ComparePredictionsOutput compare_predictions(const ConstVectorView &truth,
const ConstVectorView &pred) {
Matrix X(truth.size(), 2);
X.col(0) = 1.0;
X.col(1) = truth;
RegressionModel model(X, pred);
Vector null_residual = pred - truth;
Vector beta = model.Beta();
Vector alternative_residual = pred - X * beta;
// Under the null hypothesis, residual and alternative_residual
// will have the same distribution, but the alternative_residual
// will have used two degrees of freedom, while the null reisdual
// will have used zero.
int n = truth.size();
double SSE = alternative_residual.normsq();
double SST = null_residual.normsq();
double SSR = SST - SSE;
double Fstat = (SSE / (n - 2)) / (SSR / 2.0);
double p_value = pf(Fstat, n - 2, 2, false);
ComparePredictionsOutput result;
SpdMatrix xtx(2, 0.0);
xtx.add_inner(X);
Vector beta_standard_errors = sqrt(model.sigsq() * (xtx.inv().diag()));
result.intercept = beta[0];
result.intercept_se = beta_standard_errors[0];
result.slope = beta[1];
result.slope_se = beta_standard_errors[1];
result.SSE = SSE;
result.SST = SST;
result.Fstat = Fstat;
result.p_value = p_value;
return result;
}
void ArPosteriorSampler::draw_phi_univariate() {
int p = model_->phi().size();
Vec phi = model_->phi();
if (!model_->check_stationary(phi)) {
report_error("ArPosteriorSampler::draw_phi_univariate was called with an "
"illegal initial value of phi. That should never happen.");
}
const Spd &xtx(model_->suf()->xtx());
const Vec &xty(model_->suf()->xty());
for (int i = 0; i < p; ++i) {
double initial_phi = phi[i];
double lo = -1;
double hi = 1;
// y - xb y - xb
// bt xtx b - 2 bt xty + yty
// bt xtx b = sum_i sum_j beta[i] beta[j] xtx[i, j]
// = beta [i]^2 xtx[i,i] + 2 * sum_{j != i} beta[i] xtx[i, j] * beta[j]
// - 2 * beta[i] * xty[i];
// mean is (xty[i] - sum_{j != i} )
double ivar = xtx(i, i);
double mu = (xty[i] - (phi.dot(xtx.col(i)) - phi[i] * xtx(i, i))) / ivar;
bool ok = false;
while (!ok) {
double candidate = rtrun_norm_2_mt(rng(), mu, sqrt(1.0/ivar), lo, hi);
phi[i] = candidate;
if (ArModel::check_stationary(phi)) {
ok = true;
} else {
if (candidate > initial_phi) hi = candidate;
else lo = candidate;
}
}
}
model_->set_phi(phi);
}
Matrix MvRegSuf::conditional_beta_hat(const SelectorMatrix &included) const {
Matrix ans(xdim(), ydim());
std::map<Selector, Cholesky> chol_map;
for (int i = 0; i < ydim(); ++i) {
const Selector &inc(included.col(i));
auto it = chol_map.find(inc);
if (it == chol_map.end()) {
chol_map[it->first] = Cholesky(inc.select(xtx()));
it = chol_map.find(inc);
}
ans.col(i) = inc.expand(it->second.solve(inc.select(xty_.col(i))));
}
return ans;
}
int main() {
auto b = genRandomVector(kDim);
Matrix xtx(kDim);
Vector xty(kDim);
{
Timer tGen("Generate");
constexpr u32 kVectorPoints = 4000 * kDim;
for (u32 iVectorPoint = 0; iVectorPoint < kVectorPoints; ++iVectorPoint) {
auto p = getRandomVectorPoint(b);
for (size_t i = 0; i < p.dimension(); ++i) {
for (size_t j = 0; j < p.dimension(); ++j) {
xtx.data_[i][j] += p.a_[i] * p.a_[j];
}
}
for (size_t i = 0; i < p.dimension(); ++i) {
xty[i] += p.a_[i] * p.b_;
}
}
}
{
