def log_ml(X_train,
Y_train,
hyps,
str_cov,
prior_mu_train,
is_fixed_noise=constants.IS_FIXED_GP_NOISE,
is_cholesky=True,
debug=False):
assert isinstance(X_train, np.ndarray)
assert isinstance(Y_train, np.ndarray)
assert isinstance(hyps, np.ndarray)
assert isinstance(str_cov, str)
assert isinstance(prior_mu_train, np.ndarray)
assert isinstance(is_fixed_noise, bool)
assert isinstance(is_cholesky, bool)
assert isinstance(debug, bool)
assert len(Y_train.shape) == 2
assert len(prior_mu_train.shape) == 2
assert X_train.shape[0] == Y_train.shape[0] == prior_mu_train.shape[0]
_check_str_cov('log_ml', str_cov, X_train.shape)
hyps = utils_covariance.restore_hyps(str_cov,
hyps,
is_fixed_noise=is_fixed_noise)
new_Y_train = Y_train - prior_mu_train
if is_cholesky:
cov_X_X, lower = get_kernel_cholesky(X_train,
hyps,
str_cov,
debug=debug)
# lower_new_Y_train = scipy.linalg.cho_solve((lower, True), new_Y_train)
alpha = scipy.linalg.cho_solve((lower, True), new_Y_train)
first_term = -0.5 * np.dot(new_Y_train.T, alpha)
second_term = -1.0 * np.sum(
np.log(np.diagonal(lower) + constants.JITTER_LOG))
else:
cov_X_X, inv_cov_X_X = get_kernel_inverse(X_train,
hyps,
str_cov,
debug=debug)
first_term = -0.5 * np.dot(np.dot(new_Y_train.T, inv_cov_X_X),
new_Y_train)
second_term = -0.5 * np.log(
np.linalg.det(cov_X_X) + constants.JITTER_LOG)
third_term = -float(X_train.shape[0]) / 2.0 * np.log(2.0 * np.pi)
log_ml_ = np.squeeze(first_term + second_term + third_term)
return log_ml_
def log_pseudo_l_loocv(X_train,
Y_train,
hyps,
str_cov,
prior_mu_train,
is_fixed_noise=constants.IS_FIXED_GP_NOISE,
debug=False):
assert isinstance(X_train, np.ndarray)
assert isinstance(Y_train, np.ndarray)
assert isinstance(hyps, np.ndarray)
assert isinstance(str_cov, str)
assert isinstance(prior_mu_train, np.ndarray)
assert isinstance(is_fixed_noise, bool)
assert isinstance(debug, bool)
assert len(Y_train.shape) == 2
assert len(prior_mu_train.shape) == 2
assert X_train.shape[0] == Y_train.shape[0] == prior_mu_train.shape[0]
_check_str_cov('log_pseudo_l_loocv', str_cov, X_train.shape)
num_data = X_train.shape[0]
hyps = utils_covariance.restore_hyps(str_cov,
hyps,
is_fixed_noise=is_fixed_noise)
cov_X_X, inv_cov_X_X = get_kernel_inverse(X_train,
hyps,
str_cov,
debug=debug)
log_pseudo_l = 0.0
for ind_data in range(0, num_data):
cur_X_train = np.vstack((X_train[:ind_data], X_train[ind_data + 1:]))
cur_Y_train = np.vstack((Y_train[:ind_data], Y_train[ind_data + 1:]))
cur_X_test = np.expand_dims(X_train[ind_data], axis=0)
cur_Y_test = Y_train[ind_data]
cur_mu = np.squeeze(cur_Y_test) - np.dot(
inv_cov_X_X, Y_train)[ind_data] / inv_cov_X_X[ind_data, ind_data]
cur_sigma = np.sqrt(
1.0 / (inv_cov_X_X[ind_data, ind_data] + constants.JITTER_COV))
first_term = -0.5 * np.log(cur_sigma**2)
second_term = -0.5 * (np.squeeze(cur_Y_test - cur_mu))**2 / (cur_sigma
**2)
third_term = -0.5 * np.log(2.0 * np.pi)
cur_log_pseudo_l = first_term + second_term + third_term
log_pseudo_l += cur_log_pseudo_l
return log_pseudo_l
def test_restore_hyps():
with pytest.raises(AssertionError) as error:
utils_covariance.restore_hyps(1.2, 2.1)
with pytest.raises(AssertionError) as error:
utils_covariance.restore_hyps(1.2, np.array([1.0, 1.0]))
with pytest.raises(AssertionError) as error:
utils_covariance.restore_hyps('se', 2.1)
with pytest.raises(AssertionError) as error:
utils_covariance.restore_hyps('abc', 2.1)
with pytest.raises(AssertionError) as error:
utils_covariance.restore_hyps('se', np.array([[1.0, 1.0], [1.0, 1.0]]))
with pytest.raises(AssertionError) as error:
utils_covariance.restore_hyps('se',
np.array([1.0, 1.0, 1.0]),
is_fixed_noise=1)
with pytest.raises(AssertionError) as error:
utils_covariance.restore_hyps('se',
np.array([1.0, 1.0, 1.0]),
fixed_noise='abc')
cur_hyps = np.array([0.1, 1.0, 1.0, 1.0, 1.0])
restored_hyps = utils_covariance.restore_hyps('se', cur_hyps)
assert restored_hyps['noise'] == cur_hyps[0]
assert restored_hyps['signal'] == cur_hyps[1]
assert (restored_hyps['lengthscales'] == cur_hyps[2:]).all()
restored_hyps = utils_covariance.restore_hyps('se',
cur_hyps,
is_fixed_noise=True)
assert restored_hyps['noise'] == constants.GP_NOISE
assert restored_hyps['signal'] == cur_hyps[0]
assert (restored_hyps['lengthscales'] == cur_hyps[1:]).all()
def get_optimized_kernel(
X_train: np.ndarray,
Y_train: np.ndarray,
prior_mu: constants.TYPING_UNION_CALLABLE_NONE,
str_cov: str,
str_optimizer_method: str = constants.STR_OPTIMIZER_METHOD_GP,
str_modelselection_method: str = constants.STR_MODELSELECTION_METHOD,
use_ard: bool = constants.USE_ARD,
fix_noise: bool = constants.FIX_GP_NOISE,
debug: bool = False) -> constants.TYPING_TUPLE_TWO_ARRAYS_DICT:
"""
This function computes the kernel matrix optimized by optimization
method specified, its inverse matrix, and the optimized hyperparameters.
