def test_data_manipulation(self):
tol = 1e-1
x = np.linspace(0, 1, 101).reshape((-1, 1))
y = np.exp(-x**2).reshape(-1)
x_ = np.linspace(1.5, 2, 51).reshape((-1, 1))
y_ = 1 + np.exp(-x_**2).reshape(-1)
gp = MaternGP(x, y, noise_prior=(0.1, 0.1))
tmp = gp.empty_data()
self.assertEqual(tmp, gp)
self.assertTrue(tuple(gp.train_x.shape), (0, 1))
# GPyTorch fails when predicting with an empty dataset, so the following line fails if uncommented
# gp.predict(x)
gp.set_data(x, y)
self.assertEqual(tuple(gp.train_x.shape), (len(x), 1))
gp.optimize_hyperparameters(epochs=10)
gp_pred = gp.predict(x_).mean.cpu().numpy()
self.assertFalse(np.all(np.abs(gp_pred - y_) < tol))
tmp = gp.append_data(x_, y_)
# self.assertTrue(gp != tmp)
# self.assertEqual(tuple(gp.train_x.shape), (len(x), 1))
self.assertEqual(tuple(tmp.train_x.shape), (len(x) + len(x_), 1))
tmp.optimize_hyperparameters(epochs=10)
tmp_pred = tmp.predict(x_).mean.cpu().numpy()
self.assertTrue(np.all(np.abs(tmp_pred - y_) < tol))
def test_hyper_optimization_0(self):
warnings.simplefilter('ignore', gpytorch.utils.warnings.GPInputWarning)
tol = 1e-3
x = np.linspace(0, 1, 101).reshape((-1, 1))
y = np.exp(-x**2).reshape(-1)
gp = MaternGP(x, y, noise_constraint=(0, 1e-4))
gp.optimize_hyperparameters(epochs=20)
gp.optimize_hyperparameters(epochs=20, lr=0.01)
predictions = gp.predict(x)
y_pred = predictions.mean.cpu().numpy()
passed = np.all(np.abs(y - y_pred) < tol)
if passed:
self.assertTrue(True)
else:
x = x.reshape(-1)
f, ax = plt.subplots(1, 1, figsize=(4, 3))
lower, upper = predictions.confidence_region()
ax.plot(x, y, 'k*')
ax.plot(x, y_pred, 'b')
ax.fill_between(x,
lower.cpu().numpy(),
upper.cpu().numpy(),
alpha=0.5)
ax.legend(['Observed Data', 'Mean', 'Confidence', 'Noise'])
ax.grid(True)
#plt.show()
self.assertTrue(False) # This test is necessarily failed
def test_multi_dim_input(self):
tol = 0.1
lin = np.linspace(0, 1, 101)
x = lin.reshape((-1, 1))
x = x + x.T
y = np.exp(-lin**2)
gp = MaternGP(x, y, noise_prior=(0.1, 0.1))
gp.optimize_hyperparameters(epochs=10)
x_query = np.linspace(0.25, 0.75, 27)
y_ = np.exp(-x_query**2)
x_query = x_query.reshape((-1, 1)) + lin.reshape((1, -1))
pred = gp.predict(x_query).mean.cpu().numpy()
self.assertEqual(pred.shape, (27, ))
self.assertTrue(np.all(np.abs(pred - y_) < tol))
def test_hyper_optimization_1(self):
warnings.simplefilter('ignore', gpytorch.utils.warnings.GPInputWarning)
tol = 5e-3
lengthscale = 1.5
outputscale = 2
x = np.linspace(-1, 1, 501).reshape((-1, 1))
# Eventhough the data is generated by a Matern function, the lengthscale and outputscale learned by the Matern
# kernel GP do NOT need to coincide with the ones used to generate the data: the learned ones correspond to the
# influence of nearby points, not to the global structure of the data
y = self._matern_52(x,
lengthscale=lengthscale,
outputscale=outputscale).reshape(-1)
x_train = x[::2]
y_train = y[::2]
x_test = x[1::2]
y_test = y[1::2]
gp = MaternGP(x_train,
y_train,
nu=5 / 2,
noise_constraint=(0, 1e-5),
hyperparameters_initialization={
'covar_module.base_kernel.lengthscale': 1,
'covar_module.outputscale': 1
})
gp.optimizer = torch.optim.Adam
gp.optimize_hyperparameters(epochs=50, lr=0.01)
gp.optimize_hyperparameters(epochs=50, lr=0.001)
gp.optimize_hyperparameters(epochs=30, lr=0.0001)
predictions = gp.predict(x_test)
y_pred = predictions.mean.cpu().numpy()
passed = np.all(np.abs(y_test - y_pred) < tol)
if passed:
self.assertTrue(True)
else:
print(f'Max(diff): {np.abs(y_test - y_pred).max()}')
x_train = x_train.reshape(-1)
x_test = x_test.reshape(-1)
f, ax = plt.subplots(1, 1, figsize=(8, 8))
lower, upper = predictions.confidence_region()
ax.plot(x_train, y_train, 'k*')
ax.plot(x_test, y_pred, 'g-*')
ax.plot(x_test, y_test, 'r*')
ax.fill_between(x_test,
lower.cpu().numpy(),
upper.cpu().numpy(),
alpha=0.5)
ax.legend([
'Observed Data', 'Prediction', 'Hidden data', 'Confidence',
'Noise'
])
ax.grid(True)
#plt.show()
self.assertTrue(False)