def test_evaluate_grad_cross_cov_respect_point(self):
value = self.gp.evaluate_grad_cross_cov_respect_point(np.array([[40.0]]),
np.array([[39.0], [38.0]]),
np.array([1.0, 1.0]))
value_2 = ScaledKernel.evaluate_grad_respect_point(np.array([1.0, 1.0]),
np.array([[40.0]]),
np.array([[39.0], [38.0]]), 1,
*([MATERN52_NAME],))
assert np.all(value == value_2)
type_kernel = [MATERN52_NAME]
training_data = {
"evaluations":
[42.2851784656, 72.3121248508, 1.0113231069, 30.9309246906, 15.5288331909],
"points": [
[42.2851784656], [72.3121248508], [1.0113231069], [30.9309246906], [15.5288331909]],
"var_noise": []}
dimensions = [1]
gp = GPFittingGaussian(type_kernel, training_data, dimensions)
value = gp.evaluate_grad_cross_cov_respect_point(np.array([[40.0]]),
np.array([[39.0], [38.0]]),
np.array([1.0]))
value_2 = Matern52.evaluate_grad_respect_point(np.array([1.0]),
np.array([[40.0]]),
np.array([[39.0], [38.0]]), 1)
assert np.all(value == value_2)
def setUp(self):
np.random.seed(5)
n_points = 100
points = np.linspace(0, 100, n_points)
points = points.reshape([n_points, 1])
tasks = np.random.randint(2, size=(n_points, 1))
add = [-10, 10]
kernel = Matern52.define_kernel_from_array(1, np.array([100.0, 1.0]))
function = SampleFunctions.sample_from_gp(points, kernel)
self.function = function
for i in xrange(n_points):
function[0, i] += add[tasks[i, 0]]
points = np.concatenate((points, tasks), axis=1)
self.points = points
self.evaluations = function[0, :]
function = function[0, :]
training_data = {
'evaluations': list(function),
'points': points,
"var_noise": [],
}
gaussian_p = GPFittingGaussian(
[PRODUCT_KERNELS_SEPARABLE, MATERN52_NAME, TASKS_KERNEL_NAME],
training_data, [2, 1, 2], bounds_domain=[[0, 100], [0, 1]], type_bounds=[0, 1])
gaussian_p = gaussian_p.fit_gp_regression(random_seed=1314938)
quadrature = BayesianQuadrature(gaussian_p, [0], UNIFORM_FINITE,
parameters_distribution={TASKS: 2},
model_only_x=True)
self.mt = MultiTasks(quadrature, quadrature.parameters_distribution.get(TASKS))
def setUp(self):
np.random.seed(2)
n_points = 100
normal_noise = np.random.normal(0, 1.0, n_points)
points = np.linspace(0, 10, n_points)
points = points.reshape([n_points, 1])
kernel = Matern52.define_kernel_from_array(1, np.array([2.0]))
self.sigma2 = ParameterEntity(SIGMA2_NAME, np.array([1.0]), None)
kernel = ScaledKernel(1, kernel, self.sigma2)
function = SampleFunctions.sample_from_gp(points, kernel)
function = function[0, :]
evaluations = function + normal_noise + 10.0
self.training_data_gp = {
"evaluations": list(evaluations),
"points": points,
"var_noise": []
}
bounds = None
self.gp_gaussian = GPFittingGaussian([MATERN52_NAME],
self.training_data_gp, [1],
bounds,
max_steps_out=1000)
self.gp_gaussian_2 = GPFittingGaussian([SCALED_KERNEL, MATERN52_NAME],
self.training_data_gp, [1],
bounds,
max_steps_out=1000)
def test_optimize_2(self):
bgo_2 = BGO.from_spec(self.spec_2)
sol = bgo_2.optimize(random_seed=1, n_restarts=1)
#
# # test that after the first iterations the new points are added correctly
training_data = deepcopy(self.training_data)
training_data['points'] = np.concatenate(
(training_data['points'], np.array([[99.9863644153, 0]])), axis=0)
training_data['evaluations'] = np.concatenate(
(training_data['evaluations'], np.array([9.0335599603])))
gaussian_p_med = GPFittingGaussian(
[PRODUCT_KERNELS_SEPARABLE, MATERN52_NAME, TASKS_KERNEL_NAME],
training_data, [2, 1, 2],
bounds_domain=[[0, 100], [0, 1]],
type_bounds=[0, 1])
gaussian_p_med.update_value_parameters(self.params)
gp_med = BayesianQuadrature(gaussian_p_med, [0], UNIFORM_FINITE,
{TASKS: 2})
sbo = SBO(gp_med, np.array(self.domain.discretization_domain_x))
point = sbo.optimize(start=np.array([[10, 0]]))
npt.assert_almost_equal(point['optimal_value'],
542.4598435381,
decimal=4)
npt.assert_almost_equal(point['solution'], np.array([61.58743036, 0]))
def test_compute_posterior_parameters(self):
np.random.seed(5)
n_points = 10
normal_noise = np.random.normal(0, 0.5, n_points)
points = np.linspace(0, 500, n_points)
points = points.reshape([n_points, 1])
kernel = Matern52.define_kernel_from_array(1, np.array([100.0, 1.0]))
function = SampleFunctions.sample_from_gp(points, kernel)
function = function[0, :]
evaluations = function + normal_noise
training_data_gp = {
"evaluations": list(evaluations[1:]),
"points": points[1:, :],
"var_noise": []}
gp = GPFittingGaussian([MATERN52_NAME], training_data_gp, [1], kernel_values=[100.0, 1.0],
mean_value=[0.0], var_noise_value=[0.5**2])
new_point = np.array([points[0], points[1]])
z = gp.compute_posterior_parameters(new_point)
mean = z['mean']
cov = z['cov']
assert mean[1] - 2.0 * np.sqrt(cov[1, 1]) <= function[1]
assert function[1] <= mean[1] + 2.0 * np.sqrt(cov[1, 1])
assert mean[0] - 2.0 * np.sqrt(cov[0, 0]) <= function[0]
assert function[0] <= mean[0] + 2.0 * np.sqrt(cov[0, 0])
# Values obtained from GPy
npt.assert_almost_equal(mean, np.array([0.30891226, 0.60256237]))
npt.assert_almost_equal(cov, np.array([[0.48844879, 0.16799927], [0.16799927, 0.16536313]]))
def test_sample_new_observations(self):
np.random.seed(5)
n_points = 10
normal_noise = np.random.normal(0, 0.5, n_points)
points = np.linspace(0, 500, n_points)
points = points.reshape([n_points, 1])
kernel = Matern52.define_kernel_from_array(1, np.array([100.0, 1.0]))
function = SampleFunctions.sample_from_gp(points, kernel)
function = function[0, :]
evaluations = function + normal_noise
training_data_gp = {
"evaluations": list(evaluations[1:]),
"points": points[1:, :],
"var_noise": []}
gp = GPFittingGaussian([MATERN52_NAME], training_data_gp, [1], kernel_values=[100.0, 1.0],
mean_value=[0.0], var_noise_value=[0.5**2])
n_samples = 100
samples = gp.sample_new_observations(np.array([[30.0]]), n_samples, random_seed=1)
new_point = np.array([[30.0]])
z = gp.compute_posterior_parameters(new_point)
mean = z['mean']
cov = z['cov']
npt.assert_almost_equal(mean, np.mean(samples), decimal=1)
npt.assert_almost_equal(cov, np.var(samples), decimal=1)
def test_convert_from_numpy_to_list(self):
data = GPFittingGaussian.convert_from_list_to_numpy(self.training_data_noisy)
data_list = GPFittingGaussian.convert_from_numpy_to_list(data)
assert data_list == self.training_data_noisy
data_ = GPFittingGaussian.convert_from_list_to_numpy(self.training_data)
data_list_ = GPFittingGaussian.convert_from_numpy_to_list(data_)
assert data_list_ == self.training_data