:param X_train: inputs. Shape: (n, d) or (n, m, d).
:type X_train: numpy.ndarray
:param Y_train: outputs. Shape: (n, 1).
:type Y_train: numpy.ndarray
:param prior_mu: prior mean function or None.
:type prior_mu: callable or NoneType
:param str_cov: the name of covariance function.
:type str_cov: str.
:param str_optimizer_method: the name of optimization method.
:type str_optimizer_method: str., optional
:param str_modelselection_method: the name of model selection method.
:type str_modelselection_method: str., optional
:param use_ard: flag for using automatic relevance determination.
:type use_ard: bool., optional
:param fix_noise: flag for fixing a noise.
:type fix_noise: bool., optional
:param debug: flag for printing log messages.
:type debug: bool., optional
:returns: a tuple of kernel matrix over `X_train`, kernel matrix
inverse, and dictionary of hyperparameters.
:rtype: tuple of (numpy.ndarray, numpy.ndarray, dict.)
:raises: AssertionError, ValueError
"""
# TODO: check to input same fix_noise to convert_hyps and restore_hyps
utils_gp.validate_common_args(X_train, Y_train, str_cov, prior_mu, debug)
assert isinstance(str_optimizer_method, str)
assert isinstance(str_modelselection_method, str)
assert isinstance(use_ard, bool)
assert isinstance(fix_noise, bool)
utils_covariance.check_str_cov('get_optimized_kernel', str_cov,
X_train.shape)
assert str_optimizer_method in constants.ALLOWED_OPTIMIZER_METHOD_GP
assert str_modelselection_method in constants.ALLOWED_MODELSELECTION_METHOD
use_gradient = bool(str_optimizer_method != 'Nelder-Mead')
# TODO: Now, use_gradient is fixed as False.
# use_gradient = False
time_start = time.time()
if debug:
logger.debug('str_optimizer_method: %s', str_optimizer_method)
logger.debug('str_modelselection_method: %s',
str_modelselection_method)
logger.debug('use_gradient: %s', use_gradient)
prior_mu_train = utils_gp.get_prior_mu(prior_mu, X_train)
if str_cov in constants.ALLOWED_COV_BASE:
num_dim = X_train.shape[1]
elif str_cov in constants.ALLOWED_COV_SET:
num_dim = X_train.shape[2]
use_gradient = False
if str_modelselection_method == 'ml':
neg_log_ml_ = lambda hyps: gp_likelihood.neg_log_ml(
X_train,
Y_train,
hyps,
str_cov,
prior_mu_train,
use_ard=use_ard,
fix_noise=fix_noise,
use_gradient=use_gradient,
debug=debug)
elif str_modelselection_method == 'loocv':
# TODO: add use_ard.
neg_log_ml_ = lambda hyps: gp_likelihood.neg_log_pseudo_l_loocv(
X_train,
Y_train,
hyps,
str_cov,
prior_mu_train,
fix_noise=fix_noise,
debug=debug)
use_gradient = False
else: # pragma: no cover
raise ValueError(
'get_optimized_kernel: missing conditions for str_modelselection_method.'
