def __init__(self,
X,
Y,
kernel=None,
warping_function=None,
warping_terms=3,
normalize_X=False,
normalize_Y=False):
if kernel is None:
kernel = kern.rbf(X.shape[1])
if warping_function == None:
self.warping_function = TanhWarpingFunction_d(warping_terms)
self.warping_params = (
np.random.randn(self.warping_function.n_terms * 3 + 1, ) * 1)
self.scale_data = False
if self.scale_data:
Y = self._scale_data(Y)
self.has_uncertain_inputs = False
self.Y_untransformed = Y.copy()
self.predict_in_warped_space = False
likelihood = likelihoods.Gaussian(self.transform_data(),
normalize=normalize_Y)
GP.__init__(self, X, likelihood, kernel, normalize_X=normalize_X)
self._set_params(self._get_params())
def __init__(self,
X,
Y,
kernel=None,
warping_function=None,
warping_terms=3):
if kernel is None:
kernel = kern.RBF(X.shape[1])
if warping_function == None:
self.warping_function = TanhWarpingFunction_d(warping_terms)
self.warping_params = (
np.random.randn(self.warping_function.n_terms * 3 + 1, ) * 1)
else:
self.warping_function = warping_function
self.scale_data = False
if self.scale_data:
Y = self._scale_data(Y)
self.has_uncertain_inputs = False
self.Y_untransformed = Y.copy()
self.predict_in_warped_space = False
likelihood = likelihoods.Gaussian()
GP.__init__(self,
X,
self.transform_data(),
likelihood=likelihood,
kernel=kernel)
self.link_parameter(self.warping_function)
def __init__(self, X, Y, kernel=None, warping_function=None, warping_terms=3, normalize_X=False, normalize_Y=False):
if kernel is None:
kernel = kern.rbf(X.shape[1])
if warping_function == None:
self.warping_function = TanhWarpingFunction_d(warping_terms)
self.warping_params = (np.random.randn(self.warping_function.n_terms * 3 + 1,) * 1)
Y = self._scale_data(Y)
self.has_uncertain_inputs = False
self.Y_untransformed = Y.copy()
self.predict_in_warped_space = False
likelihood = likelihoods.Gaussian(self.transform_data(), normalize=normalize_Y)
GP.__init__(self, X, likelihood, kernel, normalize_X=normalize_X)
self._set_params(self._get_params())
def __init__(self, X, Y, kernel=None, warping_function=None, warping_terms=3):
if kernel is None:
kernel = kern.RBF(X.shape[1])
if warping_function == None:
self.warping_function = TanhWarpingFunction_d(warping_terms)
self.warping_params = (np.random.randn(self.warping_function.n_terms * 3 + 1,) * 1)
else:
self.warping_function = warping_function
self.scale_data = False
if self.scale_data:
Y = self._scale_data(Y)
self.has_uncertain_inputs = False
self.Y_untransformed = Y.copy()
self.predict_in_warped_space = False
likelihood = likelihoods.Gaussian()
GP.__init__(self, X, self.transform_data(), likelihood=likelihood, kernel=kernel)
self.link_parameter(self.warping_function)
class WarpedGP(GP):
def __init__(self,
X,
Y,
kernel=None,
warping_function=None,
warping_terms=3):
if kernel is None:
kernel = kern.RBF(X.shape[1])
if warping_function == None:
self.warping_function = TanhWarpingFunction_d(warping_terms)
self.warping_params = (
np.random.randn(self.warping_function.n_terms * 3 + 1, ) * 1)
else:
self.warping_function = warping_function
self.scale_data = False
if self.scale_data:
Y = self._scale_data(Y)
self.has_uncertain_inputs = False
self.Y_untransformed = Y.copy()
self.predict_in_warped_space = False
likelihood = likelihoods.Gaussian()
GP.__init__(self,
X,
self.transform_data(),
likelihood=likelihood,
kernel=kernel)
self.link_parameter(self.warping_function)
def _scale_data(self, Y):
self._Ymax = Y.max()
self._Ymin = Y.min()
return (Y - self._Ymin) / (self._Ymax - self._Ymin) - 0.5
def _unscale_data(self, Y):