Timer tSolve("Invert");
auto inv = xtx.invert();
tSolve.finish();
Vector bPrime = inv * xty;
LOG(INFO) << OUT(b) << OUT(length(b));
LOG(INFO) << OUT(bPrime) << OUT(length(bPrime));
auto err = b - bPrime;
LOG(INFO) << OUT(err) << OUT(length(err));
}
{
Timer tSolve("Cholesky");
auto chol = xtx.cholesky();
tSolve.finish();
Matrix xtx2 = chol*chol.transpose();
LOG(INFO) << OUT(xtx.norm2()) << OUT(xtx2.norm2()) << OUT((xtx - xtx2).norm2());
}
return 0;
}
double RM::Loglike(const Vector &sigsq_beta,
Vector &g, Matrix &h, uint nd)const{
const double log2pi = 1.83787706640935;
const double sigsq = sigsq_beta[0];
const Vector b(ConstVectorView(sigsq_beta, 1));
double n = suf()->n();
if(b.size()==0) return empty_loglike(g, h, nd);
double SSE = yty() - 2*b.dot(xty()) + xtx().Mdist(b);
double ans = -.5*(n * log2pi + n *log(sigsq)+ SSE/sigsq);
if(nd>0){ // sigsq derivs come first in CP2 vectorization
SpdMatrix xtx = this->xtx();
Vector gbeta = (xty() - xtx*b)/sigsq;
double sig4 = sigsq*sigsq;
double gsigsq = -n/(2*sigsq) + SSE/(2*sig4);
g = concat(gsigsq, gbeta);
if(nd>1){
double h11 = .5*n/sig4 - SSE/(sig4*sigsq);
h = unpartition(h11, (-1/sigsq)*gbeta, (-1/sigsq)*xtx);}}
return ans;
}
DoubleVector linearRegression(const VectorPoints& points, double rigid) {
assert(!points.empty());
Matrix xtx(points[0].dimension());
Vector xty(points[0].dimension());
for (u32 iVectorPoint = 0; iVectorPoint < points.size(); ++iVectorPoint) {
const auto& p = points[iVectorPoint];
assert(p.dimension() == xty.size());
for (size_t i = 0; i < p.dimension(); ++i) {
for (size_t j = 0; j < p.dimension(); ++j) {
xtx.data_[i][j] += p.a_[i] * p.a_[j];
}
}
for (size_t i = 0; i < p.dimension(); ++i) {
xty[i] += p.a_[i] * p.b_;
}
}
for (size_t i = 0; i < xtx.dimension(); ++i) {
xtx.data_[i][i] += rigid;
}
xtx /= points.size();
for (auto& x : xty) {
x /= points.size();
}
auto b = xtx.invert() * xty;
// cout << OUT((xtx.invert() * xtx - Matrix::one(xtx.dimension())).norm2()) << endl;
/*
for (size_t i = 0; i < points.size(); ++i) {
const auto& p = points[i];
cout << OUT(p.b_) << OUT(dot(p.a_, b)) << OUT(p.a_[p.a_.size() - 2]) << endl;
}
*/
return b;
}
SpdMatrix MvRegSuf::SSE(const Matrix &B) const {
SpdMatrix ans = yty();
ans.add_inner2(B, xty(), -1);
ans += sandwich(B.transpose(), xtx());
return ans;
}
SpdMatrix RM::xtx()const{ return xtx( coef().inc() ) ;}
//============================================================
SpdMatrix RegSuf::centered_xtx() const {
SpdMatrix ans = xtx();
ans.add_outer(xbar(), -n());
return ans;
}
double NeRegSuf::SSE()const{
SpdMatrix ivar = xtx().inv();
return yty() - ivar.Mdist(xty()); }
ostream & QrRegSuf::print(ostream &out)const{
return out << "sumsqy = " << yty() << endl
<< "xty_ = " << xty() << endl
<< "xtx = " << endl << xtx();
}
SpdMatrix QrRegSuf::xtx(const Selector &inc)const{
// if(!current) refresh_qr();
return inc.select(xtx());
}
//======================================================================
ostream & RegSuf::print(ostream &out)const{
out << "sample size: " << n() << endl
<< "xty: " << xty() << endl
<< "xtx: " << endl << xtx();
return out;
}