def test_modelrecreation(self):
par = toy_model()
pcopy = GPRegression(par.X.copy(),
par.Y.copy(),
kernel=par.kern.copy())
np.testing.assert_allclose(par.param_array, pcopy.param_array)
np.testing.assert_allclose(par.gradient_full, pcopy.gradient_full)
self.assertSequenceEqual(str(par), str(pcopy))
self.assertIsNot(par.param_array, pcopy.param_array)
self.assertIsNot(par.gradient_full, pcopy.gradient_full)
self.assertTrue(pcopy.checkgrad())
self.assert_(np.any(pcopy.gradient != 0.0))
np.testing.assert_allclose(pcopy.param_array,
par.param_array,
atol=1e-6)
par.randomize()
with tempfile.TemporaryFile('w+b') as f:
par.pickle(f)
f.seek(0)
pcopy = pickle.load(f)
np.testing.assert_allclose(par.param_array, pcopy.param_array)
np.testing.assert_allclose(par.gradient_full,
pcopy.gradient_full,
atol=1e-6)
self.assertSequenceEqual(str(par), str(pcopy))
self.assert_(pcopy.checkgrad())
def visualize_quadratic_function(self):
x_range = np.linspace(0., 1., 80)
y_range = np.linspace(0., 1., 80)
X = cartesian([x_range, y_range])
import os
if not os.path.exists("./pics/"):
os.makedirs("./pics/")
#################################
# TRAIN THE W_OPTIMIZER #
#################################
Opt = TripathyOptimizer()
for j in range(self.no_tries):
print("Try number : ", j)
W_hat = self.kernel.sample_W()
self.kernel.update_params(
W=W_hat,
s=self.kernel.inner_kernel.variance,
l=self.kernel.inner_kernel.lengthscale
)
W_hat, sn, l, s = Opt.run_two_step_optimization(self.kernel, self.sn, self.X, self.Y)
# Create the gp_regression function and pass in the predictor function as f_hat
self.kernel.update_params(W=W_hat, l=l, s=s)
gp_reg = GPRegression(self.X, self.Y, self.kernel, noise_var=sn)
y = self.function.f( np.dot(X, self.real_W).T )
y_hat = gp_reg.predict(self.X)[0].squeeze()
#################################
# END TRAIN THE W_OPTIMIZER #
#################################
fig = plt.figure()
ax = Axes3D(fig)
# First plot the real function
ax.scatter(X[:,0], X[:, 1], y, s=1)
ax.scatter(self.X[:,0], self.X[:, 1], y_hat, cmap=plt.cm.jet)
fig.savefig('./pics/Iter_' + str(j) + '.png', )
# plt.show()
plt.close(fig)
# Save the W just in case
l = loss(
self.kernel,
W_hat,
sn,
s,
l,
self.X,
self.Y
)
np.savetxt("./pics/Iter_" + str(j) + "__" + "Loss_" + str(l) + ".txt", W_hat)
def fit_single_GP_model(X, Y, parameter_list, ard=False):
kernel = RBF(X.shape[1],
ARD=parameter_list[3],
lengthscale=parameter_list[0],
variance=parameter_list[1])
gp = GPRegression(X=X, Y=Y, kernel=kernel, noise_var=parameter_list[2])
gp.likelihood.variance.fix(1e-2)
gp.optimize()
return gp
def compare_against_mmd_test():
data = loadmat("../data/02-solar.mat")
X = data["X"]
y = data["y"]
X_train, y_train, X_test, y_test, N, N_test = prepare_dataset(X, y)
kernel = RBF(input_dim=1, variance=0.608, lengthscale=0.207)
m = GPRegression(X_train, y_train, kernel, noise_var=0.283)
m.optimize()
pred_mean, pred_std = m.predict(X_test)
s = GaussianQuadraticTest(None)
gradients = compute_gp_regression_gradients(y_test, pred_mean, pred_std)
U_matrix, stat = s.get_statistic_multiple_custom_gradient(y_test[:, 0], gradients[:, 0])
num_test_samples = 10000