return (Y + 0.5) * (self._Ymax - self._Ymin) + self._Ymin
def parameters_changed(self):
self.Y[:] = self.transform_data()
super(WarpedGP, self).parameters_changed()
Kiy = self.posterior.woodbury_vector.flatten()
grad_y = self.warping_function.fgrad_y(self.Y_untransformed)
grad_y_psi, grad_psi = self.warping_function.fgrad_y_psi(
self.Y_untransformed, return_covar_chain=True)
djac_dpsi = ((1.0 / grad_y[:, :, None, None]) *
grad_y_psi).sum(axis=0).sum(axis=0)
dquad_dpsi = (Kiy[:, None, None, None] *
grad_psi).sum(axis=0).sum(axis=0)
warping_grads = -dquad_dpsi + djac_dpsi
self.warping_function.psi.gradient[:] = warping_grads[:, :-1]
self.warping_function.d.gradient[:] = warping_grads[0, -1]
def transform_data(self):
Y = self.warping_function.f(self.Y_untransformed.copy()).copy()
return Y
def log_likelihood(self):
ll = GP.log_likelihood(self)
jacobian = self.warping_function.fgrad_y(self.Y_untransformed)
return ll + np.log(jacobian).sum()
def plot_warping(self):
self.warping_function.plot(self.Y_untransformed.min(),
self.Y_untransformed.max())
def predict(self, Xnew, which_parts='all', pred_init=None):
# normalize X values
# Xnew = (Xnew.copy() - self._Xoffset) / self._Xscale
mu, var = GP._raw_predict(self, Xnew)
# now push through likelihood
mean, var = self.likelihood.predictive_values(mu, var)
if self.predict_in_warped_space:
mean = self.warping_function.f_inv(mean, y=pred_init)
var = self.warping_function.f_inv(var)
if self.scale_data:
mean = self._unscale_data(mean)
return mean, var
class WarpedGP(GP):
def __init__(self,
X,
Y,
kernel=None,
warping_function=None,
warping_terms=3,
normalize_X=False,
normalize_Y=False):
if kernel is None:
kernel = kern.rbf(X.shape[1])
if warping_function == None:
self.warping_function = TanhWarpingFunction_d(warping_terms)
self.warping_params = (
np.random.randn(self.warping_function.n_terms * 3 + 1, ) * 1)
self.scale_data = False
if self.scale_data:
Y = self._scale_data(Y)
self.has_uncertain_inputs = False
self.Y_untransformed = Y.copy()
self.predict_in_warped_space = False
likelihood = likelihoods.Gaussian(self.transform_data(),
normalize=normalize_Y)
GP.__init__(self, X, likelihood, kernel, normalize_X=normalize_X)
self._set_params(self._get_params())
def _scale_data(self, Y):
self._Ymax = Y.max()
self._Ymin = Y.min()
return (Y - self._Ymin) / (self._Ymax - self._Ymin) - 0.5
def _unscale_data(self, Y):
return (Y + 0.5) * (self._Ymax - self._Ymin) + self._Ymin
def _set_params(self, x):
self.warping_params = x[:self.warping_function.num_parameters]
Y = self.transform_data()
self.likelihood.set_data(Y)
GP._set_params(self, x[self.warping_function.num_parameters:].copy())
def _get_params(self):
return np.hstack((self.warping_params.flatten().copy(),
GP._get_params(self).copy()))
def _get_param_names(self):
warping_names = self.warping_function._get_param_names()
param_names = GP._get_param_names(self)
return warping_names + param_names
def transform_data(self):
Y = self.warping_function.f(self.Y_untransformed.copy(),
self.warping_params).copy()
return Y
def log_likelihood(self):
ll = GP.log_likelihood(self)
jacobian = self.warping_function.fgrad_y(self.Y_untransformed,
self.warping_params)
return ll + np.log(jacobian).sum()
def _log_likelihood_gradients(self):
ll_grads = GP._log_likelihood_gradients(self)
alpha = np.dot(self.Ki, self.likelihood.Y.flatten())
warping_grads = self.warping_function_gradients(alpha)
warping_grads = np.append(warping_grads[:, :-1].flatten(),
warping_grads[0, -1])
return np.hstack((warping_grads.flatten(), ll_grads.flatten()))
