def test_regression_model():
param_true = np.array([1.0, 2.0]).reshape((1, -1))
from UQpy.run_model.model_execution.PythonModel import PythonModel
model = PythonModel(model_script='pfn_models.py',
model_object_name='model_quadratic',
var_names=['theta_0', 'theta_1'])
h_func = RunModel(model=model)
h_func.run(samples=param_true)
# Add noise
error_covariance = 1.
data_clean = np.array(h_func.qoi_list[0])
noise = Normal(loc=0., scale=np.sqrt(error_covariance)).rvs(
nsamples=4, random_state=1).reshape((4, ))
data_3 = data_clean + noise
candidate_model = ComputationalModel(n_parameters=2,
runmodel_object=h_func,
error_covariance=error_covariance)
optimizer = MinimizeOptimizer(method='nelder-mead')
ml_estimator = MLE(inference_model=candidate_model,
data=data_3,
n_optimizations=1,
random_state=1,
optimizer=optimizer)
assert ml_estimator.mle[0] == 0.8689097631871134
assert ml_estimator.mle[1] == 2.0030767805841143
def test_mle_optimizer(setup):
h_func = setup
candidate_model = ComputationalModel(n_parameters=2,
runmodel_object=h_func,
error_covariance=np.ones(4))
ml_estimator = MLE(inference_model=candidate_model,
data=data,
initial_parameters=[0., 0.],
random_state=123)
assert round(ml_estimator.mle[0], 3) == -0.039
def test_user_loglike_uniform():
candidate_model = LogLikelihoodModel(
n_parameters=2, log_likelihood=user_log_likelihood_uniform)
optimizer = MinimizeOptimizer(method='nelder-mead',
bounds=((-2, 2), (-2, 2)))
ml_estimator = MLE(inference_model=candidate_model,
data=data,
n_optimizations=2,
optimizer=optimizer,
random_state=123)
assert round(ml_estimator.mle[0], 3) == 0.786
def test_user_loglike(setup):
h_func = setup
candidate_model = ComputationalModel(n_parameters=2,
runmodel_object=h_func,
log_likelihood=user_log_likelihood)
optimizer = MinimizeOptimizer(method='nelder-mead',
bounds=((-2, 2), (-2, 2)))
ml_estimator = MLE(inference_model=candidate_model,
optimizer=optimizer,
data=data,
n_optimizations=2,
random_state=123)
assert round(ml_estimator.mle[0], 3) == -0.039
def test_simple_probability_model():
np.random.seed(1)
mu, sigma = 0, 0.1 # true mean and standard deviation
data_1 = np.random.normal(mu, sigma, 1000).reshape((-1, 1))
# set parameters to be learnt as None
dist = Normal(loc=None, scale=None)
candidate_model = DistributionModel(distributions=dist, n_parameters=2)
ml_estimator = MLE(inference_model=candidate_model,
data=data_1,
n_optimizations=3,
random_state=1)
assert ml_estimator.mle[0] == 0.003881247615960185
assert ml_estimator.mle[1] == 0.09810041339322118
param_true = np.array([1.0, 2.0]).reshape((1, -1))
print('Shape of true parameter vector: {}'.format(param_true.shape))
model = PythonModel(model_script='local_pfn_models.py', model_object_name='model_quadratic', delete_files=True,
var_names=['theta_0', 'theta_1'])
h_func = RunModel(model=model)
h_func.run(samples=param_true)
# Add noise
error_covariance = 1.
data_clean = np.array(h_func.qoi_list[0])
noise = Normal(loc=0., scale=np.sqrt(error_covariance)).rvs(nsamples=50).reshape((50,))
data_3 = data_clean + noise
print('Shape of data: {}'.format(data_3.shape))
#%% md
#
# Then we create an instance of the Model class, using model_type='python', and we perform maximum likelihood estimation
# of the two parameters.
#%%
candidate_model = ComputationalModel(n_parameters=2, runmodel_object=h_func, error_covariance=error_covariance)
optimizer = MinimizeOptimizer(method='nelder-mead')
ml_estimator = MLE(inference_model=candidate_model, data=data_3, n_optimizations=1)
print('fitted parameters: theta_0={0:.3f} (true=1.), and theta_1={1:.3f} (true=2.)'.format(
ml_estimator.mle[0], ml_estimator.mle[1]))
#%%
names = ['model_linear', 'model_quadratic', 'model_cubic']
estimators = []
for i in range(3):
model = PythonModel(model_script='pfn_models.py',
model_object_name=names[i],
var_names=['theta_{}'.format(j) for j in range(i + 1)])
h_func = RunModel(model=model)
M = ComputationalModel(runmodel_object=h_func,
n_parameters=i + 1,
name=names[i],
error_covariance=error_covariance)
estimators.append(MLE(inference_model=M, data=data_1))
#%% md
#
# Apart from the data, candidate models and method (:class:`.BIC`, :class:`.AIC`...),
# :class:`.InformationModelSelection` also takes as inputs lists of
# inputs to the maximum likelihood class. Those inputs should be lists of length
# len(candidate_models).
#%%
from UQpy.utilities.MinimizeOptimizer import MinimizeOptimizer
optimizer = MinimizeOptimizer(method='nelder-mead')
selector = InformationModelSelection(parameter_estimators=estimators,
criterion=BIC(),
n_optimizations=[1] * 3)
candidate_model = DistributionModel(n_parameters=5, distributions=d_guess)
print(candidate_model.list_params)
#%% md
#
# When calling MLEstimation, the function minimize from the scipy.optimize package is used by default. The user can
# define bounds for the optimization, a seed, the algorithm to be used, and set the algorithm to perform several
# optimization iterations, starting at a different random seed every time.
#%%
optimizer = MinimizeOptimizer(bounds=[[-5, 5], [0, 10], [-5, 5], [0, 10],
[1.1, 4]],
method="SLSQP")
ml_estimator = MLE(inference_model=candidate_model,
data=data_2,
optimizer=optimizer)
ml_estimator = MLE(inference_model=candidate_model,
data=data_2,
optimizer=optimizer,
initial_parameters=[1., 1., 1., 1., 4.])
print(
'ML estimates of the mean={0:.3f} and std. dev={1:.3f} of 1st marginal (true: 0.0, 1.0)'
.format(ml_estimator.mle[0], ml_estimator.mle[1]))
print(
'ML estimates of the mean={0:.3f} and std. dev={1:.3f} of 2nd marginal (true: 0.0, 1.0)'
.format(ml_estimator.mle[2], ml_estimator.mle[3]))
print('ML estimates of the copula parameter={0:.3f} (true: 2.0)'.format(
ml_estimator.mle[4]))
# Define the models to be compared, for each model one must create an instance of the model class
m0 = DistributionModel(distributions=Gamma(a=None, loc=None, scale=None),
n_parameters=3,
name='gamma')
m1 = DistributionModel(distributions=Exponential(loc=None, scale=None),
n_parameters=2,
name='exponential')
m2 = DistributionModel(distributions=ChiSquare(df=None, loc=None, scale=None),
n_parameters=3,
name='chi-square')
candidate_models = [m0, m1, m2]
mle1 = MLE(inference_model=m0, random_state=0, data=data)
mle2 = MLE(inference_model=m1, random_state=0, data=data)
mle3 = MLE(inference_model=m2, random_state=0, data=data)
#%% md
#
# Perform model selection using different information criteria
#%%
from UQpy.inference import BIC, AIC, AICc
criteria = [BIC(), AIC(), AICc()]
sorted_names = []
criterion_value = []
param = []