null_samples = bootstrap_null(U_matrix, num_bootstrap=num_test_samples)
# null_samples = sample_null_simulated_gp(s, pred_mean, pred_std, num_test_samples)
p_value_ours = 1.0 - np.mean(null_samples <= stat)
y_rep = np.random.randn(len(X_test)) * pred_std.flatten() + pred_mean.flatten()
y_rep = np.atleast_2d(y_rep).T
A = np.hstack((X_test, y_test))
B = np.hstack((X_test, y_rep))
feats_p = RealFeatures(A.T)
feats_q = RealFeatures(B.T)
width = 1
kernel = GaussianKernel(10, width)
mmd = QuadraticTimeMMD()
mmd.set_kernel(kernel)
mmd.set_p(feats_p)
mmd.set_q(feats_q)
mmd_stat = mmd.compute_statistic()
# sample from null
num_null_samples = 10000
mmd_null_samples = np.zeros(num_null_samples)
for i in range(num_null_samples):
# fix y_rep from above, and change the other one (that would replace y_test)
y_rep2 = np.random.randn(len(X_test)) * pred_std.flatten() + pred_mean.flatten()
y_rep2 = np.atleast_2d(y_rep2).T
A = np.hstack((X_test, y_rep2))
feats_p = RealFeatures(A.T)
width = 1
kernel = GaussianKernel(10, width)
mmd = QuadraticTimeMMD()
mmd.set_kernel(kernel)
mmd.set_p(feats_p)
mmd.set_q(feats_q)
mmd_null_samples[i] = mmd.compute_statistic()
p_value_mmd = 1.0 - np.mean(mmd_null_samples <= mmd_stat)
return p_value_ours, p_value_mmd
def test_visualize_augmented_sinusoidal_function(self):
self.init()
import os
if not os.path.exists("./pics/camelback/"):
os.makedirs("./pics/")
os.makedirs("./pics/camelback/")
#################################
# TRAIN THE W_OPTIMIZER #
#################################
Opt = TripathyOptimizer()
print("Real hidden matrix is: ", self.real_W)
for j in range(self.no_tries):
print("Try number : ", j)
W_hat = self.kernel.sample_W()
self.kernel.update_params(
W=W_hat,
s=self.kernel.inner_kernel.variance,
l=self.kernel.inner_kernel.lengthscale
)
W_hat, sn, l, s = Opt.run_two_step_optimization(self.kernel, self.sn, self.X, self.Y)
# Create the gp_regression function and pass in the predictor function as f_hat
self.kernel.update_params(W=W_hat, l=l, s=s)
gp_reg = GPRegression(self.X, self.Y, self.kernel, noise_var=sn)
y_hat = gp_reg.predict(self.X)[0].squeeze()
#################################
# END TRAIN THE W_OPTIMIZER #
#################################
# Save the W just in case
l = loss(
self.kernel,
W_hat,
sn,
s,
l,
self.X,
self.Y
)
np.savetxt("./pics/camelback/Iter_" + str(j) + "__" + "Loss_" + str(l) + ".txt", W_hat)
def check_if_matrix_is_found(self):
print("Starting to optimize stuf...")
import os
if not os.path.exists("./featureSelection/"):
os.makedirs("./featureSelection/")
#################################
# TRAIN THE W_OPTIMIZER #
#################################
Opt = TripathyOptimizer()
print("Real hidden matrix is: ", self.real_W)
# Start with the approximation of the real matrix
W_hat = self.kernel.sample_W()
self.kernel.update_params(W=W_hat,
s=self.kernel.inner_kernel.variance,
l=self.kernel.inner_kernel.lengthscale)
W_hat, sn, l, s = Opt.try_two_step_optimization_with_restarts(
self.kernel, self.phi_X, self.Y)
# Create the gp_regression function and pass in the predictor function as f_hat
self.kernel.update_params(W=W_hat, l=l, s=s)
gp_reg = GPRegression(self.phi_X, self.Y, self.kernel, noise_var=sn)