def test_convert_from_list_to_numpy(self):
data = GPFittingGaussian.convert_from_list_to_numpy(self.training_data_noisy)
assert np.all(data['points'] == np.array([[42.2851784656]]))
assert data['evaluations'] == np.array([41.0101845096])
assert data['var_noise'] == np.array([0.0181073779])
data_ = GPFittingGaussian.convert_from_list_to_numpy(self.training_data)
assert np.all(data_['points'] == np.array(
[[42.2851784656], [72.3121248508], [1.0113231069], [30.9309246906], [15.5288331909]]))
assert np.all(data_['evaluations'] == np.array([42.2851784656, 72.3121248508, 1.0113231069,
30.9309246906, 15.5288331909]))
assert data_['var_noise'] is None
def test_set_samplers(self):
type_kernel = [TASKS_KERNEL_NAME]
training_data = {
"evaluations": [42.2851784656, 72.3121248508],
"points": [[0], [1]],
"var_noise": []}
dimensions = [2]
gp_tk = GPFittingGaussian(type_kernel, training_data, dimensions)
assert gp_tk.length_scale_indexes is None
assert len(gp_tk.slice_samplers) == 1
value = gp_tk.sample_parameters(1, random_seed=1)[-1]
gp_tk_ = GPFittingGaussian(type_kernel, training_data, dimensions, n_burning=1,
random_seed=1)
assert np.all(gp_tk_.start_point_sampler == value)
type_kernel = [PRODUCT_KERNELS_SEPARABLE, MATERN52_NAME, TASKS_KERNEL_NAME]
training_data = {
"evaluations": [42.2851784656, 72.3121248508],
"points": [[0, 0], [1, 0]],
"var_noise": []}
dimensions = [2, 1, 1]
gp = GPFittingGaussian(type_kernel, training_data, dimensions, n_burning=1, random_seed=1)
gp2 = GPFittingGaussian(type_kernel, training_data, dimensions)
value2 = gp2.sample_parameters(1, random_seed=1)[-1]
assert np.all(gp.start_point_sampler == value2)
def test_optimize_posterior_mean_samples(self):
np.random.seed(5)
n_points = 100
points = np.linspace(0, 100, n_points)
points = points.reshape([n_points, 1])
tasks = np.random.randint(2, size=(n_points, 1))
add = [10, -10]
kernel = Matern52.define_kernel_from_array(1, np.array([100.0, 1.0]))
function = SampleFunctions.sample_from_gp(points, kernel)
max_value = function[0, np.argmax(function)]
max_point = points[np.argmax(function), 0]
for i in xrange(n_points):
function[0, i] += add[tasks[i, 0]]
points = np.concatenate((points, tasks), axis=1)
function = function[0, :]
training_data = {
'evaluations': list(function),
'points': points,
"var_noise": [],
}
gaussian_p = GPFittingGaussian(
[PRODUCT_KERNELS_SEPARABLE, MATERN52_NAME, TASKS_KERNEL_NAME],
training_data, [2, 1, 2],
bounds_domain=[[0, 100]],
max_steps_out=1000)
gaussian_p = gaussian_p.fit_gp_regression(random_seed=1314938)
gp = BayesianQuadrature(gaussian_p, [0], UNIFORM_FINITE, {TASKS: 2})
random_seed = 10
n_samples_parameters = 15
gp.gp.thinning = 10
gp.gp.n_burning = 500
sol_2 = gp.optimize_posterior_mean(
random_seed=random_seed,
n_best_restarts=2,
n_samples_parameters=n_samples_parameters,
start_new_chain=True)
assert max_point == sol_2['solution']
npt.assert_almost_equal(max_value, sol_2['optimal_value'], decimal=3)
def test_gradient_vector_b(self):
np.random.seed(5)
n_points = 10
points = np.linspace(0, 100, n_points)
points = points.reshape([n_points, 1])
tasks = np.random.randint(2, size=(n_points, 1))
add = [10, -10]
kernel = Matern52.define_kernel_from_array(1, np.array([100.0, 1.0]))
function = SampleFunctions.sample_from_gp(points, kernel)
for i in xrange(n_points):
function[0, i] += add[tasks[i, 0]]
points = np.concatenate((points, tasks), axis=1)
function = function[0, :]
training_data = {
'evaluations': list(function),
'points': points,
"var_noise": [],
}
gaussian_p = GPFittingGaussian(
[PRODUCT_KERNELS_SEPARABLE, MATERN52_NAME, TASKS_KERNEL_NAME],
training_data, [2, 1, 2],
bounds_domain=[[0, 100]])
gaussian_p = gaussian_p.fit_gp_regression(random_seed=1314938)
gp = BayesianQuadrature(gaussian_p, [0], UNIFORM_FINITE, {TASKS: 2})
# gp = self.gp_complete
candidate_point = np.array([[84.0, 1]])
points = np.array([[99.5], [12.1], [70.2]])
value = gp.gradient_vector_b(candidate_point, points, cache=False)
dh_ = 0.0000001
dh = [dh_]
finite_diff = FiniteDifferences.forward_difference(
lambda point: gp.compute_posterior_parameters_kg(
points, point.reshape((1, len(point))), cache=False)['b'],
candidate_point[0, :], np.array(dh))
npt.assert_almost_equal(finite_diff[0], value[:, 0], decimal=5)
assert np.all(finite_diff[1] == value[:, 1])
value_2 = gp.gradient_vector_b(candidate_point, points, cache=True)
assert np.all(value_2 == value)
def test_serialize(self):
self.gp.add_points_evaluations(self.new_point, self.evaluation)
dict = self.gp.serialize()
n = len(self.training_data['points'])
ls = np.mean([abs(self.training_data['points'][j][0] - self.training_data['points'][h][0])
for j in xrange(n) for h in xrange(n)]) / 0.324
data = {
"evaluations": [42.2851784656, 72.3121248508, 1.0113231069, 30.9309246906,
15.5288331909, 80.0],
"points": [
[42.2851784656], [72.3121248508], [1.0113231069], [30.9309246906], [15.5288331909],
[80.0]],
"var_noise": []
}
st_sampler = [592.54740339691523, 32.413676860959995, 83.633554944444455,
592.54740339691523]
assert dict == {
'type_kernel': [SCALED_KERNEL, MATERN52_NAME],
'training_data': self.training_data,
'dimensions': [1],
'kernel_values': [ls, np.var(self.training_data['evaluations'])],
'mean_value': [np.mean(self.training_data['evaluations'])],
'var_noise_value': [np.var(self.training_data['evaluations'])],
'thinning': 0,
'data': data,
"bounds_domain": [],
'n_burning': 0,
'max_steps_out': 1,
'bounds_domain': [[0, 100]],
'type_bounds': [0],
'name_model': 'gp_fitting_gaussian',
'problem_name': '',
'training_name': '',
'same_correlation': False,
'start_point_sampler': st_sampler,
'samples_parameters': dict['samples_parameters'],
}
gp = GPFittingGaussian([MATERN52_NAME], self.training_data, dimensions=[1])
dict = gp.serialize()
assert dict['bounds_domain'] == []
def test_train(self):
np.random.seed(5)
n_points = 10
normal_noise = np.random.normal(0, 0.5, n_points)
points = np.linspace(0, 500, n_points)
points = points.reshape([n_points, 1])
kernel = Matern52.define_kernel_from_array(1, np.array([100.0, 1.0]))
function = SampleFunctions.sample_from_gp(points, kernel)
function = function[0, :]
evaluations = function + normal_noise
training_data_gp = {
"evaluations": list(evaluations),
"points": points,
"var_noise": []}
new_gp = GPFittingGaussian.train([MATERN52_NAME], [1], True, training_data_gp, None,
random_seed=1314938)
gp_gaussian = GPFittingGaussian([MATERN52_NAME], training_data_gp, [1])
