# 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 GPy.util.warping_functions import TanhWarpingFunction_d from GPy import kern 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, var, gh_samples, pred_init=None): arg1 = gh_samples.dot(var.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, var, 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, var, gh_samples)) / np.sqrt(np.pi) def _get_warped_variance(self, mean, var, pred_init=None, deg_gauss_hermite=100): 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, var, gh_samples, pred_init=pred_init) ** 2) / np.sqrt(np.pi) arg2 = self._get_warped_mean(mean, var, 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: if median: #print 'MEDIAN!' wmean = self.warping_function.f_inv(mean, y=pred_init) else: #print 'MEAN!' wmean = self._get_warped_mean(mean, var, pred_init=pred_init, deg_gauss_hermite=deg_gauss_hermite).T #var = self.warping_function.f_inv(var) wvar = self._get_warped_variance(mean, var, pred_init=pred_init, deg_gauss_hermite=deg_gauss_hermite).T else: wmean = mean #wvar = var wvar = self.warping_function.f_inv(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) #print a.shape new_a = self.warping_function.f_inv(a) new_b = self.warping_function.f_inv(b) return [new_a, new_b] #return self.likelihood.predictive_quantiles(m, v, quantiles, Y_metadata) if __name__ == '__main__': X = np.random.randn(100, 1) Y = np.sin(X) + np.random.randn(100, 1)*0.05 m = WarpedGP(X, Y)