# Maybe predict even more values ? (plot the entire surface?)
y_hat = gp_reg.predict(self.phi_X)[0].squeeze()
#################################
# END TRAIN THE W_OPTIMIZER #
#################################
# Save the W just in case
l = loss(self.kernel, W_hat, sn, s, l, self.phi_X, self.Y)
np.savetxt(
config['basepath'] + "/featureSelection/" + str(l) +
"_BestLoss.txt", W_hat)
np.savetxt(
config['basepath'] + "/featureSelection/" + str(l) +
"_realMatr.txt", self.real_W)
# Create the gp_regression function and pass in the predictor function as f_hat
self.plot_3d(y_hat, title=str(l) + "_BestLoss")
def test_add_observer(self):
par = toy_model()
par.name = "original"
par.count = 0
par.add_observer(self, self._callback, 1)
pcopy = GPRegression(par.X.copy(), par.Y.copy(), kernel=par.kern.copy())
self.assertNotIn(par.observers[0], pcopy.observers)
pcopy = par.copy()
pcopy.name = "copy"
self.assertTrue(par.checkgrad())
self.assertTrue(pcopy.checkgrad())
self.assertTrue(pcopy.kern.checkgrad())
import ipdb;ipdb.set_trace()
self.assertIn(par.observers[0], pcopy.observers)
self.assertEqual(par.count, 3)
self.assertEqual(pcopy.count, 6) # 3 of each call to checkgrad
def dloss_ds(kernel, fix_W, fix_sn, s, fix_l, X, Y):
# TODO: write some tests that check if changeing X or Y affect this derivative correctly!
kernel.update_params(W=fix_W, s=s, l=fix_l)
Y = Y.reshape((-1, 1))
# The following line modifies `kernel`, so don't remove it
gp_reg = GPRegression(X, Y, kernel, noise_var=fix_sn)
grads = kernel.inner_kernel.variance.gradient
return grads
def test_add_observer(self):
par = toy_model()
par.name = "original"
par.count = 0
par.add_observer(self, self._callback, 1)
pcopy = GPRegression(par.X.copy(),
par.Y.copy(),
kernel=par.kern.copy())
self.assertNotIn(par.observers[0], pcopy.observers)
pcopy = par.copy()
pcopy.name = "copy"
self.assertTrue(par.checkgrad())
self.assertTrue(pcopy.checkgrad())
self.assertTrue(pcopy.kern.checkgrad())
import ipdb
ipdb.set_trace()
self.assertIn(par.observers[0], pcopy.observers)
self.assertEqual(par.count, 3)
self.assertEqual(pcopy.count, 6) # 3 of each call to checkgrad
def test_modelrecreation(self):
par = toy_model()
pcopy = GPRegression(par.X.copy(), par.Y.copy(), kernel=par.kern.copy())
np.testing.assert_allclose(par.param_array, pcopy.param_array)
np.testing.assert_allclose(par.gradient_full, pcopy.gradient_full)
self.assertSequenceEqual(str(par), str(pcopy))
self.assertIsNot(par.param_array, pcopy.param_array)
self.assertIsNot(par.gradient_full, pcopy.gradient_full)
self.assertTrue(pcopy.checkgrad())
self.assert_(np.any(pcopy.gradient!=0.0))
np.testing.assert_allclose(pcopy.param_array, par.param_array, atol=1e-6)
par.randomize()
with tempfile.TemporaryFile('w+b') as f:
par.pickle(f)
f.seek(0)
pcopy = pickle.load(f)
np.testing.assert_allclose(par.param_array, pcopy.param_array)
np.testing.assert_allclose(par.gradient_full, pcopy.gradient_full, atol=1e-6)
self.assertSequenceEqual(str(par), str(pcopy))
self.assert_(pcopy.checkgrad())
def test_gp_regression(self):
"""
The prediction of GPRegression sohuld be 1D!