gp_2 = gp_gaussian.fit_gp_regression(random_seed=1314938)
npt.assert_almost_equal(new_gp.var_noise.value[0], gp_2.var_noise.value[0], decimal=6)
npt.assert_almost_equal(new_gp.mean.value[0], gp_2.mean.value[0], decimal=6)
npt.assert_almost_equal(new_gp.kernel_values, gp_2.kernel_values)
gp_gaussian = GPFittingGaussian([MATERN52_NAME], training_data_gp, [1])
new_gp_2 = GPFittingGaussian.train([MATERN52_NAME], [1], False, training_data_gp, None)
npt.assert_almost_equal(new_gp_2.var_noise.value[0], gp_gaussian.var_noise.value[0])
npt.assert_almost_equal(new_gp_2.mean.value[0], gp_gaussian.mean.value[0], decimal=6)
npt.assert_almost_equal(new_gp_2.kernel_values, gp_gaussian.kernel_values)
def test_deserialize(self):
params = {
'type_kernel': [MATERN52_NAME],
'training_data': self.training_data,
'dimensions': [1],
}
gp = GPFittingGaussian.deserialize(params)
assert gp.type_kernel == [MATERN52_NAME]
assert gp.training_data == self.training_data
assert gp.dimensions == [1]
def test_mle_parameters(self):
# Results compared with the ones given by GPy
np.random.seed(1)
add = -45.946926660233636
llh = self.gp_gaussian.log_likelihood(1.0, 0.0, np.array([100.0, 1.0]))
npt.assert_almost_equal(llh + add, -59.8285565516, decimal=6)
opt = self.gp_gaussian.mle_parameters(start=np.array([1.0, 0.0, 14.0, 0.9]))
assert opt['optimal_value'] + add >= -67.1494227694
compare = self.gp_gaussian.log_likelihood(9, 10.0, np.array([100.2, 1.1]))
assert self.gp_gaussian_central.log_likelihood(9, 0.0, np.array([100.2, 1.1])) == compare
np.random.seed(5)
n_points = 10
normal_noise = np.random.normal(0, 0.5, n_points)
points = np.linspace(0, 500, n_points)
points = points.reshape([n_points, 1])
kernel = Matern52.define_kernel_from_array(1, np.array([100.0, 1.0]))
function = SampleFunctions.sample_from_gp(points, kernel)
function = function[0, :]
evaluations = function + normal_noise
training_data_gp = {
"evaluations": list(evaluations),
"points": points,
"var_noise": []}
gp_gaussian = GPFittingGaussian([MATERN52_NAME], training_data_gp, [1])
opt_3 = gp_gaussian.mle_parameters(random_seed=1314938)
np.random.seed(1314938)
start = gp_gaussian.sample_parameters_posterior(1)[0, :]
opt_4 = gp_gaussian.mle_parameters(start)
npt.assert_almost_equal(opt_3['optimal_value'], opt_4['optimal_value'])
npt.assert_almost_equal(opt_3['solution'], opt_4['solution'], decimal=4)
def setUp(self):
training_data_complex = {
"evaluations": [1.0, 1.1],
"points": [[42.2851784656, 0], [42.3851784656, 1]],
"var_noise": []
}
self.complex_gp_2 = GPFittingGaussian(
[PRODUCT_KERNELS_SEPARABLE, MATERN52_NAME, TASKS_KERNEL_NAME],
training_data_complex, [2, 1, 2])
self.gp = BayesianQuadrature(self.complex_gp_2, [0], UNIFORM_FINITE,
{TASKS: 2})
def setUp(self):
self.bounds_domain_x = BoundsEntity({
'lower_bound': 0,
'upper_bound': 100,
})
spec_domain = {
'dim_x': 1,
'choose_noise': True,
'bounds_domain_x': [self.bounds_domain_x],
'number_points_each_dimension': [100],
'problem_name': 'a',
}
self.domain = DomainService.from_dict(spec_domain)
dict = {
'problem_name':
'test_problem_with_tasks',
'dim_x':
1,
'choose_noise':
True,
'bounds_domain_x':
[BoundsEntity({
'lower_bound': 0,
'upper_bound': 100
})],
'number_points_each_dimension': [100],
'method_optimization':
'sbo',
'training_name':
'test_bgo',
'bounds_domain': [[0, 100], [0, 1]],
'n_training':
4,
'type_kernel':
[PRODUCT_KERNELS_SEPARABLE, MATERN52_NAME, TASKS_KERNEL_NAME],
'noise':
False,
'random_seed':
5,
'parallel':
False,
'type_bounds': [0, 1],
'dimensions': [2, 1, 2],
'name_model':
'gp_fitting_gaussian',
'mle':
True,
'thinning':
0,
'n_burning':
0,
'max_steps_out':
1,
'training_data':
None,
'x_domain': [0],
'distribution':
UNIFORM_FINITE,
'parameters_distribution':
None,
'minimize':
False,
'n_iterations':
5,
}
self.spec = RunSpecEntity(dict)
self.acquisition_function = None
self.gp_model = None
###Define other BGO object
np.random.seed(5)
n_points = 100
points = np.linspace(0, 100, n_points)
points = points.reshape([n_points, 1])
tasks = np.random.randint(2, size=(n_points, 1))
add = [10, -10]
kernel = Matern52.define_kernel_from_array(1, np.array([100.0, 1.0]))
function = SampleFunctions.sample_from_gp(points, kernel)
for i in xrange(n_points):
function[0, i] += add[tasks[i, 0]]
points = np.concatenate((points, tasks), axis=1)
self.points = points
function = function[0, :]
points_ls = [list(points[i, :]) for i in xrange(n_points)]
training_data_med = {
'evaluations': list(function[0:5]),
'points': points_ls[0:5],
"var_noise": [],
}
self.training_data = training_data_med
training_data = {
'evaluations': list(function),
'points': points,
"var_noise": [],
}
gaussian_p = GPFittingGaussian(
[PRODUCT_KERNELS_SEPARABLE, MATERN52_NAME, TASKS_KERNEL_NAME],
training_data, [2, 1, 2],
bounds_domain=[[0, 100], [0, 1]],
type_bounds=[0, 1])
gaussian_p = gaussian_p.fit_gp_regression(random_seed=1314938)
params = gaussian_p.get_value_parameters_model
self.params = params
dict = {
'problem_name':
'test_simulated_gp',
'dim_x':
1,
'choose_noise':
True,
'bounds_domain_x':
[BoundsEntity({
'lower_bound': 0,
'upper_bound': 100
})],
'number_points_each_dimension': [100],
'method_optimization':
'sbo',
'training_name':
'test_sbo',
'bounds_domain': [[0, 100], [0, 1]],
'n_training':
5,
'type_kernel':
[PRODUCT_KERNELS_SEPARABLE, MATERN52_NAME, TASKS_KERNEL_NAME],
'noise':
False,
'random_seed':
5,
'parallel':
False,
'type_bounds': [0, 1],
'dimensions': [2, 1, 2],
'name_model':
'gp_fitting_gaussian',
'mle':
False,
'thinning':
0,
'n_burning':
0,
'max_steps_out':
1,
'training_data':
training_data_med,
'x_domain': [0],
'distribution':
UNIFORM_FINITE,
'parameters_distribution':
None,
'minimize':
False,
'n_iterations':
1,
'var_noise_value': [params[0]],
'mean_value': [params[1]],
'kernel_values':
list(params[2:]),
'cache':
False,
'debug':
False,
}
self.spec_2 = RunSpecEntity(dict)
def setUp(self):
self.training_data_complex = {
"evaluations": [1.0, 1.1],
"points": [[42.2851784656, 0], [42.3851784656, 0]],
"var_noise": []
}
self.complex_gp = GPFittingGaussian(
[PRODUCT_KERNELS_SEPARABLE, MATERN52_NAME, TASKS_KERNEL_NAME],
self.training_data_complex, [2, 1, 1])
self.gp = BayesianQuadrature(self.complex_gp, [0], UNIFORM_FINITE,
{TASKS: 1})
training_data_complex = {
"evaluations": [1.0, 1.1],
"points": [[42.2851784656, 0], [42.3851784656, 1]],
"var_noise": []
}
self.complex_gp_2 = GPFittingGaussian(