def warping_function_gradients(self, Kiy):
grad_y = self.warping_function.fgrad_y(self.Y_untransformed,
self.warping_params)
grad_y_psi, grad_psi = self.warping_function.fgrad_y_psi(
self.Y_untransformed, self.warping_params, return_covar_chain=True)
djac_dpsi = ((1.0 / grad_y[:, :, None, None]) *
grad_y_psi).sum(axis=0).sum(axis=0)
dquad_dpsi = (Kiy[:, None, None, None] *
grad_psi).sum(axis=0).sum(axis=0)
return -dquad_dpsi + djac_dpsi
def plot_warping(self):
self.warping_function.plot(self.warping_params,
self.Y_untransformed.min(),
self.Y_untransformed.max())
def predict(self, Xnew, which_parts='all', full_cov=False, pred_init=None):
# normalize X values
Xnew = (Xnew.copy() - self._Xoffset) / self._Xscale
mu, var = GP._raw_predict(self,
Xnew,
full_cov=full_cov,
which_parts=which_parts)
# now push through likelihood
mean, var, _025pm, _975pm = self.likelihood.predictive_values(
mu, var, full_cov)
if self.predict_in_warped_space:
mean = self.warping_function.f_inv(mean,
self.warping_params,
y=pred_init)
var = self.warping_function.f_inv(var, self.warping_params)
if self.scale_data:
mean = self._unscale_data(mean)
return mean, var, _025pm, _975pm
class WarpedGP(GP):
def __init__(self, X, Y, kernel=None, warping_function=None, warping_terms=3, normalize_X=False, normalize_Y=False):
if kernel is None:
kernel = kern.rbf(X.shape[1])
if warping_function == None:
self.warping_function = TanhWarpingFunction_d(warping_terms)
self.warping_params = (np.random.randn(self.warping_function.n_terms * 3 + 1,) * 1)
self.scale_data = False
if self.scale_data:
Y = self._scale_data(Y)
self.has_uncertain_inputs = False
self.Y_untransformed = Y.copy()
self.predict_in_warped_space = False
likelihood = likelihoods.Gaussian(self.transform_data(), normalize=normalize_Y)
GP.__init__(self, X, likelihood, kernel, normalize_X=normalize_X)
self._set_params(self._get_params())
def getstate(self):
return GP.getstate(self)
def setstate(self, state):
return GP.setstate(self, state)
def _scale_data(self, Y):
self._Ymax = Y.max()
self._Ymin = Y.min()
return (Y - self._Ymin) / (self._Ymax - self._Ymin) - 0.5
def _unscale_data(self, Y):
return (Y + 0.5) * (self._Ymax - self._Ymin) + self._Ymin
def _set_params(self, x):
self.warping_params = x[:self.warping_function.num_parameters]
Y = self.transform_data()
self.likelihood.set_data(Y)
GP._set_params(self, x[self.warping_function.num_parameters:].copy())
def _get_params(self):
return np.hstack((self.warping_params.flatten().copy(), GP._get_params(self).copy()))
def _get_param_names(self):
warping_names = self.warping_function._get_param_names()
param_names = GP._get_param_names(self)
return warping_names + param_names
def transform_data(self):
Y = self.warping_function.f(self.Y_untransformed.copy(), self.warping_params).copy()
return Y
def log_likelihood(self):
ll = GP.log_likelihood(self)
jacobian = self.warping_function.fgrad_y(self.Y_untransformed, self.warping_params)
return ll + np.log(jacobian).sum()
def _log_likelihood_gradients(self):
ll_grads = GP._log_likelihood_gradients(self)
alpha = np.dot(self.Ki, self.likelihood.Y.flatten())
warping_grads = self.warping_function_gradients(alpha)
warping_grads = np.append(warping_grads[:, :-1].flatten(), warping_grads[0, -1])
return np.hstack((warping_grads.flatten(), ll_grads.flatten()))
def warping_function_gradients(self, Kiy):
grad_y = self.warping_function.fgrad_y(self.Y_untransformed, self.warping_params)
grad_y_psi, grad_psi = self.warping_function.fgrad_y_psi(self.Y_untransformed, self.warping_params,
return_covar_chain=True)