)
hyps_converted = utils_covariance.convert_hyps(str_cov,
utils_covariance.get_hyps(
str_cov,
num_dim,
use_ard=use_ard),
fix_noise=fix_noise)
if str_optimizer_method in ['BFGS', 'SLSQP']:
result_optimized = scipy.optimize.minimize(neg_log_ml_,
hyps_converted,
method=str_optimizer_method,
jac=use_gradient,
options={'disp': False})
if debug:
logger.debug('negative log marginal likelihood: %.6f',
result_optimized.fun)
logger.debug('scipy message: %s', result_optimized.message)
result_optimized = result_optimized.x
elif str_optimizer_method in ['L-BFGS-B', 'SLSQP-Bounded']:
if str_optimizer_method == 'SLSQP-Bounded':
str_optimizer_method = 'SLSQP'
bounds = utils_covariance.get_range_hyps(str_cov,
num_dim,
use_ard=use_ard,
fix_noise=fix_noise)
result_optimized = scipy.optimize.minimize(neg_log_ml_,
hyps_converted,
method=str_optimizer_method,
bounds=bounds,
jac=use_gradient,
options={'disp': False})
if debug:
logger.debug('negative log marginal likelihood: %.6f',
result_optimized.fun)
logger.debug('scipy message: %s', result_optimized.message)
result_optimized = result_optimized.x
elif str_optimizer_method in ['Nelder-Mead']:
result_optimized = scipy.optimize.minimize(neg_log_ml_,
hyps_converted,
method=str_optimizer_method,
options={'disp': False})
if debug:
logger.debug('negative log marginal likelihood: %.6f',
result_optimized.fun)
logger.debug('scipy message: %s', result_optimized.message)
result_optimized = result_optimized.x
else: # pragma: no cover
raise ValueError(
'get_optimized_kernel: missing conditions for str_optimizer_method'
)
hyps = utils_covariance.restore_hyps(str_cov,
result_optimized,
use_ard=use_ard,
fix_noise=fix_noise)
hyps = utils_covariance.validate_hyps_dict(hyps, str_cov, num_dim)
cov_X_X, inv_cov_X_X, _ = covariance.get_kernel_inverse(
X_train, hyps, str_cov, fix_noise=fix_noise, debug=debug)
time_end = time.time()
if debug:
logger.debug('hyps optimized: %s', utils_logger.get_str_hyps(hyps))
logger.debug('time consumed to construct gpr: %.4f sec.',
time_end - time_start)
return cov_X_X, inv_cov_X_X, hyps
def get_optimized_kernel(
X_train,
Y_train,
prior_mu,
str_cov,
str_optimizer_method=constants.STR_OPTIMIZER_METHOD_GP,
str_modelselection_method=constants.STR_MODELSELECTION_METHOD,
is_fixed_noise=constants.IS_FIXED_GP_NOISE,
debug=False):
# TODO: check to input same is_fixed_noise to convert_hyps and restore_hyps
assert isinstance(X_train, np.ndarray)
assert isinstance(Y_train, np.ndarray)
assert callable(prior_mu) or prior_mu is None
assert isinstance(str_cov, str)
assert isinstance(str_optimizer_method, str)
assert isinstance(str_modelselection_method, str)
assert isinstance(is_fixed_noise, bool)
assert isinstance(debug, bool)
assert len(Y_train.shape) == 2
assert X_train.shape[0] == Y_train.shape[0]
_check_str_cov('get_optimized_kernel', str_cov, X_train.shape)
assert str_optimizer_method in constants.ALLOWED_OPTIMIZER_METHOD_GP
assert str_modelselection_method in constants.ALLOWED_MODELSELECTION_METHOD
time_start = time.time()
if debug:
print('[DEBUG] get_optimized_kernel in gp.py: str_optimizer_method {}'.
format(str_optimizer_method))
print(
'[DEBUG] get_optimized_kernel in gp.py: str_modelselection_method {}'
.format(str_modelselection_method))
prior_mu_train = get_prior_mu(prior_mu, X_train)
if str_cov in constants.ALLOWED_GP_COV_BASE:
num_dim = X_train.shape[1]
elif str_cov in constants.ALLOWED_GP_COV_SET:
num_dim = X_train.shape[2]
if str_modelselection_method == 'ml':
neg_log_ml = lambda hyps: -1.0 * log_ml(X_train,
Y_train,
hyps,
str_cov,
prior_mu_train,
is_fixed_noise=is_fixed_noise,
debug=debug)
elif str_modelselection_method == 'loocv':
neg_log_ml = lambda hyps: -1.0 * log_pseudo_l_loocv(X_train,
Y_train,
hyps,
str_cov,
prior_mu_train,
is_fixed_noise=
is_fixed_noise,
debug=debug)
else: # pragma: no cover
raise ValueError(
'get_optimized_kernel: missing conditions for str_modelselection_method.'
)
hyps_converted = utils_covariance.convert_hyps(
str_cov,
utils_covariance.get_hyps(str_cov, num_dim),
is_fixed_noise=is_fixed_noise,
)
if str_optimizer_method == 'BFGS':
result_optimized = scipy.optimize.minimize(neg_log_ml,
hyps_converted,
method=str_optimizer_method)
result_optimized = result_optimized.x
elif str_optimizer_method == 'L-BFGS-B':
bounds = utils_covariance.get_range_hyps(str_cov,
num_dim,
is_fixed_noise=is_fixed_noise)
result_optimized = scipy.optimize.minimize(neg_log_ml,
hyps_converted,
method=str_optimizer_method,
bounds=bounds)
result_optimized = result_optimized.x
# TODO: Fill this conditions
elif str_optimizer_method == 'DIRECT': # pragma: no cover
raise NotImplementedError(
'get_optimized_kernel: allowed str_optimizer_method, but it is not implemented.'
)
elif str_optimizer_method == 'CMA-ES': # pragma: no cover
raise NotImplementedError(
'get_optimized_kernel: allowed str_optimizer_method, but it is not implemented.'