[PRODUCT_KERNELS_SEPARABLE, MATERN52_NAME, TASKS_KERNEL_NAME],
training_data_complex, [3, 1, 2])
self.gp_2 = BayesianQuadrature(self.complex_gp_2, [0], UNIFORM_FINITE,
{TASKS: 2})
np.random.seed(5)
n_points = 100
points = np.linspace(0, 100, n_points)
points = points.reshape([n_points, 1])
tasks = np.random.randint(2, size=(n_points, 1))
add = [10, -10]
kernel = Matern52.define_kernel_from_array(1, np.array([100.0, 1.0]))
function = SampleFunctions.sample_from_gp(points, kernel)
self.original_function = function
self.max_value = function[0, np.argmax(function)]
self.max_point = points[np.argmax(function), 0]
for i in xrange(n_points):
function[0, i] += add[tasks[i, 0]]
points = np.concatenate((points, tasks), axis=1)
function = function[0, :]
training_data = {
'evaluations': list(function),
'points': points,
"var_noise": [],
}
training_data_2 = {
'evaluations': list(function[[0, 30, 50, 90, 99]]),
'points': points[[0, 30, 50, 90, 99], :],
"var_noise": [],
}
gaussian_p = GPFittingGaussian(
[PRODUCT_KERNELS_SEPARABLE, MATERN52_NAME, TASKS_KERNEL_NAME],
training_data, [2, 1, 2],
bounds_domain=[[0, 100]])
gaussian_p = gaussian_p.fit_gp_regression(random_seed=1314938)
gaussian_p_2 = GPFittingGaussian(
[PRODUCT_KERNELS_SEPARABLE, MATERN52_NAME, TASKS_KERNEL_NAME],
training_data_2, [2, 1, 2],
bounds_domain=[[0, 100]])
gaussian_p_2 = gaussian_p.fit_gp_regression(random_seed=1314938)
self.gp_complete_2 = BayesianQuadrature(gaussian_p_2, [0],
UNIFORM_FINITE, {TASKS: 2})
self.gp_complete = BayesianQuadrature(gaussian_p, [0], UNIFORM_FINITE,
{TASKS: 2})
class TestSliceSampling(unittest.TestCase):
def setUp(self):
np.random.seed(2)
n_points = 100
normal_noise = np.random.normal(0, 1.0, n_points)
points = np.linspace(0, 10, n_points)
points = points.reshape([n_points, 1])
kernel = Matern52.define_kernel_from_array(1, np.array([2.0]))
self.sigma2 = ParameterEntity(SIGMA2_NAME, np.array([1.0]), None)
kernel = ScaledKernel(1, kernel, self.sigma2)
function = SampleFunctions.sample_from_gp(points, kernel)
function = function[0, :]
evaluations = function + normal_noise + 10.0
self.training_data_gp = {
"evaluations": list(evaluations),
"points": points,
"var_noise": []
}
bounds = None
self.gp_gaussian = GPFittingGaussian([MATERN52_NAME],
self.training_data_gp, [1],
bounds,
max_steps_out=1000)
self.gp_gaussian_2 = GPFittingGaussian([SCALED_KERNEL, MATERN52_NAME],
self.training_data_gp, [1],
bounds,
max_steps_out=1000)
def test_slice_sample(self):
# Benchmark numbers from Ryan's code.
np.random.seed(1)
point = np.array([0.1, 0.7, 0.8, 0.2])
new_point = self.gp_gaussian_2.sample_parameters(1, point, 1)[0]
benchmark_point = \
np.array([0.17721380376549206, 0.67091995290377726, 2.23209165, 0.17489317792506012])
npt.assert_almost_equal(new_point, benchmark_point)
np.random.seed(1)
point = np.array([0.1, 0.7, 0.8, 0.2])
sampler = self.gp_gaussian.slice_samplers[0]
sampler.doubling_step = False
new_point = self.gp_gaussian_2.sample_parameters(1, point, 1)[0]
npt.assert_almost_equal(new_point, benchmark_point)
def test_acceptable(self):
sampler = self.gp_gaussian.slice_samplers[0]
accept = sampler.acceptable(0.75, 1000000, 0, 1.5, np.array([1.0, 0]),
np.array([0.1, 0.7]), np.array([0.8]),
*(self.gp_gaussian, ))
assert accept is False
sampler.doubling_step = False
accept_2 = sampler.acceptable(0.75, 1000000, 0, 1.5, np.array([1.0,
0]),
np.array([0.1, 0.7]), np.array([0.8]),
*(self.gp_gaussian, ))
assert accept_2 is True
def test_find_x_interval(self):
sampler = self.gp_gaussian.slice_samplers[0]
sampler.doubling_step = False
interval = sampler.find_x_interval(-2000, 0, 1.5, np.array([1.0, 0]),
np.array([0.1, 0.7]),
np.array([0.8]),
*(self.gp_gaussian, ))
assert interval == (1001.5, -1.0)
def test_find_sample(self):
sampler = self.gp_gaussian.slice_samplers[0]
with self.assertRaises(Exception):
sampler.find_sample(0, 1.5, -1000, np.array([1.0, 0]),
np.array([-1.0, 0.7]), np.array([0.8]),
*(self.gp_gaussian, ))
expect(sampler).directional_log_prob.and_return(np.nan)
with self.assertRaises(Exception):
sampler.find_sample(0, 1.5, -1000, np.array([1.0, 0, 0]),
np.array([-1.0, 0.7, 0.2]), np.array([0.8]),
*(self.gp_gaussian, ))
class TestGPFittingGaussian(unittest.TestCase):
def setUp(self):
type_kernel = [SCALED_KERNEL, MATERN52_NAME]
self.training_data = {
"evaluations":
[42.2851784656, 72.3121248508, 1.0113231069, 30.9309246906, 15.5288331909],
"points": [
[42.2851784656], [72.3121248508], [1.0113231069], [30.9309246906], [15.5288331909]],
"var_noise": []}
dimensions = [1]
self.gp = GPFittingGaussian(type_kernel, self.training_data, dimensions,
bounds_domain=[[0, 100]])
self.training_data_3 = {
"evaluations": [42.2851784656, 72.3121248508, 1.0113231069, 30.9309246906,
15.5288331909],
"points": [
[42.2851784656], [72.3121248508], [1.0113231069], [30.9309246906], [15.5288331909]],
"var_noise": [0.5, 0.8, 0.7, 0.9, 1.0]}
self.gp_3 = GPFittingGaussian(type_kernel, self.training_data_3, dimensions,
bounds_domain=[[0, 100]])
self.training_data_simple = {
"evaluations": [5],
"points": [[5]],
"var_noise": []}
dimensions = [1]
self.simple_gp = GPFittingGaussian(type_kernel, self.training_data_simple, dimensions,
bounds_domain=[[0, 100]])
self.training_data_complex = {
"evaluations": [1.0],
"points": [[42.2851784656, 0]],
"var_noise": [0.5]}
self.complex_gp = GPFittingGaussian(
[PRODUCT_KERNELS_SEPARABLE, MATERN52_NAME, TASKS_KERNEL_NAME],
self.training_data_complex, [2, 1, 1], bounds_domain=[[0, 100], [0]])
self.training_data_complex_2 = {
"evaluations": [1.0, 2.0, 3.0],
"points": [[42.2851784656, 0], [10.532, 0], [9.123123, 1]],
"var_noise": [0.5, 0.2, 0.1]}
self.complex_gp_2 = GPFittingGaussian(
[PRODUCT_KERNELS_SEPARABLE, MATERN52_NAME, TASKS_KERNEL_NAME],
self.training_data_complex_2, [3, 1, 2], bounds_domain=[[0, 100], [0, 1]])
self.new_point = np.array([[80.0]])
self.evaluation = np.array([80.0])
self.training_data_noisy = {
"evaluations": [41.0101845096],
"points": [[42.2851784656]],
"var_noise": [0.0181073779]}
self.gp_noisy = GPFittingGaussian(type_kernel, self.training_data_noisy, dimensions,
bounds_domain=[[0, 100]])
np.random.seed(2)
n_points = 50
normal_noise = np.random.normal(0, 0.5, n_points)
points = np.linspace(0, 500, n_points)
points = points.reshape([n_points, 1])
kernel = Matern52.define_kernel_from_array(1, np.array([100.0, 1.0]))
function = SampleFunctions.sample_from_gp(points, kernel)
function = function[0, :]
