactor, opt->x, opt->xn, direct, opt->onbound, opt->n);
opt->fn = fbound;
*newbound = 1;
UpdateActiveSet
(opt->xn, direct, ((struct scaleinfo *) opt->state)->scale, opt->H,
opt->lb, opt->ub, opt->onbound, opt->n);
OPTMESS(printf("Newton step hit boundary, appears optimal (maxfactor = %e)\n",maxfactor);)
goto optexit;