)
# INFO: It is allowed, but a condition is missed.
else: # pragma: no cover
raise ValueError(
'get_optimized_kernel: missing conditions for str_optimizer_method'
)
hyps = utils_covariance.restore_hyps(str_cov,
result_optimized,
is_fixed_noise=is_fixed_noise)
hyps, _ = utils_covariance.validate_hyps_dict(hyps, str_cov, num_dim)
cov_X_X, inv_cov_X_X = get_kernel_inverse(X_train,
hyps,
str_cov,
debug=debug)
time_end = time.time()
if debug:
print('[DEBUG] get_optimized_kernel in gp.py: optimized hyps for gpr',
hyps)
print('[DEBUG] get_optimized_kernel in gp.py: time consumed',
time_end - time_start, 'sec.')
return cov_X_X, inv_cov_X_X, hyps
def neg_log_ml(X_train: np.ndarray,
Y_train: np.ndarray,
hyps: np.ndarray,
str_cov: str,
prior_mu_train: np.ndarray,
use_ard: bool = constants.USE_ARD,
fix_noise: bool = constants.FIX_GP_NOISE,
use_gradient: bool = True,
debug: bool = False) -> constants.TYPING_UNION_FLOAT_FA:
"""
This function computes a negative log marginal likelihood.
:param X_train: inputs. Shape: (n, d) or (n, m, d).
:type X_train: numpy.ndarray
:param Y_train: outputs. Shape: (n, 1).
:type Y_train: numpy.ndarray
:param hyps: hyperparameters for Gaussian process. Shape: (h, ).
:type hyps: numpy.ndarray
:param str_cov: the name of covariance function.
:type str_cov: str.
:param prior_mu_train: the prior values computed by get_prior_mu(). Shape: (n, 1).
:type prior_mu_train: numpy.ndarray
:param use_ard: flag for automatic relevance determination.
:type use_ard: bool., optional
:param fix_noise: flag for fixing a noise.
:type fix_noise: bool., optional
:param use_gradient: flag for computing and returning gradients of
negative log marginal likelihood.
:type use_gradient: bool., optional
:param debug: flag for printing log messages.
:type debug: bool., optional
:returns: negative log marginal likelihood, or (negative log marginal
likelihood, gradients of the likelihood).
:rtype: float, or tuple of (float, np.ndarray)
:raises: AssertionError
"""
utils_gp.validate_common_args(X_train, Y_train, str_cov, None, debug)
assert isinstance(hyps, np.ndarray)
assert isinstance(prior_mu_train, np.ndarray)
assert isinstance(use_ard, bool)
assert isinstance(fix_noise, bool)
assert isinstance(use_gradient, bool)
assert len(prior_mu_train.shape) == 2
assert X_train.shape[0] == Y_train.shape[0] == prior_mu_train.shape[0]
utils_covariance.check_str_cov('neg_log_ml', str_cov, X_train.shape)
num_X = float(X_train.shape[0])
hyps = utils_covariance.restore_hyps(str_cov,
hyps,
use_ard=use_ard,
fix_noise=fix_noise,
use_gp=False)
new_Y_train = Y_train - prior_mu_train
nu = hyps['dof']
cov_X_X, inv_cov_X_X, grad_cov_X_X = covariance.get_kernel_inverse(
X_train,
hyps,
str_cov,
fix_noise=fix_noise,
use_gradient=use_gradient,
debug=debug)
alpha = np.dot(inv_cov_X_X, new_Y_train)
beta = np.squeeze(np.dot(np.dot(new_Y_train.T, inv_cov_X_X), new_Y_train))
first_term = -0.5 * num_X * np.log((nu - 2.0) * np.pi)
sign_second_term, second_term = np.linalg.slogdet(cov_X_X)
# TODO: it should be checked.
if sign_second_term <= 0: # pragma: no cover
second_term = 0.0
second_term = -0.5 * second_term
third_term = np.log(
scipy.special.gamma(
(nu + num_X) / 2.0) / scipy.special.gamma(nu / 2.0))
fourth_term = -0.5 * (nu + num_X) * np.log(1.0 + beta / (nu - 2.0))
log_ml_ = np.squeeze(first_term + second_term + third_term + fourth_term)
log_ml_ /= num_X
if use_gradient:
assert grad_cov_X_X is not None
grad_log_ml_ = np.zeros(grad_cov_X_X.shape[2] + 1)
first_term_grad = ((nu + num_X) /
(nu + beta - 2.0) * np.dot(alpha, alpha.T) -
inv_cov_X_X)
nu_grad = -num_X / (2.0 * (nu - 2.0))\
+ scipy.special.digamma((nu + num_X) / 2.0)\
- scipy.special.digamma(nu / 2.0)\
- 0.5 * np.log(1.0 + beta / (nu - 2.0))\
+ (nu + num_X) * beta / (2.0 * (nu - 2.0)**2 + 2.0 * beta * (nu - 2.0))
if fix_noise:
grad_log_ml_[0] = nu_grad
else:
grad_log_ml_[1] = nu_grad
for ind in range(0, grad_cov_X_X.shape[2]):
cur_grad = 0.5 * np.trace(
np.dot(first_term_grad, grad_cov_X_X[:, :, ind]))
if fix_noise:
grad_log_ml_[ind + 1] = cur_grad
else:
if ind == 0:
cur_ind = 0
else:
cur_ind = ind + 1
grad_log_ml_[cur_ind] = cur_grad
if use_gradient:
return -1.0 * log_ml_, -1.0 * grad_log_ml_ / num_X
return -1.0 * log_ml_
def get_optimized_kernel(
X_train,
Y_train,
prior_mu,
str_cov,
str_optimizer_method=constants.STR_OPTIMIZER_METHOD_GP,
str_modelselection_method=constants.STR_MODELSELECTION_METHOD,
is_fixed_noise=constants.IS_FIXED_GP_NOISE,
debug=False):
"""
This function computes the kernel matrix optimized by optimization method specified, its inverse matrix, and the optimized hyperparameters.