evaluations = function + normal_noise
self.training_data_gp = {
"evaluations": list(evaluations),
"points": points,
"var_noise": []}
self.gp_gaussian = GPFittingGaussian([SCALED_KERNEL, MATERN52_NAME], self.training_data_gp,
[1])
self.gp_gaussian_2 = GPFittingGaussian([MATERN52_NAME], self.training_data_gp, [1],
bounds_domain=[[0, 100]])
self.training_data_gp_2 = {
"evaluations": list(evaluations - 10.0),
"points": points,
"var_noise": []}
self.gp_gaussian_central = GPFittingGaussian([SCALED_KERNEL, MATERN52_NAME],
self.training_data_gp_2, [1],
bounds_domain=[[0, 100]])
def test_add_points_evaluations(self):
self.gp.add_points_evaluations(self.new_point, self.evaluation)
assert np.all(self.gp.data['evaluations'] == np.concatenate(
(self.training_data['evaluations'], [80.0])))
assert np.all(self.gp.data['points'] == np.concatenate(
(self.training_data['points'], [[80.0]])))
assert self.gp.data['var_noise'] is None
assert self.gp.training_data == self.training_data
self.gp_noisy.add_points_evaluations(self.new_point, self.evaluation, np.array([0.00001]))
assert np.all(self.gp_noisy.data['evaluations'] == np.concatenate(
(self.training_data_noisy['evaluations'], [80.0])))
assert np.all(self.gp_noisy.data['points'] == np.concatenate(
(self.training_data_noisy['points'], [[80.0]])))
assert np.all(self.gp_noisy.data['var_noise'] == np.concatenate(
(self.training_data_noisy['var_noise'], [0.00001])))
assert self.gp_noisy.training_data == self.training_data_noisy
def test_convert_from_list_to_numpy(self):
data = GPFittingGaussian.convert_from_list_to_numpy(self.training_data_noisy)
assert np.all(data['points'] == np.array([[42.2851784656]]))
assert data['evaluations'] == np.array([41.0101845096])
assert data['var_noise'] == np.array([0.0181073779])
data_ = GPFittingGaussian.convert_from_list_to_numpy(self.training_data)
assert np.all(data_['points'] == np.array(
[[42.2851784656], [72.3121248508], [1.0113231069], [30.9309246906], [15.5288331909]]))
assert np.all(data_['evaluations'] == np.array([42.2851784656, 72.3121248508, 1.0113231069,
30.9309246906, 15.5288331909]))
assert data_['var_noise'] is None
def test_convert_from_numpy_to_list(self):
data = GPFittingGaussian.convert_from_list_to_numpy(self.training_data_noisy)
data_list = GPFittingGaussian.convert_from_numpy_to_list(data)
assert data_list == self.training_data_noisy
data_ = GPFittingGaussian.convert_from_list_to_numpy(self.training_data)
data_list_ = GPFittingGaussian.convert_from_numpy_to_list(data_)
assert data_list_ == self.training_data
def test_serialize(self):
self.gp.add_points_evaluations(self.new_point, self.evaluation)
dict = self.gp.serialize()
n = len(self.training_data['points'])
ls = np.mean([abs(self.training_data['points'][j][0] - self.training_data['points'][h][0])
for j in xrange(n) for h in xrange(n)]) / 0.324
data = {
"evaluations": [42.2851784656, 72.3121248508, 1.0113231069, 30.9309246906,
15.5288331909, 80.0],
"points": [
[42.2851784656], [72.3121248508], [1.0113231069], [30.9309246906], [15.5288331909],
[80.0]],
"var_noise": []
}
st_sampler = [592.54740339691523, 32.413676860959995, 83.633554944444455,
592.54740339691523]
assert dict == {
'type_kernel': [SCALED_KERNEL, MATERN52_NAME],
'training_data': self.training_data,
'dimensions': [1],
'kernel_values': [ls, np.var(self.training_data['evaluations'])],
'mean_value': [np.mean(self.training_data['evaluations'])],
'var_noise_value': [np.var(self.training_data['evaluations'])],
'thinning': 0,
'data': data,
"bounds_domain": [],
'n_burning': 0,
'max_steps_out': 1,
'bounds_domain': [[0, 100]],
'type_bounds': [0],
'name_model': 'gp_fitting_gaussian',
'problem_name': '',
'training_name': '',
'same_correlation': False,
'start_point_sampler': st_sampler,
'samples_parameters': dict['samples_parameters'],
}
gp = GPFittingGaussian([MATERN52_NAME], self.training_data, dimensions=[1])
dict = gp.serialize()
assert dict['bounds_domain'] == []
def test_deserialize(self):
params = {
'type_kernel': [MATERN52_NAME],
'training_data': self.training_data,
'dimensions': [1],
}
gp = GPFittingGaussian.deserialize(params)
assert gp.type_kernel == [MATERN52_NAME]
assert gp.training_data == self.training_data
assert gp.dimensions == [1]
def test_get_parameters_model(self):
parameters = self.gp.get_parameters_model
parameters_values = [parameter.value for parameter in parameters]
var = np.var(self.training_data['evaluations'])
n = len(self.training_data['evaluations'])
ls = np.mean([abs(self.training_data['points'][j][0] -
self.training_data['points'][h][0]) for j in xrange(n) for h in
xrange(n)]) / 0.324
assert parameters_values[0] == var
assert parameters_values[1] == np.mean(self.training_data['evaluations'])
assert np.all(parameters_values[2] == ls)
assert parameters_values[3] == var
def test_get_value_parameters_model(self):
var = np.var(self.training_data['evaluations'])
mean = np.mean(self.training_data['evaluations'])
n = len(self.training_data['evaluations'])
ls = np.mean([abs(self.training_data['points'][j][0] -
self.training_data['points'][h][0]) for j in xrange(n) for h in
xrange(n)]) / 0.324
parameters = self.gp.get_value_parameters_model
assert np.all(parameters == np.array([var, mean, ls, var]))
def test_cached_data(self):
self.gp._updated_cached_data((3, 5, 1), -1, SOL_CHOL_Y_UNBIASED)
assert self.gp.cache_sol_chol_y_unbiased[(3, 5, 1)] == -1
assert self.gp.cache_sol_chol_y_unbiased.keys() == [(3, 5, 1)]
assert self.gp._get_cached_data((3, 5, 1), SOL_CHOL_Y_UNBIASED) == -1
self.gp._updated_cached_data((3, 5), 0, CHOL_COV)
assert self.gp.cache_chol_cov[(3, 5)] == 0
assert self.gp.cache_chol_cov.keys() == [(3, 5)]
assert self.gp.cache_sol_chol_y_unbiased == {}
assert self.gp._get_cached_data((3, 5), CHOL_COV) == 0
assert self.gp._get_cached_data((3, 0), CHOL_COV) is False
def test_chol_cov_including_noise(self):
chol, cov = self.simple_gp._chol_cov_including_noise(1.0, np.array([1.0, 1.0]))
assert cov == np.array([[2.0]])
assert chol == np.array([[np.sqrt(2.0)]])
chol, cov = self.simple_gp._chol_cov_including_noise(1.0, np.array([1.0, 1.0]))
assert cov == np.array([[2.0]])
assert chol == np.array([[np.sqrt(2.0)]])
chol, cov = self.complex_gp._chol_cov_including_noise(1.0, np.array([1.0, 0.0]))
assert cov == np.array([[2.5]])
assert chol == np.array([[np.sqrt(2.5)]])
def test_log_likelihood(self):
llh = self.complex_gp.log_likelihood(1.0, 1.0, np.array([1.0, 0.0]))
