# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
# Licensed under the BSD 3-clause license (see LICENSE.txt)
import numpy as np
#from ..util.warping_functions import *
from ..core import GP
from .. import likelihoods
from paramz import ObsAr
#from GPy.util.warping_functions import TanhFunction
from ..util.warping_functions import TanhFunction
from GPy import kern
[docs]class WarpedGP(GP):
"""
This defines a GP Regression model that applies a
warping function to the output.
"""
def __init__(self, X, Y, kernel=None, warping_function=None, warping_terms=3, normalizer=False):
if kernel is None:
kernel = kern.RBF(X.shape[1])
if warping_function == None:
self.warping_function = TanhFunction(warping_terms)
self.warping_params = (np.random.randn(self.warping_function.n_terms * 3 + 1) * 1)
else:
self.warping_function = warping_function
likelihood = likelihoods.Gaussian()
super(WarpedGP, self).__init__(X, Y.copy(), likelihood=likelihood, kernel=kernel, normalizer=normalizer)
self.Y_normalized = self.Y_normalized.copy()
self.Y_untransformed = self.Y_normalized.copy()
self.predict_in_warped_space = True
self.link_parameter(self.warping_function)
[docs] def set_XY(self, X=None, Y=None):
super(WarpedGP, self).set_XY(X, Y)
self.Y_untransformed = self.Y_normalized.copy()
self.update_model(True)
[docs] def parameters_changed(self):
"""
Notice that we update the warping function gradients here.
"""
self.Y_normalized[:] = self.transform_data()
super(WarpedGP, self).parameters_changed()
Kiy = self.posterior.woodbury_vector.flatten()
self.warping_function.update_grads(self.Y_untransformed, Kiy)
[docs] def log_likelihood(self):
"""
Notice we add the jacobian of the warping function here.
"""
ll = GP.log_likelihood(self)
jacobian = self.warping_function.fgrad_y(self.Y_untransformed)
return ll + np.log(jacobian).sum()
[docs] 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=20):
"""
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=20):
"""
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)
[docs] def predict(self, Xnew, kern=None, pred_init=None, Y_metadata=None,
median=False, deg_gauss_hermite=20, likelihood=None):
"""
Prediction results depend on:
- The value of the self.predict_in_warped_space flag
- The median flag passed as argument
The likelihood keyword is never used, it is just to follow the plotting API.
"""
#mu, var = GP._raw_predict(self, Xnew)
# now push through likelihood
#mean, var = self.likelihood.predictive_values(mu, var)
mean, var = super(WarpedGP, self).predict(Xnew, kern=kern, full_cov=False, likelihood=likelihood)
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
return wmean, wvar
[docs] def predict_quantiles(self, X, quantiles=(2.5, 97.5), Y_metadata=None, likelihood=None, kern=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)]
"""
qs = super(WarpedGP, self).predict_quantiles(X, quantiles, Y_metadata=Y_metadata, likelihood=likelihood, kern=kern)
if self.predict_in_warped_space:
return [self.warping_function.f_inv(q) for q in qs]
return qs
#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)
#if not self.predict_in_warped_space:
# return [a, b]
#new_a = self.warping_function.f_inv(a)
#new_b = self.warping_function.f_inv(b)
#return [new_a, new_b]
[docs] def log_predictive_density(self, x_test, y_test, Y_metadata=None):
"""
Calculation of the log predictive density. Notice we add
the jacobian of the warping function here.
.. math:
p(y_{*}|D) = p(y_{*}|f_{*})p(f_{*}|\mu_{*}\\sigma^{2}_{*})
:param x_test: test locations (x_{*})
:type x_test: (Nx1) array
:param y_test: test observations (y_{*})
:type y_test: (Nx1) array
:param Y_metadata: metadata associated with the test points
"""
mu_star, var_star = self._raw_predict(x_test)
fy = self.warping_function.f(y_test)
ll_lpd = self.likelihood.log_predictive_density(fy, mu_star, var_star, Y_metadata=Y_metadata)
return ll_lpd + np.log(self.warping_function.fgrad_y(y_test))
if __name__ == '__main__':
X = np.random.randn(100, 1)
Y = np.sin(X) + np.random.randn(100, 1)*0.05
m = WarpedGP(X, Y)