:param X_train: inputs. Shape: (n, d) or (n, m, d).
:type X_train: numpy.ndarray
:param Y_train: outputs. Shape: (n, 1).
:type Y_train: numpy.ndarray
:param prior_mu: prior mean function or None.
:type prior_mu: function or NoneType
:param str_cov: the name of covariance function.
:type str_cov: str.
:param str_optimizer_method: the name of optimization method.
:type str_optimizer_method: str., optional
:param str_modelselection_method: the name of model selection method.
:type str_modelselection_method: str., optional
:param is_fixed_noise: flag for fixing a noise.
:type is_fixed_noise: bool., optional
:param debug: flag for printing log messages.
:type debug: bool., optional
:returns: a tuple of kernel matrix over `X_train`, kernel matrix inverse, and dictionary of hyperparameters.
:rtype: tuple of (numpy.ndarray, numpy.ndarray, dict.)
:raises: AssertionError, ValueError
"""
# TODO: check to input same is_fixed_noise to convert_hyps and restore_hyps
assert isinstance(X_train, np.ndarray)
assert isinstance(Y_train, np.ndarray)
assert callable(prior_mu) or prior_mu is None
assert isinstance(str_cov, str)
assert isinstance(str_optimizer_method, str)
assert isinstance(str_modelselection_method, str)
assert isinstance(is_fixed_noise, bool)
assert isinstance(debug, bool)
assert len(Y_train.shape) == 2
assert X_train.shape[0] == Y_train.shape[0]
_check_str_cov('get_optimized_kernel', str_cov, X_train.shape)
assert str_optimizer_method in constants.ALLOWED_OPTIMIZER_METHOD_GP
assert str_modelselection_method in constants.ALLOWED_MODELSELECTION_METHOD
# TODO: fix this.
is_gradient = True
time_start = time.time()
if debug:
print('[DEBUG] get_optimized_kernel in gp.py: str_optimizer_method {}'.
format(str_optimizer_method))
print(
'[DEBUG] get_optimized_kernel in gp.py: str_modelselection_method {}'
.format(str_modelselection_method))
prior_mu_train = get_prior_mu(prior_mu, X_train)
if str_cov in constants.ALLOWED_GP_COV_BASE:
num_dim = X_train.shape[1]
elif str_cov in constants.ALLOWED_GP_COV_SET:
num_dim = X_train.shape[2]
is_gradient = False
if str_modelselection_method == 'ml':
neg_log_ml_ = lambda hyps: neg_log_ml(X_train,
Y_train,
hyps,
str_cov,
prior_mu_train,
is_fixed_noise=is_fixed_noise,
is_gradient=is_gradient,
debug=debug)
elif str_modelselection_method == 'loocv':
neg_log_ml_ = lambda hyps: neg_log_pseudo_l_loocv(X_train,
Y_train,
hyps,
str_cov,
prior_mu_train,
is_fixed_noise=
is_fixed_noise,
debug=debug)
is_gradient = False
else: # pragma: no cover
raise ValueError(
'get_optimized_kernel: missing conditions for str_modelselection_method.'
)
hyps_converted = utils_covariance.convert_hyps(
str_cov,
utils_covariance.get_hyps(str_cov, num_dim),
is_fixed_noise=is_fixed_noise,
)
if str_optimizer_method == 'BFGS':
result_optimized = scipy.optimize.minimize(neg_log_ml_,
hyps_converted,
method=str_optimizer_method,
jac=is_gradient,
options={'disp': False})
result_optimized = result_optimized.x
elif str_optimizer_method == 'L-BFGS-B':
bounds = utils_covariance.get_range_hyps(str_cov,
num_dim,
is_fixed_noise=is_fixed_noise)
result_optimized = scipy.optimize.minimize(neg_log_ml_,
hyps_converted,
method=str_optimizer_method,
bounds=bounds,
jac=is_gradient,
options={'disp': False})
result_optimized = result_optimized.x
# TODO: Fill this conditions
elif str_optimizer_method == 'DIRECT': # pragma: no cover
raise NotImplementedError(
'get_optimized_kernel: allowed str_optimizer_method, but it is not implemented.'
)
elif str_optimizer_method == 'CMA-ES': # pragma: no cover
raise NotImplementedError(
'get_optimized_kernel: allowed str_optimizer_method, but it is not implemented.'