assert llh == -0.45814536593707761
def test_grad_log_likelihood(self):
grad = self.complex_gp_2.grad_log_likelihood(1.0, 1.0, np.array([1.0, 0.0, 0.0, 0.0]))
dh = 0.0000001
finite_diff = FiniteDifferences.forward_difference(
lambda params: self.complex_gp_2.log_likelihood(
params[0], params[1], params[2:]
),
np.array([1.0, 1.0, 1.0, 0.0, 0.0, 0.0]), np.array([dh]))
for i in range(6):
npt.assert_almost_equal(finite_diff[i], grad[i])
grad_2 = self.complex_gp_2.grad_log_likelihood(1.82, 123.1,
np.array([5.0, 1.0, -5.5, 10.0]))
dh = 0.00000001
finite_diff_2 = FiniteDifferences.forward_difference(
lambda params: self.complex_gp_2.log_likelihood(
params[0], params[1], params[2:]
),
np.array([1.82, 123.1, 5.0, 1.0, -5.5, 10.0]), np.array([dh]))
for i in range(6):
npt.assert_almost_equal(finite_diff_2[i], grad_2[i], decimal=3)
grad_3 = self.gp_3.grad_log_likelihood(1.82, 123.1, np.array([5.0, 7.3]))
dh = 0.0000001
finite_diff_3 = FiniteDifferences.forward_difference(
lambda params: self.gp_3.log_likelihood(
params[0], params[1], params[2:]
),
np.array([1.82, 123.1, 5.0, 7.3]), np.array([dh]))
for i in range(4):
npt.assert_almost_equal(finite_diff_3[i], grad_3[i], decimal=5)
grad_4 = self.gp_gaussian.grad_log_likelihood(1.0, 0.0, np.array([14.0, 0.9]))
dh = 0.0000001
finite_diff_4 = FiniteDifferences.forward_difference(
lambda params: self.gp_gaussian.log_likelihood(
params[0], params[1], params[2:]
),
np.array([1.0, 0.0, 14.0, 0.9]), np.array([dh]))
for i in range(4):
npt.assert_almost_equal(finite_diff_4[i], grad_4[i], decimal=5)
def test_grad_log_likelihood_dict(self):
grad = self.complex_gp_2.grad_log_likelihood_dict(
1.82, 123.1, np.array([5.0, 1.0, -5.5, 10.0]))
grad_2 = self.complex_gp_2.grad_log_likelihood(1.82, 123.1,
np.array([5.0, 1.0, -5.5, 10.0]))
assert grad_2[0] == grad['var_noise']
assert grad_2[1] == grad['mean']
assert np.all(grad_2[2:] == grad['kernel_params'])
def test_mle_parameters(self):
# Results compared with the ones given by GPy
np.random.seed(1)
add = -45.946926660233636
llh = self.gp_gaussian.log_likelihood(1.0, 0.0, np.array([100.0, 1.0]))
npt.assert_almost_equal(llh + add, -59.8285565516, decimal=6)
opt = self.gp_gaussian.mle_parameters(start=np.array([1.0, 0.0, 14.0, 0.9]))
assert opt['optimal_value'] + add >= -67.1494227694
compare = self.gp_gaussian.log_likelihood(9, 10.0, np.array([100.2, 1.1]))
assert self.gp_gaussian_central.log_likelihood(9, 0.0, np.array([100.2, 1.1])) == compare
np.random.seed(5)
n_points = 10
normal_noise = np.random.normal(0, 0.5, n_points)
points = np.linspace(0, 500, n_points)
points = points.reshape([n_points, 1])
kernel = Matern52.define_kernel_from_array(1, np.array([100.0, 1.0]))
function = SampleFunctions.sample_from_gp(points, kernel)
function = function[0, :]
evaluations = function + normal_noise
training_data_gp = {
"evaluations": list(evaluations),
"points": points,
"var_noise": []}
gp_gaussian = GPFittingGaussian([MATERN52_NAME], training_data_gp, [1])
opt_3 = gp_gaussian.mle_parameters(random_seed=1314938)
np.random.seed(1314938)
start = gp_gaussian.sample_parameters_posterior(1)[0, :]
opt_4 = gp_gaussian.mle_parameters(start)
npt.assert_almost_equal(opt_3['optimal_value'], opt_4['optimal_value'])
npt.assert_almost_equal(opt_3['solution'], opt_4['solution'], decimal=4)
def test_objective_llh(self):
funct = deepcopy(self.gp_gaussian.log_likelihood)
def llh(a, b, c):
return float(funct(a, b, c)) / 0.0
self.gp_gaussian.log_likelihood = llh
assert self.gp_gaussian.objective_llh(np.array([1.0, 3.0, 14.0, 0.9])) == -np.inf
def test_sample_parameters_prior(self):
sample = self.gp_gaussian.sample_parameters_prior(1, 1)[0]
assert len(sample) == 4
np.random.seed(1)
lambda_ = np.abs(np.random.standard_cauchy(size=(1, 1)))
a = np.abs(np.random.randn(1, 1) * lambda_ * np.var(self.training_data_gp['evaluations']))
assert sample[0] == a[0][0]
a = np.random.randn(1, 1) + np.mean(self.training_data_gp['evaluations'])
assert sample[1] == a[0][0]
n = self.training_data_gp['points'].shape[0]
mean_ls = np.mean([abs(self.training_data_gp['points'][j, 0] -
self.training_data_gp['points'][h, 0]) for j in xrange(n) for h in
xrange(n)]) / 0.324
a = SMALLEST_POSITIVE_NUMBER + np.random.rand(1, 1) * (mean_ls - SMALLEST_POSITIVE_NUMBER)
assert sample[2] == a
mean_var = np.var(self.training_data_gp['evaluations'])
a = np.random.lognormal(mean=np.sqrt(mean_var), sigma=1.0, size=1) ** 2
assert sample[3] == a[0]
def test_log_prob_parameters(self):
prob = self.gp_gaussian.log_prob_parameters(np.array([1.0, 3.0, 14.0, 0.9]))
lp = self.gp_gaussian.log_likelihood(1.0, 3.0, np.array([14.0, 0.9])) - 10.13680717
npt.assert_almost_equal(prob, lp)
def test_set_samplers(self):
type_kernel = [TASKS_KERNEL_NAME]
training_data = {
"evaluations": [42.2851784656, 72.3121248508],
"points": [[0], [1]],
"var_noise": []}
dimensions = [2]
gp_tk = GPFittingGaussian(type_kernel, training_data, dimensions)
assert gp_tk.length_scale_indexes is None
assert len(gp_tk.slice_samplers) == 1
value = gp_tk.sample_parameters(1, random_seed=1)[-1]
gp_tk_ = GPFittingGaussian(type_kernel, training_data, dimensions, n_burning=1,
random_seed=1)
assert np.all(gp_tk_.start_point_sampler == value)
type_kernel = [PRODUCT_KERNELS_SEPARABLE, MATERN52_NAME, TASKS_KERNEL_NAME]
training_data = {
"evaluations": [42.2851784656, 72.3121248508],
"points": [[0, 0], [1, 0]],
"var_noise": []}
dimensions = [2, 1, 1]
gp = GPFittingGaussian(type_kernel, training_data, dimensions, n_burning=1, random_seed=1)
gp2 = GPFittingGaussian(type_kernel, training_data, dimensions)
value2 = gp2.sample_parameters(1, random_seed=1)[-1]
assert np.all(gp.start_point_sampler == value2)
def test_sample_parameters_posterior(self):
start = self.gp.samples_parameters[-1]
sample = self.gp.sample_parameters_posterior(1, 1)
np.random.seed(1)
sample2 = self.gp.sample_parameters_posterior(1, start_point=start)
assert np.all(sample == sample2)
assert sample.shape == (1, 4)
start = self.gp.samples_parameters[-1]
sample3 = self.gp.sample_parameters_posterior(2, 1)
sample4 = self.gp.sample_parameters(2, random_seed=1, start_point=start)
assert np.all(sample4[0] == sample3[0, :])
assert np.all(sample4[1] == sample3[1, :])
def test_fit_gp_regression(self):
np.random.seed(5)
n_points = 10
normal_noise = np.random.normal(0, 0.5, n_points)
points = np.linspace(0, 500, n_points)
points = points.reshape([n_points, 1])