:return:
"""
self.init()
test_samples = 10
Xrand = np.random.rand(test_samples, self.real_dim)
# Check shape of GP
gp_reg = GPRegression(self.X,
self.Y,
kernel=self.kernel,
noise_var=self.sn)
y_hat = gp_reg.predict(Xrand)[
0] # Apparently, this predicts both mean and variance...
assert y_hat.shape == (test_samples, 1), y_hat.shape
def loss(kernel, W, sn, s, l, X, Y):
"""
:param W: The orthogonal projection matrix
:param sn: The noise-variance for the regression
:param s: The kernel scalar hyperparameter
:param l: The kernel lengthscales hyperparameter (array)
:param X: The data to optimize over (observations)
:param Y: The data to optimize over (target values)
:return: A scalar value describing the "loss" of the given model
"""
assert kernel.real_dim == X.shape[1]
assert Y.shape[0] == X.shape[0]
# Laziliy implementing GPy's function!
# # TODO: check if the kernel inherits the correct methods
# TODO: change that GPRegression is not newly created maybe, but instead only the parameters are changed or so
kernel.update_params(W, l, s)
Y = Y.reshape((-1, 1))
gp_reg = GPRegression(X, Y, kernel, noise_var=sn)
return gp_reg.log_likelihood()
def fit_all_models(self):
functions = {}
num_features = self.Z.shape[1]
kernel = RBF(num_features, ARD=False, lengthscale=1., variance=1.)
gp_Y = GPRegression(X=self.Z, Y=self.Y, kernel=kernel, noise_var=1.)
gp_Y.optimize()
num_features = self.X.shape[1]
kernel = RBF(num_features, ARD=False, lengthscale=1., variance=1.)
gp_Z = GPRegression(X=self.X, Y=self.Z, kernel=kernel)
gp_Z.optimize()
functions = OrderedDict([('Y', gp_Y), ('Z', gp_Z), ('X', [])])
return functions
def test_if_function_is_found(self):
"""
Replace these tests by the actual optimizer function!
:return:
"""
self.init()
print("Real matrix is: ", self.real_W)
all_tries = []
for i in range(self.tries):
# Initialize random guess
W_hat = self.kernel.sample_W()
# Find a good W!
for i in range(self.max_iter):
W_hat = self.w_optimizer.optimize_stiefel_manifold(W_hat)
print("Difference to real W is: ", (W_hat - self.real_W))
assert W_hat.shape == self.real_W.shape
self.kernel.update_params(
W=W_hat,
l=self.kernel.inner_kernel.lengthscale,
s=self.kernel.inner_kernel.variance
)
# TODO: update the gaussian process with the new kernels parameters! (i.e. W_hat)
# Create the gp_regression function and pass in the predictor function as f_hat
gp_reg = GPRegression(self.X, self.Y, self.kernel, noise_var=self.sn)
res = self.metrics.mean_difference_points(
fnc=self.function._f,
fnc_hat=gp_reg.predict,
A=self.real_W,
A_hat=W_hat,
X=self.X
)
all_tries.append(res)
print(all_tries)
assert np.asarray(all_tries).any()
def refit_models(self, observational_samples):
X = np.asarray(observational_samples['X'])[:, np.newaxis]
Z = np.asarray(observational_samples['Z'])[:, np.newaxis]
Y = np.asarray(observational_samples['Y'])[:, np.newaxis]
functions = {}
num_features = Z.shape[1]
kernel = RBF(num_features, ARD=False, lengthscale=1., variance=1.)
gp_Y = GPRegression(X=Z, Y=Y, kernel=kernel, noise_var=1.)
gp_Y.optimize()
num_features = X.shape[1]
kernel = RBF(num_features, ARD=False, lengthscale=1., variance=1.)
gp_Z = GPRegression(X=X, Y=Z, kernel=kernel)
gp_Z.optimize()
functions = OrderedDict([('Y', gp_Y), ('Z', gp_Z), ('X', [])])
return functions
def dloss_dW(kernel, W, fix_sn, fix_s, fix_l, X, Y):
"""
The derivative of the loss functions up to a parameter "param"
:param kernel:
:param W:
:param fix_sn:
:param fix_s:
:param fix_l:
:param X:
:param Y:
:return:
"""
kernel.update_params(W=W, l=fix_l, s=fix_s)
Y = Y.reshape((-1, 1))
