bool FirthRegression::FitFirthModel(Matrix & X, Vector & y, int nrrounds)
{
this-> Reset(X);
G_to_Eigen(X, &this->w->X);
G_to_Eigen(y, &this->w->y);
int rounds = 0;
// double lastDeviance, currentDeviance;
Eigen::MatrixXf xw; // W^(1/2) * X
// Newton-Raphson
while (rounds < nrrounds) {
// std::cout << "beta = " << this->w->beta << "\n";
this->w->eta = this->w->X * this->w->beta;
this->w->p = (1.0 + (-this->w->eta.array()).exp()).inverse();
this->w->V = this->w->p.array() * (1.0 - this->w->p.array());
xw = (this->w->V.array().sqrt().matrix().asDiagonal() * this->w->X).eval(); // W^(1/2) * X
this->w->D = xw.transpose() * xw; // X' V X
this->w->covB = this->w->D.eval().ldlt().solve(Eigen::MatrixXf::Identity(this->w->D.rows(), this->w->D.rows()));
// double rel = ((this->w->D * this->w->covB).array() - Eigen::MatrixXf::Identity(this->w->D.rows(), this->w->D.rows()).array()).matrix().norm() / this->w->D.rows() / this->w->D.rows();
// // printf("norm = %g\n", rel);
// if (rel > 1e-6) { // use relative accuracy to evalute convergence
if ((this->w->D * this->w->covB - Eigen::MatrixXf::Identity(this->w->D.rows(), this->w->D.rows())).norm() > 1e-3) {
// cannot inverse
// printToFile(this->w->D, "matD", "D");
// printToFile(this->w->covB, "matCovB", "B");
return false;
}
this->w->h = (xw * this->w->covB * xw.transpose()).diagonal();
this->w->r = this->w->X.transpose() * (this->w->y - this->w->p + (this->w->h.array() * (0.5 - this->w->p.array())).matrix()); // X' (y-mu)
this->w->delta_beta = this->w->covB * this->w->r;
this->w->beta += this->w->delta_beta;
// printf("norm = %g\n", this->w->delta_beta.norm());
// use relative accuracy to evalute convergence
if (rounds > 1 && (this->w->beta.norm() > 0 && this->w->delta_beta.norm() / this->w->beta.norm() < 1e-6)) {
rounds = 0;
break;
}
rounds ++;
}
if (rounds == nrrounds)
{
printf("Not enough iterations!");
return false;
}
// this->w->covB = this->w->D.eval().llt().solve(Eigen::MatrixXf::Identity(this->w->D.rows(), this->w->D.rows()));
Eigen_to_G(this->w->beta, &B);
Eigen_to_G(this->w->covB, &covB);
Eigen_to_G(this->w->p, &p);
Eigen_to_G(this->w->V, &V);
return true;
}
bool FirthRegression::FitFirthModel(Matrix & X, Vector & succ, Vector& total, int nrrounds) {
this-> Reset(X);
G_to_Eigen(X, &this->w->X);
G_to_Eigen(succ, &this->w->succ);
G_to_Eigen(total, &this->w->total);
int rounds = 0;
// double lastDeviance, currentDeviance;
Eigen::MatrixXf xw; // W^(1/2) * X
// Newton-Raphson
while (rounds < nrrounds) {
// beta = beta + solve( t(X)%*%diag(p*(1-p)) %*%X) %*% t(X) %*% (Y-p);
this->w->eta = this->w->X * this->w->beta;
this->w->p = (-this->w->eta.array().exp() + 1.0).inverse();
this->w->V = this->w->p.array() * (1.0 - this->w->p.array()) * this->w->total.array();
xw = (this->w->V.array().sqrt().matrix().asDiagonal() * this->w->X).eval();
this->w->D = xw.transpose() * xw; // this->w->X.transpose() * this->w->V.asDiagonal() * this->w->X; // X' V X
this->w->covB = this->w->D.eval().llt().solve(Eigen::MatrixXf::Identity(this->w->D.rows(), this->w->D.rows()));
// double rel = ((this->w->D * this->w->covB).array() - Eigen::MatrixXf::Identity(this->w->D.rows(), this->w->D.rows()).array()).matrix().norm() / this->w->D.rows() / this->w->D.rows();
// if (rel > 1e-6) { // use relative accuracy to evalute convergence
if ((this->w->D * this->w->covB - Eigen::MatrixXf::Identity(this->w->D.rows(), this->w->D.rows())).norm() > 1e-3) {
// cannot inverse
return false;
}
this->w->h = (xw.transpose() * this->w->covB * xw).diagonal();
this->w->r = this->w->X.transpose() * (this->w->succ.array() - this->w->total.array() * this->w->p.array()
+ this->w->total.array() * this->w->h.array() * (0.5 - this->w->p.array())).matrix();
this->w->delta_beta = this->w->covB * this->w->r;
this->w->beta += this->w->delta_beta;
if (rounds > 1 && (this->w->beta.norm() > 0 && this->w->delta_beta.norm() / this->w->beta.norm() < 1e-6)) {
rounds = 0;
break;
}
rounds ++;
}
if (rounds == nrrounds)
{
printf("Not enough iterations!");
return false;
}
Eigen_to_G(this->w->beta, &B);
Eigen_to_G(this->w->covB, &covB);
Eigen_to_G(this->w->p, &p);
Eigen_to_G(this->w->V, &V);
return true;
}
void CholeskyInverseMatrix(Matrix& in, Matrix* out) {
if (in.rows != in.cols) return;
const int n = in.rows;
Eigen::MatrixXf x, res;
G_to_Eigen(in, &x);
res = x.ldlt().solve(Eigen::MatrixXf::Identity(n, n));
Eigen_to_G(res, out);
}