kernel = Matern52.define_kernel_from_array(1, np.array([100.0, 1.0]))
function = SampleFunctions.sample_from_gp(points, kernel)
function = function[0, :]
evaluations = function + normal_noise
training_data_gp = {
"evaluations": list(evaluations),
"points": points,
"var_noise": []}
gp_gaussian = GPFittingGaussian([MATERN52_NAME], training_data_gp, [1])
gp_gaussian_2 = GPFittingGaussian([MATERN52_NAME], training_data_gp, [1])
new_gp = gp_gaussian.fit_gp_regression(random_seed=1314938)
results = gp_gaussian_2.mle_parameters(random_seed=1314938)
results = results['solution']
npt.assert_almost_equal(new_gp.var_noise.value[0], results[0], decimal=6)
npt.assert_almost_equal(new_gp.mean.value[0], results[1], decimal=6)
npt.assert_almost_equal(new_gp.kernel_values, results[2:], decimal=1)
def test_train(self):
np.random.seed(5)
n_points = 10
normal_noise = np.random.normal(0, 0.5, n_points)
points = np.linspace(0, 500, n_points)
points = points.reshape([n_points, 1])
kernel = Matern52.define_kernel_from_array(1, np.array([100.0, 1.0]))
function = SampleFunctions.sample_from_gp(points, kernel)
function = function[0, :]
evaluations = function + normal_noise
training_data_gp = {
"evaluations": list(evaluations),
"points": points,
"var_noise": []}
new_gp = GPFittingGaussian.train([MATERN52_NAME], [1], True, training_data_gp, None,
random_seed=1314938)
gp_gaussian = GPFittingGaussian([MATERN52_NAME], training_data_gp, [1])
gp_2 = gp_gaussian.fit_gp_regression(random_seed=1314938)
npt.assert_almost_equal(new_gp.var_noise.value[0], gp_2.var_noise.value[0], decimal=6)
npt.assert_almost_equal(new_gp.mean.value[0], gp_2.mean.value[0], decimal=6)
npt.assert_almost_equal(new_gp.kernel_values, gp_2.kernel_values)
gp_gaussian = GPFittingGaussian([MATERN52_NAME], training_data_gp, [1])
new_gp_2 = GPFittingGaussian.train([MATERN52_NAME], [1], False, training_data_gp, None)
npt.assert_almost_equal(new_gp_2.var_noise.value[0], gp_gaussian.var_noise.value[0])
npt.assert_almost_equal(new_gp_2.mean.value[0], gp_gaussian.mean.value[0], decimal=6)
npt.assert_almost_equal(new_gp_2.kernel_values, gp_gaussian.kernel_values)
def test_compute_posterior_parameters(self):
np.random.seed(5)
n_points = 10
normal_noise = np.random.normal(0, 0.5, n_points)
points = np.linspace(0, 500, n_points)
points = points.reshape([n_points, 1])
kernel = Matern52.define_kernel_from_array(1, np.array([100.0, 1.0]))
function = SampleFunctions.sample_from_gp(points, kernel)
function = function[0, :]
evaluations = function + normal_noise
training_data_gp = {
"evaluations": list(evaluations[1:]),
"points": points[1:, :],
"var_noise": []}
gp = GPFittingGaussian([MATERN52_NAME], training_data_gp, [1], kernel_values=[100.0, 1.0],
mean_value=[0.0], var_noise_value=[0.5**2])
new_point = np.array([points[0], points[1]])
z = gp.compute_posterior_parameters(new_point)
mean = z['mean']
cov = z['cov']
assert mean[1] - 2.0 * np.sqrt(cov[1, 1]) <= function[1]
assert function[1] <= mean[1] + 2.0 * np.sqrt(cov[1, 1])
assert mean[0] - 2.0 * np.sqrt(cov[0, 0]) <= function[0]
assert function[0] <= mean[0] + 2.0 * np.sqrt(cov[0, 0])
# Values obtained from GPy
npt.assert_almost_equal(mean, np.array([0.30891226, 0.60256237]))
npt.assert_almost_equal(cov, np.array([[0.48844879, 0.16799927], [0.16799927, 0.16536313]]))
def test_sample_new_observations(self):
np.random.seed(5)
n_points = 10
normal_noise = np.random.normal(0, 0.5, n_points)
points = np.linspace(0, 500, n_points)
points = points.reshape([n_points, 1])
kernel = Matern52.define_kernel_from_array(1, np.array([100.0, 1.0]))
function = SampleFunctions.sample_from_gp(points, kernel)
function = function[0, :]
evaluations = function + normal_noise
training_data_gp = {
"evaluations": list(evaluations[1:]),
"points": points[1:, :],
"var_noise": []}
gp = GPFittingGaussian([MATERN52_NAME], training_data_gp, [1], kernel_values=[100.0, 1.0],
mean_value=[0.0], var_noise_value=[0.5**2])
n_samples = 100
samples = gp.sample_new_observations(np.array([[30.0]]), n_samples, random_seed=1)
new_point = np.array([[30.0]])
z = gp.compute_posterior_parameters(new_point)
mean = z['mean']
cov = z['cov']
npt.assert_almost_equal(mean, np.mean(samples), decimal=1)
npt.assert_almost_equal(cov, np.var(samples), decimal=1)
def test_cross_validation_mle_parameters(self):
type_kernel = [MATERN52_NAME]
np.random.seed(5)
n_points = 10
normal_noise = np.random.normal(0, 0.01, n_points)
points = np.linspace(0, 100, n_points)
points = points.reshape([n_points, 1])
kernel = Matern52.define_kernel_from_array(1, np.array([100.0]))
function = SampleFunctions.sample_from_gp(points, kernel)
function = function[0, :]
evaluations = function + normal_noise
training_data = {
"evaluations": evaluations,
"points": points,
"var_noise": None}
dimensions = [1]
problem_name = 'a'
result = \
ValidationGPModel.cross_validation_mle_parameters(type_kernel, training_data,
dimensions, problem_name,
start=np.array([0.01**2, 0.0, 100.0]))
compare = 'results/diagnostic_kernel/a/validation_kernel_histogram_a_' + MATERN52_NAME + \
'_same_correlation_False_10_None.png'
assert result['filename_histogram'] == compare
assert np.all(result['y_eval'] == evaluations)
assert result['n_data'] == n_points
assert result['filename_plot'] == 'results/diagnostic_kernel/a/' \
'validation_kernel_mean_vs_observations_a_' + \
MATERN52_NAME + '_same_correlation_False_10_None' + '.png'
assert result['success_proportion'] >= 0.9
noise = np.random.normal(0, 0.000001, n_points)
evaluations_noisy = evaluations + noise
training_data_2 = {
"evaluations": evaluations_noisy,
"points": points,
"var_noise": np.array(n_points * [0.000001**2])}
result_2 = \
ValidationGPModel.cross_validation_mle_parameters(type_kernel, training_data_2,
dimensions, problem_name,
start=np.array([0.01**2, 0.0, 100.0]))
compare = 'results/diagnostic_kernel/a/validation_kernel_histogram_a_' + MATERN52_NAME + \
'_same_correlation_False_10_None.png'
assert result_2['filename_histogram'] == compare
assert np.all(result_2['y_eval'] == evaluations_noisy)
assert result_2['n_data'] == n_points
compare = 'results/diagnostic_kernel/a/validation_kernel_mean_vs_observations_a_' + \
MATERN52_NAME + '_same_correlation_False_10_None.png'
assert result_2['filename_plot'] == compare
assert result_2['success_proportion'] >= 0.9
def test_cross_validation_mle_parameters_2(self):
type_kernel = [MATERN52_NAME]
np.random.seed(5)
n_points = 10
normal_noise = np.random.normal(0, 0.01, n_points)