djac_dpsi = ((1.0 / grad_y[:, :, None, None]) * grad_y_psi).sum(axis=0).sum(axis=0)
dquad_dpsi = (Kiy[:, None, None, None] * grad_psi).sum(axis=0).sum(axis=0)
return -dquad_dpsi + djac_dpsi
def plot_warping(self):
self.warping_function.plot(self.warping_params, self.Y_untransformed.min(), self.Y_untransformed.max())
def predict(self, Xnew, which_parts='all', full_cov=False, pred_init=None):
# normalize X values
Xnew = (Xnew.copy() - self._Xoffset) / self._Xscale
mu, var = GP._raw_predict(self, Xnew, full_cov=full_cov, which_parts=which_parts)
# now push through likelihood
mean, var, _025pm, _975pm = self.likelihood.predictive_values(mu, var, full_cov)
if self.predict_in_warped_space:
mean = self.warping_function.f_inv(mean, self.warping_params, y=pred_init)
var = self.warping_function.f_inv(var, self.warping_params)
if self.scale_data:
mean = self._unscale_data(mean)
return mean, var, _025pm, _975pm
class WarpedGP(GP):
def __init__(self,
X,
Y,
kernel=None,
warping_function=None,
warping_terms=3):
if kernel is None:
kernel = kern.RBF(X.shape[1])
if warping_function == None:
self.warping_function = TanhWarpingFunction_d(warping_terms)
self.warping_params = (
np.random.randn(self.warping_function.n_terms * 3 + 1) * 1)
else:
self.warping_function = warping_function
self.scale_data = False
if self.scale_data:
Y = self._scale_data(Y)
#self.has_uncertain_inputs = False
self.Y_untransformed = Y.copy()
self.predict_in_warped_space = True
likelihood = likelihoods.Gaussian()
GP.__init__(self,
X,
self.transform_data(),
likelihood=likelihood,
kernel=kernel)
self.link_parameter(self.warping_function)
def _scale_data(self, Y):
self._Ymax = Y.max()
self._Ymin = Y.min()
return (Y - self._Ymin) / (self._Ymax - self._Ymin) - 0.5
def _unscale_data(self, Y):
return (Y + 0.5) * (self._Ymax - self._Ymin) + self._Ymin
def parameters_changed(self):
self.Y[:] = self.transform_data()
super(WarpedGP, self).parameters_changed()
Kiy = self.posterior.woodbury_vector.flatten()
grad_y = self.warping_function.fgrad_y(self.Y_untransformed)
grad_y_psi, grad_psi = self.warping_function.fgrad_y_psi(
self.Y_untransformed, return_covar_chain=True)
djac_dpsi = ((1.0 / grad_y[:, :, None, None]) *
grad_y_psi).sum(axis=0).sum(axis=0)
dquad_dpsi = (Kiy[:, None, None, None] *
grad_psi).sum(axis=0).sum(axis=0)
warping_grads = -dquad_dpsi + djac_dpsi
self.warping_function.psi.gradient[:] = warping_grads[:, :-1]
self.warping_function.d.gradient[:] = warping_grads[0, -1]
def transform_data(self):
Y = self.warping_function.f(self.Y_untransformed.copy()).copy()
return Y
def log_likelihood(self):
ll = GP.log_likelihood(self)
jacobian = self.warping_function.fgrad_y(self.Y_untransformed)
return ll + np.log(jacobian).sum()
def plot_warping(self):
self.warping_function.plot(self.Y_untransformed.min(),
self.Y_untransformed.max())
def _get_warped_term(self, mean, std, gh_samples, pred_init=None):
arg1 = gh_samples.dot(std.T) * np.sqrt(2)
arg2 = np.ones(shape=gh_samples.shape).dot(mean.T)
return self.warping_function.f_inv(arg1 + arg2, y=pred_init)
def _get_warped_mean(self,
mean,
std,
pred_init=None,
deg_gauss_hermite=100):
"""
Calculate the warped mean by using Gauss-Hermite quadrature.
"""
gh_samples, gh_weights = np.polynomial.hermite.hermgauss(
deg_gauss_hermite)
gh_samples = gh_samples[:, None]
gh_weights = gh_weights[None, :]
return gh_weights.dot(self._get_warped_term(
mean, std, gh_samples)) / np.sqrt(np.pi)
def _get_warped_variance(self,
mean,
std,
pred_init=None,
deg_gauss_hermite=100):
"""
Calculate the warped variance by using Gauss-Hermite quadrature.
