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_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 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 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_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_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_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_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)
from stratified_bayesian_optimization.util.json_file import JSONFile
from stratified_bayesian_optimization.kernels.matern52 import Matern52
from stratified_bayesian_optimization.lib.sample_functions import SampleFunctions
decimals = 10
random_seed = 5
np.random.seed(random_seed)
n_points = 1000
points = np.linspace(0, 100, n_points)
points = np.round(points, decimals=decimals)
points = points.reshape([n_points, 1])
tasks = np.array([[0, 1]])
add = [10, -10]
kernel = Matern52.define_kernel_from_array(1, np.array([100.0, 1.0]))
function = SampleFunctions.sample_from_gp(points, kernel)
function = function[0, :]
final_function = {}
for task in range(2):
final_function[task] = []
for i in xrange(n_points):
point = np.concatenate((points[i, :], np.array([task])))
final_function[task].append(function[i] + add[task])
filename = path.join('problems', 'test_simulated_gp',
'simulated_function_with_%d_%d' % (n_points, random_seed))
JSONFile.write({'function': final_function, 'points': points}, filename)
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]])