# TODO: same logic with the GPRegression. Do we actually need this here? Does this call change-params?
gp_reg = GPRegression(X, Y, kernel, noise_var=fix_sn)
assert kernel.W_grad.shape == W.shape
return kernel.W_grad
def dloss_dW(kernel, W, fix_sn, fix_s, fix_l, X, Y):
"""
The derivative of the loss functions up to a parameter "param"
:param kernel:
:param W:
:param fix_sn:
:param fix_s:
:param fix_l:
:param X:
:param Y:
:return:
"""
kernel.update_params(W=W, l=fix_l, s=fix_s)
Y = Y.reshape((-1, 1))
# TODO: same logic with the GPRegression. Do we actually need this here? Does this call change-params?
gp_reg = GPRegression(X, Y, kernel, noise_var=fix_sn)
# return gp_reg.log_likelihood()
# print("Gradient dictionary is: ", [ key for key, value in gp_reg.grad_dict.items() ])
# This outputs ['dL_dK', 'dL_dthetaL', 'dL_dm']
assert kernel.W_grad.shape == W.shape
return kernel.W_grad
def visualize_augmented_sinusoidal_function(self):
x_range = np.linspace(0., 1., 80)
y_range = np.linspace(0., 1., 80)
X = cartesian([x_range, y_range])
import os
if not os.path.exists("./pics-twostep/"):
os.makedirs("./pics-twostep/")
#################################
# TRAIN THE W_OPTIMIZER #
#################################
Opt = TripathyOptimizer()
print("Real hidden matrix is: ", self.real_W)
W_hat = self.kernel.sample_W()
self.kernel.update_params(
W=W_hat,
s=self.kernel.inner_kernel.variance,
l=self.kernel.inner_kernel.lengthscale
)
W_hat, sn, l, s = Opt.try_two_step_optimization_with_restarts(self.kernel, self.X, self.Y)
# TODO: Check if these values are attained over multiple iterations (check if assert otherwise fails)
# Create the gp_regression function and pass in the predictor function as f_hat
self.kernel.update_params(W=W_hat, l=l, s=s)
gp_reg = GPRegression(self.X, self.Y, self.kernel, noise_var=sn)
y = self.function.f( np.dot(X, self.real_W).T )
if self.PLOT_MEAN:
y_hat = gp_reg.predict(X)[0].squeeze()
else:
y_hat = gp_reg.predict(self.X)[0].squeeze()
#################################
# END TRAIN THE W_OPTIMIZER #
#################################
fig = plt.figure()
ax = Axes3D(fig)
# First plot the real function
ax.scatter(X[:,0], X[:, 1], y, s=1)
if self.PLOT_MEAN:
ax.scatter(X[:, 0], X[:, 1], y_hat, cmap=plt.cm.jet)
else:
ax.scatter(self.X[:,0], self.X[:, 1], y_hat, cmap=plt.cm.jet)
# Save the W just in case
l = loss(
self.kernel,
W_hat,
sn,
s,
l,
self.X,
self.Y
)
fig.savefig('./pics-twostep/BestLoss_' + str(l) + '.png', )
plt.show()
plt.close(fig)
np.savetxt("./pics-twostep/BestLoss_" + str(l) + ".txt", W_hat)
def toy_model():
X = np.linspace(0, 1, 50)[:, None]
Y = np.sin(X)
m = GPRegression(X=X, Y=Y)
return m
_, samples[i] = s.get_statistic_multiple_custom_gradient(fake_y_test[:, 0], fake_gradients[:, 0])
return samples
if __name__ == '__main__':
data = loadmat("../data/02-solar.mat")
X = data['X']
y = data['y']
X_train, y_train, X_test, y_test, N, N_test = prepare_dataset(X, y)
print "num_train:", len(X_train)
print "num_test:", len(X_test)
kernel = RBF(input_dim=1, variance=1., lengthscale=1.)
m = GPRegression(X_train, y_train, kernel)
m.optimize()
res = 100
pred_mean, pred_std = m.predict(X_test)
plt.plot(X_test, pred_mean, 'b-')
plt.plot(X_test, pred_mean + 2 * pred_std, 'b--')
plt.plot(X_test, pred_mean - 2 * pred_std, 'b--')
plt.plot(X_train, y_train, 'b.', markersize=3)
plt.plot(X_test, y_test, 'r.', markersize=5)
plt.grid(True)
plt.xlabel(r"$X$")
plt.ylabel(r"$y$")
plt.savefig("gp_regression_data_fit.eps", bbox_inches='tight')
plt.show()