"""
gh_samples, gh_weights = np.polynomial.hermite.hermgauss(
deg_gauss_hermite)
gh_samples = gh_samples[:, None]
gh_weights = gh_weights[None, :]
arg1 = gh_weights.dot(
self._get_warped_term(mean, std, gh_samples, pred_init=pred_init)**
2) / np.sqrt(np.pi)
arg2 = self._get_warped_mean(mean,
std,
pred_init=pred_init,
deg_gauss_hermite=deg_gauss_hermite)
return arg1 - (arg2**2)
def predict(self,
Xnew,
which_parts='all',
pred_init=None,
full_cov=False,
Y_metadata=None,
median=False,
deg_gauss_hermite=100):
# normalize X values
# Xnew = (Xnew.copy() - self._Xoffset) / self._Xscale
mu, var = GP._raw_predict(self, Xnew)
# now push through likelihood
mean, var = self.likelihood.predictive_values(mu, var)
if self.predict_in_warped_space:
std = np.sqrt(var)
if median:
wmean = self.warping_function.f_inv(mean, y=pred_init)
else:
wmean = self._get_warped_mean(
mean,
std,
pred_init=pred_init,
deg_gauss_hermite=deg_gauss_hermite).T
wvar = self._get_warped_variance(
mean,
std,
pred_init=pred_init,
deg_gauss_hermite=deg_gauss_hermite).T
else:
wmean = mean
wvar = var
if self.scale_data:
pred = self._unscale_data(pred)
return wmean, wvar
def predict_quantiles(self, X, quantiles=(2.5, 97.5), Y_metadata=None):
"""
Get the predictive quantiles around the prediction at X
:param X: The points at which to make a prediction
:type X: np.ndarray (Xnew x self.input_dim)
:param quantiles: tuple of quantiles, default is (2.5, 97.5) which is the 95% interval
:type quantiles: tuple
:returns: list of quantiles for each X and predictive quantiles for interval combination
:rtype: [np.ndarray (Xnew x self.input_dim), np.ndarray (Xnew x self.input_dim)]
"""
m, v = self._raw_predict(X, full_cov=False)
if self.normalizer is not None:
m, v = self.normalizer.inverse_mean(
m), self.normalizer.inverse_variance(v)
a, b = self.likelihood.predictive_quantiles(m, v, quantiles,
Y_metadata)
#return [a, b]
if not self.predict_in_warped_space:
return [a, b]
#print a.shape
new_a = self.warping_function.f_inv(a)
new_b = self.warping_function.f_inv(b)
return [new_a, new_b]
class WarpedGP(GP):
def __init__(self, X, Y, kernel=None, warping_function=None, warping_terms=3):
if kernel is None:
kernel = kern.RBF(X.shape[1])
if warping_function == None:
self.warping_function = TanhWarpingFunction_d(warping_terms)
self.warping_params = (np.random.randn(self.warping_function.n_terms * 3 + 1,) * 1)
else:
self.warping_function = warping_function
self.scale_data = False
if self.scale_data:
Y = self._scale_data(Y)
self.has_uncertain_inputs = False
self.Y_untransformed = Y.copy()
self.predict_in_warped_space = False
likelihood = likelihoods.Gaussian()
GP.__init__(self, X, self.transform_data(), likelihood=likelihood, kernel=kernel)
self.link_parameter(self.warping_function)
def _scale_data(self, Y):
self._Ymax = Y.max()
self._Ymin = Y.min()
return (Y - self._Ymin) / (self._Ymax - self._Ymin) - 0.5
def _unscale_data(self, Y):
return (Y + 0.5) * (self._Ymax - self._Ymin) + self._Ymin
def parameters_changed(self):
self.Y[:] = self.transform_data()
super(WarpedGP, self).parameters_changed()
Kiy = self.posterior.woodbury_vector.flatten()
grad_y = self.warping_function.fgrad_y(self.Y_untransformed)
grad_y_psi, grad_psi = self.warping_function.fgrad_y_psi(self.Y_untransformed,
return_covar_chain=True)
djac_dpsi = ((1.0 / grad_y[:, :, None, None]) * grad_y_psi).sum(axis=0).sum(axis=0)
dquad_dpsi = (Kiy[:, None, None, None] * grad_psi).sum(axis=0).sum(axis=0)
warping_grads = -dquad_dpsi + djac_dpsi
self.warping_function.psi.gradient[:] = warping_grads[:, :-1]
self.warping_function.d.gradient[:] = warping_grads[0, -1]
def transform_data(self):
Y = self.warping_function.f(self.Y_untransformed.copy()).copy()
return Y
def log_likelihood(self):
ll = GP.log_likelihood(self)
jacobian = self.warping_function.fgrad_y(self.Y_untransformed)
return ll + np.log(jacobian).sum()
def plot_warping(self):
self.warping_function.plot(self.Y_untransformed.min(), self.Y_untransformed.max())
def predict(self, Xnew, which_parts='all', pred_init=None):
# normalize X values
# Xnew = (Xnew.copy() - self._Xoffset) / self._Xscale
mu, var = GP._raw_predict(self, Xnew)
# now push through likelihood
mean, var = self.likelihood.predictive_values(mu, var)
if self.predict_in_warped_space:
mean = self.warping_function.f_inv(mean, y=pred_init)
var = self.warping_function.f_inv(var)
if self.scale_data:
mean = self._unscale_data(mean)
return mean, var