)
else: # pragma: no cover
raise ValueError(
'get_optimized_kernel: missing conditions for str_optimizer_method'
)
hyps = utils_covariance.restore_hyps(str_cov,
result_optimized,
is_fixed_noise=is_fixed_noise)
hyps, _ = utils_covariance.validate_hyps_dict(hyps, str_cov, num_dim)
cov_X_X, inv_cov_X_X, grad_cov_X_X = get_kernel_inverse(
X_train, hyps, str_cov, is_fixed_noise=is_fixed_noise, debug=debug)
time_end = time.time()
if debug:
print('[DEBUG] get_optimized_kernel in gp.py: optimized hyps for gpr',
hyps)
print('[DEBUG] get_optimized_kernel in gp.py: time consumed',
time_end - time_start, 'sec.')
return cov_X_X, inv_cov_X_X, hyps
def neg_log_pseudo_l_loocv(X_train,
Y_train,
hyps,
str_cov,
prior_mu_train,
is_fixed_noise=constants.IS_FIXED_GP_NOISE,
debug=False):
"""
It computes a negative log pseudo-likelihood using leave-one-out cross-validation.
:param X_train: inputs. Shape: (n, d) or (n, m, d).
:type X_train: numpy.ndarray
:param Y_train: outputs. Shape: (n, 1).
:type Y_train: numpy.ndarray
:param hyps: hyperparameters for Gaussian process. Shape: (h, ).
:type hyps: numpy.ndarray
:param str_cov: the name of covariance function.
:type str_cov: str.
:param prior_mu_train: the prior values computed by get_prior_mu(). Shape: (n, 1).
:type prior_mu_train: numpy.ndarray
:param is_fixed_noise: flag for fixing a noise.
:type is_fixed_noise: bool., optional
:param debug: flag for printing log messages.
:type debug: bool., optional
:returns: negative log pseudo-likelihood.
:rtype: float
:raises: AssertionError
"""
assert isinstance(X_train, np.ndarray)
assert isinstance(Y_train, np.ndarray)
assert isinstance(hyps, np.ndarray)
assert isinstance(str_cov, str)
assert isinstance(prior_mu_train, np.ndarray)
assert isinstance(is_fixed_noise, bool)
assert isinstance(debug, bool)
assert len(Y_train.shape) == 2
assert len(prior_mu_train.shape) == 2
assert X_train.shape[0] == Y_train.shape[0] == prior_mu_train.shape[0]
_check_str_cov('neg_log_pseudo_l_loocv', str_cov, X_train.shape)
num_data = X_train.shape[0]
hyps = utils_covariance.restore_hyps(str_cov,
hyps,
is_fixed_noise=is_fixed_noise)
cov_X_X, inv_cov_X_X, grad_cov_X_X = get_kernel_inverse(
X_train, hyps, str_cov, is_fixed_noise=is_fixed_noise, debug=debug)
log_pseudo_l_ = 0.0
for ind_data in range(0, num_data):
cur_X_train = np.vstack((X_train[:ind_data], X_train[ind_data + 1:]))
cur_Y_train = np.vstack((Y_train[:ind_data], Y_train[ind_data + 1:]))
cur_X_test = np.expand_dims(X_train[ind_data], axis=0)
cur_Y_test = Y_train[ind_data]
cur_mu = np.squeeze(cur_Y_test) - np.dot(
inv_cov_X_X, Y_train)[ind_data] / inv_cov_X_X[ind_data, ind_data]
cur_sigma = np.sqrt(
1.0 / (inv_cov_X_X[ind_data, ind_data] + constants.JITTER_COV))
first_term = -0.5 * np.log(cur_sigma**2)
second_term = -0.5 * (np.squeeze(cur_Y_test - cur_mu))**2 / (cur_sigma
**2)
third_term = -0.5 * np.log(2.0 * np.pi)
cur_log_pseudo_l_ = first_term + second_term + third_term
log_pseudo_l_ += cur_log_pseudo_l_
log_pseudo_l_ /= num_data
log_pseudo_l_ *= -1.0
return log_pseudo_l_
def neg_log_ml(X_train,
Y_train,
hyps,
str_cov,
prior_mu_train,
is_fixed_noise=constants.IS_FIXED_GP_NOISE,
is_cholesky=True,
is_gradient=True,
debug=False):
"""
This function computes a negative log marginal likelihood.
:param X_train: inputs. Shape: (n, d) or (n, m, d).
:type X_train: numpy.ndarray
:param Y_train: outputs. Shape: (n, 1).
:type Y_train: numpy.ndarray
:param hyps: hyperparameters for Gaussian process. Shape: (h, ).
:type hyps: numpy.ndarray
:param str_cov: the name of covariance function.
:type str_cov: str.
:param prior_mu_train: the prior values computed by get_prior_mu(). Shape: (n, 1).
:type prior_mu_train: numpy.ndarray
:param is_fixed_noise: flag for fixing a noise.
:type is_fixed_noise: bool., optional
:param is_cholesky: flag for using a cholesky decomposition.
:type is_cholesky: bool., optional
:param is_gradient: flag for computing and returning gradients of negative log marginal likelihood.
:type is_gradient: bool., optional
:param debug: flag for printing log messages.
:type debug: bool., optional
:returns: negative log marginal likelihood, or (negative log marginal likelihood, gradients of the likelihood).