points = np.linspace(0, 100, n_points)
points = points.reshape([n_points, 1])
kernel = Matern52.define_kernel_from_array(1, np.array([100.0]))
function = SampleFunctions.sample_from_gp(points, kernel)
function = function[0, :]
evaluations = function + normal_noise
training_data = {
"evaluations": evaluations,
"points": points,
"var_noise": None}
dimensions = [1]
problem_name = 'a'
result = \
ValidationGPModel.cross_validation_mle_parameters(type_kernel, training_data,
dimensions, problem_name,
start=np.array([-1]))
assert result['success_proportion'] == -1
def test_check_value_within_ci(self):
assert ValidationGPModel.check_value_within_ci(0, 1.0, 1.0)
assert not ValidationGPModel.check_value_within_ci(3.1, 1.0, 1.0)
assert not ValidationGPModel.check_value_within_ci(-1.1, 1.0, 1.0)
assert ValidationGPModel.check_value_within_ci(0, 1.0, 1.0, var_noise=0.00001)
def test_evaluate_cross_cov(self):
value = self.complex_gp.evaluate_cross_cov(np.array([[2.0, 0.0]]), np.array([[1.0, 0.0]]),
np.array([1.0, 0.0]))
assert value == np.array([[0.52399410883182029]])
def test_evaluate_grad_cross_cov_respect_point(self):
value = self.gp.evaluate_grad_cross_cov_respect_point(np.array([[40.0]]),
np.array([[39.0], [38.0]]),
np.array([1.0, 1.0]))
value_2 = ScaledKernel.evaluate_grad_respect_point(np.array([1.0, 1.0]),
np.array([[40.0]]),
np.array([[39.0], [38.0]]), 1,
*([MATERN52_NAME],))
assert np.all(value == value_2)
type_kernel = [MATERN52_NAME]
training_data = {
"evaluations":
[42.2851784656, 72.3121248508, 1.0113231069, 30.9309246906, 15.5288331909],
"points": [
[42.2851784656], [72.3121248508], [1.0113231069], [30.9309246906], [15.5288331909]],
"var_noise": []}
dimensions = [1]
gp = GPFittingGaussian(type_kernel, training_data, dimensions)
value = gp.evaluate_grad_cross_cov_respect_point(np.array([[40.0]]),
np.array([[39.0], [38.0]]),
np.array([1.0]))
value_2 = Matern52.evaluate_grad_respect_point(np.array([1.0]),
np.array([[40.0]]),
np.array([[39.0], [38.0]]), 1)
assert np.all(value == value_2)
def test_evaluate_hessian_respect_point(self):
type_kernel = [MATERN52_NAME]
training_data = {
"evaluations":
[42.2851784656, 72.3121248508, 1.0113231069, 30.9309246906, 15.5288331909],
"points": [
[42.2851784656], [72.3121248508], [1.0113231069], [30.9309246906], [15.5288331909]],
"var_noise": []}
dimensions = [1]
gp = GPFittingGaussian(type_kernel, training_data, dimensions)
value = gp.evaluate_hessian_cross_cov_respect_point(np.array([[40.0]]),
np.array([[39.0], [38.0]]),
np.array([1.0]))
value_2 = Matern52.evaluate_hessian_respect_point(np.array([1.0]),
np.array([[40.0]]),
np.array([[39.0], [38.0]]), 1)
assert np.all(value == value_2)
def test_get_historical_best_solution(self):
max_ = self.gp.get_historical_best_solution()
assert max_ == 72.3121248508
max_ = self.gp_3.get_historical_best_solution(noisy_evaluations=True)
assert max_ == self.gp_3.compute_posterior_parameters(
np.array([[72.3121248508]]), only_mean=True)['mean']
def test_gradient_posterior_parameters(self):
point = np.array([[49.5]])
grad = self.gp_gaussian.gradient_posterior_parameters(point)
dh = 0.0000001
finite_diff = FiniteDifferences.forward_difference(
lambda x: self.gp_gaussian.compute_posterior_parameters(
x.reshape((1, len(x))), only_mean=True)['mean'],
np.array([49.5]), np.array([dh]))
npt.assert_almost_equal(grad['mean'], finite_diff[0])
dh = 0.0000001
finite_diff = FiniteDifferences.forward_difference(
lambda x: self.gp_gaussian.compute_posterior_parameters(
x.reshape((1, len(x))))['cov'],
np.array([49.5]), np.array([dh]))
npt.assert_almost_equal(grad['cov'], finite_diff[0])
def setUp(self):
type_kernel = [SCALED_KERNEL, MATERN52_NAME]
self.training_data = {
"evaluations":
[42.2851784656, 72.3121248508, 1.0113231069, 30.9309246906, 15.5288331909],
"points": [
[42.2851784656], [72.3121248508], [1.0113231069], [30.9309246906], [15.5288331909]],
"var_noise": []}
dimensions = [1]
self.gp = GPFittingGaussian(type_kernel, self.training_data, dimensions,
bounds_domain=[[0, 100]])
self.training_data_3 = {
"evaluations": [42.2851784656, 72.3121248508, 1.0113231069, 30.9309246906,
15.5288331909],
"points": [
[42.2851784656], [72.3121248508], [1.0113231069], [30.9309246906], [15.5288331909]],
"var_noise": [0.5, 0.8, 0.7, 0.9, 1.0]}
self.gp_3 = GPFittingGaussian(type_kernel, self.training_data_3, dimensions,
bounds_domain=[[0, 100]])
self.training_data_simple = {
"evaluations": [5],
"points": [[5]],
"var_noise": []}
dimensions = [1]
self.simple_gp = GPFittingGaussian(type_kernel, self.training_data_simple, dimensions,
bounds_domain=[[0, 100]])
self.training_data_complex = {
"evaluations": [1.0],
"points": [[42.2851784656, 0]],
"var_noise": [0.5]}
self.complex_gp = GPFittingGaussian(
[PRODUCT_KERNELS_SEPARABLE, MATERN52_NAME, TASKS_KERNEL_NAME],
self.training_data_complex, [2, 1, 1], bounds_domain=[[0, 100], [0]])
self.training_data_complex_2 = {
"evaluations": [1.0, 2.0, 3.0],
"points": [[42.2851784656, 0], [10.532, 0], [9.123123, 1]],
"var_noise": [0.5, 0.2, 0.1]}
self.complex_gp_2 = GPFittingGaussian(
[PRODUCT_KERNELS_SEPARABLE, MATERN52_NAME, TASKS_KERNEL_NAME],
self.training_data_complex_2, [3, 1, 2], bounds_domain=[[0, 100], [0, 1]])
self.new_point = np.array([[80.0]])
self.evaluation = np.array([80.0])
self.training_data_noisy = {
"evaluations": [41.0101845096],
"points": [[42.2851784656]],
"var_noise": [0.0181073779]}
self.gp_noisy = GPFittingGaussian(type_kernel, self.training_data_noisy, dimensions,
bounds_domain=[[0, 100]])
np.random.seed(2)
n_points = 50
normal_noise = np.random.normal(0, 0.5, n_points)
points = np.linspace(0, 500, n_points)
points = points.reshape([n_points, 1])
kernel = Matern52.define_kernel_from_array(1, np.array([100.0, 1.0]))
function = SampleFunctions.sample_from_gp(points, kernel)
function = function[0, :]
evaluations = function + normal_noise
self.training_data_gp = {
"evaluations": list(evaluations),
"points": points,
"var_noise": []}
self.gp_gaussian = GPFittingGaussian([SCALED_KERNEL, MATERN52_NAME], self.training_data_gp,
[1])
self.gp_gaussian_2 = GPFittingGaussian([MATERN52_NAME], self.training_data_gp, [1],
bounds_domain=[[0, 100]])
self.training_data_gp_2 = {
"evaluations": list(evaluations - 10.0),
"points": points,
"var_noise": []}
self.gp_gaussian_central = GPFittingGaussian([SCALED_KERNEL, MATERN52_NAME],
self.training_data_gp_2, [1],
bounds_domain=[[0, 100]])