def _fit_gp(X, covX, t):
xx, xy, yy = covX[0, 0], covX[0, 1], covX[1, 1]
# Perform hyper-parameter optimization with different
# initial points and choose the GP with best model evidence
theta0 = np.array((t.std(), sqrt(xx), sqrt(yy), xy, .01))
from gp import GaussianProcess, sqexp2D_covariancef
best_gp = GaussianProcess.fit(X, t, sqexp2D_covariancef, theta0)
from sklearn.model_selection import ParameterSampler
from scipy.stats import uniform
grid = {
'sigmaf': uniform(0.1 * t.std(), 10 * t.std()),
'cov_xx': uniform(50, 2000),
'cov_yy': uniform(50, 2000),
'noise_prec': uniform(0.1, 10)
}
for i, sample in enumerate(ParameterSampler(grid, n_iter=500)):
sys.stdout.write('iter: %d/500 evidence: %.4f\r' %
(i, best_gp.model_evidence()))
sys.stdout.flush()
theta0 = np.array((sample['sigmaf'], sample['cov_xx'],
sample['cov_yy'], 0, sample['noise_prec']))
gp = GaussianProcess.fit(X, t, sqexp2D_covariancef, theta0)
if gp.model_evidence() > best_gp.model_evidence():
best_gp = gp
return best_gp
def _fit_gp(X, covX, t):
xx, xy, yy = covX[0,0], covX[0,1], covX[1,1]
# Perform hyper-parameter optimization with different
# initial points and choose the GP with best model evidence
theta0 = np.array(( t.std(), sqrt(xx), sqrt(yy), xy, 10. ))
best_gp = GaussianProcess.fit(X, t, sqexp2D_covariancef, theta0)
for tau in xrange(50, 800, 100):
theta0 = np.array(( t.std(), tau, tau, 0, 10. ))
gp = GaussianProcess.fit(X, t, sqexp2D_covariancef, theta0)
if gp.model_evidence() > best_gp.model_evidence():
best_gp = gp
return best_gp
class TestGP:
def setUp(self):
self.gp = GaussianProcess()
def test_sparse(self):
N = 1000
x = 1000*np.random.rand(N)
y = np.sin(x) + 0.1*np.random.randn(N)
# do it using dense algebra
Kxx = self.gp.K(x,x).todense()
alpha = np.linalg.solve(Kxx,y)
# sparse algebra
self.gp.fit(x,y)
assert np.linalg.norm(alpha-self.gp._alpha) < 1e-10
import numpy as np
from matplotlib import pyplot
from gp import GaussianProcess, sqexp1D_covariancef
if __name__ == "__main__":
# --------------------------------------
x = (np.random.random(100) - 0.5) * 2
t = np.array(map(lambda a: a ** 2 + 0.05 * np.random.randn(), x))
t = t - np.mean(t)
# Find the best set of hyper-parameters
theta0 = [np.std(t), 1, 10]
gp = GaussianProcess.fit(x, t, sqexp1D_covariancef, theta0)
# Plot predictions and samples from the Gaussian Process
q = np.arange(-1.2, 1.2, 0.051)
mean, cov = gp.predict(q, cov=True)
assert (mean == gp.predict(q)).all()
sig_bnd = np.sqrt(np.diag(cov))
for s in np.random.multivariate_normal(mean, cov, 5):
pyplot.plot(q, s, "y-")
pyplot.plot(x, t, ".")
pyplot.plot(q, mean, "r-")
pyplot.plot(q, mean + 2 * sig_bnd, "k-")
pyplot.plot(q, mean - 2 * sig_bnd, "k-")
pyplot.show(block=True)
from gp import GaussianProcess, sqexp2D_covariancef
if __name__ == "__main__":
#--------------------------------------
# sample training data
x = np.array([
np.array([i, j]) for i in np.arange(-1, 1, 0.2)
for j in np.arange(-1, 1, 0.2)
])
t = np.array(
[r[0]**2 + r[1]**2 + r[0] * r[1] + 0.1 * np.random.randn() for r in x])
t = t - np.mean(t)
# Find the best set of hyper-parameters
theta0 = [np.std(t), 1, 1, 0, 10]
gp = GaussianProcess.fit(x, t, sqexp2D_covariancef, theta0)
print gp.covf.theta
# Plot predictions and samples from the Gaussian Process
q = np.array([
np.array([i, j]) for i in np.arange(-1.1, 1.1, 0.2)
for j in np.arange(-1.1, 1.1, 0.2)
])
mean, cov = gp.predict(q, cov=True)
assert (mean == gp.predict(q)).all()
sig_bnd = np.sqrt(np.diag(cov))
mlab.points3d(x[:, 0], x[:, 1], t, t, scale_mode='none', scale_factor=0.01)
pts = mlab.points3d(q[:, 0],