:rtype: float, or tuple of (float, float)
:raises: AssertionError
"""
assert isinstance(X_train, np.ndarray)
assert isinstance(Y_train, np.ndarray)
assert isinstance(hyps, np.ndarray)
assert isinstance(str_cov, str)
assert isinstance(prior_mu_train, np.ndarray)
assert isinstance(is_fixed_noise, bool)
assert isinstance(is_cholesky, bool)
assert isinstance(is_gradient, bool)
assert isinstance(debug, bool)
assert len(Y_train.shape) == 2
assert len(prior_mu_train.shape) == 2
assert X_train.shape[0] == Y_train.shape[0] == prior_mu_train.shape[0]
_check_str_cov('neg_log_ml', str_cov, X_train.shape)
hyps = utils_covariance.restore_hyps(str_cov,
hyps,
is_fixed_noise=is_fixed_noise)
new_Y_train = Y_train - prior_mu_train
if is_cholesky:
cov_X_X, lower, grad_cov_X_X = get_kernel_cholesky(
X_train,
hyps,
str_cov,
is_fixed_noise=is_fixed_noise,
is_gradient=is_gradient,
debug=debug)
alpha = scipy.linalg.cho_solve((lower, True), new_Y_train)
first_term = -0.5 * np.dot(new_Y_train.T, alpha)
second_term = -1.0 * np.sum(
np.log(np.diagonal(lower) + constants.JITTER_LOG))
if is_gradient:
assert grad_cov_X_X is not None
first_term_grad = np.einsum("ik,jk->ijk", alpha, alpha)
first_term_grad -= np.expand_dims(scipy.linalg.cho_solve(
(lower, True), np.eye(cov_X_X.shape[0])),
axis=2)
grad_log_ml_ = 0.5 * np.einsum("ijl,ijk->kl", first_term_grad,
grad_cov_X_X)
grad_log_ml_ = np.sum(grad_log_ml_, axis=1)
else:
# TODO: is_gradient is fixed.
is_gradient = False
cov_X_X, inv_cov_X_X, grad_cov_X_X = get_kernel_inverse(
X_train,
hyps,
str_cov,
is_fixed_noise=is_fixed_noise,
is_gradient=is_gradient,
debug=debug)
first_term = -0.5 * np.dot(np.dot(new_Y_train.T, inv_cov_X_X),
new_Y_train)
second_term = -0.5 * np.log(
np.linalg.det(cov_X_X) + constants.JITTER_LOG)
third_term = -float(X_train.shape[0]) / 2.0 * np.log(2.0 * np.pi)
log_ml_ = np.squeeze(first_term + second_term + third_term)
log_ml_ /= X_train.shape[0]
if is_gradient:
return -1.0 * log_ml_, -1.0 * grad_log_ml_ / X_train.shape[0]
else:
return -1.0 * log_ml_
def neg_log_ml(X_train: np.ndarray, Y_train: np.ndarray, hyps: np.ndarray,
str_cov: str, prior_mu_train: np.ndarray,
use_ard: bool=constants.USE_ARD,
fix_noise: bool=constants.FIX_GP_NOISE,
use_cholesky: bool=True,
use_gradient: bool=True,
debug: bool=False
) -> constants.TYPING_UNION_FLOAT_FA:
"""
This function computes a negative log marginal likelihood.
:param X_train: inputs. Shape: (n, d) or (n, m, d).
:type X_train: numpy.ndarray
:param Y_train: outputs. Shape: (n, 1).
:type Y_train: numpy.ndarray
:param hyps: hyperparameters for Gaussian process. Shape: (h, ).
:type hyps: numpy.ndarray
:param str_cov: the name of covariance function.
:type str_cov: str.
:param prior_mu_train: the prior values computed by get_prior_mu(). Shape: (n, 1).
:type prior_mu_train: numpy.ndarray
:param use_ard: flag for automatic relevance determination.
:type use_ard: bool., optional
:param fix_noise: flag for fixing a noise.
:type fix_noise: bool., optional
:param use_cholesky: flag for using a cholesky decomposition.
:type use_cholesky: bool., optional
:param use_gradient: flag for computing and returning gradients of
negative log marginal likelihood.
:type use_gradient: bool., optional
:param debug: flag for printing log messages.
:type debug: bool., optional
:returns: negative log marginal likelihood, or (negative log marginal
likelihood, gradients of the likelihood).
:rtype: float, or tuple of (float, np.ndarray)
:raises: AssertionError
"""
# TODO: add use_ard.
utils_gp.validate_common_args(X_train, Y_train, str_cov, None, debug)
assert isinstance(hyps, np.ndarray)
assert isinstance(prior_mu_train, np.ndarray)
assert isinstance(use_ard, bool)
assert isinstance(fix_noise, bool)
assert isinstance(use_cholesky, bool)
assert isinstance(use_gradient, bool)
assert len(prior_mu_train.shape) == 2
assert X_train.shape[0] == Y_train.shape[0] == prior_mu_train.shape[0]
utils_covariance.check_str_cov('neg_log_ml', str_cov, X_train.shape)
hyps = utils_covariance.restore_hyps(str_cov, hyps, use_ard=use_ard, fix_noise=fix_noise)
new_Y_train = Y_train - prior_mu_train
if use_cholesky:
cov_X_X, lower, grad_cov_X_X = covariance.get_kernel_cholesky(X_train,
hyps, str_cov, fix_noise=fix_noise, use_gradient=use_gradient,
debug=debug)
alpha = scipy.linalg.cho_solve((lower, True), new_Y_train)
first_term = -0.5 * np.dot(new_Y_train.T, alpha)
second_term = -1.0 * np.sum(np.log(np.diagonal(lower) + constants.JITTER_LOG))
if use_gradient:
assert grad_cov_X_X is not None
first_term_grad = np.einsum("ik,jk->ijk", alpha, alpha)
first_term_grad -= np.expand_dims(scipy.linalg.cho_solve((lower, True),
np.eye(cov_X_X.shape[0])), axis=2)
grad_log_ml_ = 0.5 * np.einsum("ijl,ijk->kl", first_term_grad, grad_cov_X_X)
grad_log_ml_ = np.sum(grad_log_ml_, axis=1)
else:
# TODO: use_gradient is fixed.
use_gradient = False
cov_X_X, inv_cov_X_X, grad_cov_X_X = covariance.get_kernel_inverse(X_train,
hyps, str_cov, fix_noise=fix_noise, use_gradient=use_gradient,
debug=debug)
first_term = -0.5 * np.dot(np.dot(new_Y_train.T, inv_cov_X_X), new_Y_train)
sign_second_term, second_term = np.linalg.slogdet(cov_X_X)
# TODO: It should be checked.
if sign_second_term <= 0: # pragma: no cover
second_term = 0.0
second_term = -0.5 * second_term
third_term = -float(X_train.shape[0]) / 2.0 * np.log(2.0 * np.pi)
log_ml_ = np.squeeze(first_term + second_term + third_term)
log_ml_ /= X_train.shape[0]
if use_gradient:
return -1.0 * log_ml_, -1.0 * grad_log_ml_ / X_train.shape[0]
return -1.0 * log_ml_
def test_restore_hyps():
with pytest.raises(AssertionError) as error:
package_target.restore_hyps(1.2, 2.1)
with pytest.raises(AssertionError) as error:
package_target.restore_hyps(1.2, np.array([1.0, 1.0]))
with pytest.raises(AssertionError) as error:
package_target.restore_hyps('se', 2.1)
with pytest.raises(AssertionError) as error:
package_target.restore_hyps('abc', 2.1)
with pytest.raises(AssertionError) as error:
package_target.restore_hyps('se', np.array([[1.0, 1.0], [1.0, 1.0]]))
with pytest.raises(AssertionError) as error:
package_target.restore_hyps('se', np.array([1.0, 1.0, 1.0]), use_ard=1)
with pytest.raises(AssertionError) as error:
package_target.restore_hyps('se',
np.array([1.0, 1.0, 1.0]),
use_ard='abc')
with pytest.raises(AssertionError) as error:
package_target.restore_hyps('se',
np.array([1.0, 1.0, 1.0]),
fix_noise=1)
with pytest.raises(AssertionError) as error:
package_target.restore_hyps('se',
np.array([1.0, 1.0, 1.0]),
noise='abc')
with pytest.raises(AssertionError) as error:
package_target.restore_hyps('se', np.array([1.0, 1.0, 1.0]), use_gp=1)
with pytest.raises(AssertionError) as error:
package_target.restore_hyps('se',
np.array([1.0, 1.0, 1.0]),
use_gp='abc')
with pytest.raises(AssertionError) as error:
package_target.restore_hyps('se',
np.array([0.1, 1.0, 1.0, 1.0]),
use_ard=False)
cur_hyps = np.array([0.1, 1.0, 1.0, 1.0, 1.0])
restored_hyps = package_target.restore_hyps('se',
cur_hyps,
fix_noise=False)
assert restored_hyps['noise'] == cur_hyps[0]
assert restored_hyps['signal'] == cur_hyps[1]
assert (restored_hyps['lengthscales'] == cur_hyps[2:]).all()
restored_hyps = package_target.restore_hyps('se', cur_hyps, fix_noise=True)
assert restored_hyps['noise'] == constants.GP_NOISE
assert restored_hyps['signal'] == cur_hyps[0]
assert (restored_hyps['lengthscales'] == cur_hyps[1:]).all()
cur_hyps = np.array([0.1, 100.0, 20.0, 1.0, 1.0, 1.0])
restored_hyps = package_target.restore_hyps('se',
cur_hyps,
fix_noise=False,
use_gp=False)
assert restored_hyps['noise'] == cur_hyps[0]
assert restored_hyps['dof'] == cur_hyps[1]
assert restored_hyps['signal'] == cur_hyps[2]
assert (restored_hyps['lengthscales'] == cur_hyps[3:]).all()
cur_hyps = np.array([100.0, 20.0, 1.0, 1.0, 1.0])
restored_hyps = package_target.restore_hyps('se',
cur_hyps,
fix_noise=True,
use_gp=False)
assert restored_hyps['noise'] == constants.GP_NOISE
assert restored_hyps['dof'] == cur_hyps[0]
assert restored_hyps['signal'] == cur_hyps[1]
assert (restored_hyps['lengthscales'] == cur_hyps[2:]).all()
cur_hyps = np.array([0.1, 1.0, 4.0])
restored_hyps = package_target.restore_hyps('se',
cur_hyps,
fix_noise=False)
assert restored_hyps['noise'] == cur_hyps[0]
assert restored_hyps['signal'] == cur_hyps[1]
assert restored_hyps['lengthscales'] == cur_hyps[2]
