mirror of
https://github.com/SheffieldML/GPy.git
synced 2026-05-09 12:02:38 +02:00
Merge branch 'wgps_improvements' of https://github.com/beckdaniel/GPy into beckdaniel-wgps_improvements
This commit is contained in:
mzwiessele
commit
9be51df4f1
5 changed files with 261 additions and 242 deletions
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@ -550,3 +550,34 @@ def parametric_mean_function(max_iters=100, optimize=True, plot=True):
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return m
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def warped_gp_cubic_sine(max_iters=100):
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"""
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A test replicating the cubic sine regression problem from
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Snelson's paper.
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"""
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X = (2 * np.pi) * np.random.random(151) - np.pi
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Y = np.sin(X) + np.random.normal(0,0.2,151)
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Y = np.array([np.power(abs(y),float(1)/3) * (1,-1)[y<0] for y in Y])
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X = X[:, None]
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Y = Y[:, None]
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warp_k = GPy.kern.RBF(1)
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warp_f = GPy.util.warping_functions.TanhFunction(n_terms=2)
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warp_m = GPy.models.WarpedGP(X, Y, kernel=warp_k, warping_function=warp_f)
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warp_m['.*\.d'].constrain_fixed(1.0)
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m = GPy.models.GPRegression(X, Y)
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m.optimize_restarts(parallel=False, robust=True, num_restarts=5, max_iters=max_iters)
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warp_m.optimize_restarts(parallel=False, robust=True, num_restarts=5, max_iters=max_iters)
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#m.optimize(max_iters=max_iters)
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#warp_m.optimize(max_iters=max_iters)
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print(warp_m)
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print(warp_m['.*warp.*'])
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warp_m.predict_in_warped_space = False
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warp_m.plot(title="Warped GP - Latent space")
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warp_m.predict_in_warped_space = True
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warp_m.plot(title="Warped GP - Warped space")
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m.plot(title="Standard GP")
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warp_m.plot_warping()
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pb.show()
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@ -2,24 +2,27 @@
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# Licensed under the BSD 3-clause license (see LICENSE.txt)
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import numpy as np
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from ..util.warping_functions import *
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#from ..util.warping_functions import *
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from ..core import GP
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from .. import likelihoods
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from GPy.util.warping_functions import TanhWarpingFunction_d
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from paramz import ObsAr
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#from GPy.util.warping_functions import TanhFunction
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from ..util.warping_functions import TanhFunction
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from GPy import kern
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class WarpedGP(GP):
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"""
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This defines a GP Regression model that applies a
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warping function to the output.
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"""
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def __init__(self, X, Y, kernel=None, warping_function=None, warping_terms=3):
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if kernel is None:
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kernel = kern.RBF(X.shape[1])
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if warping_function == None:
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self.warping_function = TanhWarpingFunction_d(warping_terms)
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self.warping_function = TanhFunction(warping_terms)
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self.warping_params = (np.random.randn(self.warping_function.n_terms * 3 + 1) * 1)
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else:
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self.warping_function = warping_function
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self.scale_data = False
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if self.scale_data:
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Y = self._scale_data(Y)
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@ -27,10 +30,13 @@ class WarpedGP(GP):
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self.Y_untransformed = Y.copy()
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self.predict_in_warped_space = True
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likelihood = likelihoods.Gaussian()
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GP.__init__(self, X, self.transform_data(), likelihood=likelihood, kernel=kernel)
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self.link_parameter(self.warping_function)
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def set_XY(self, X=None, Y=None):
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self.Y_untransformed = Y.copy()
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GP.set_XY(self, X, self.transform_data())
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def _scale_data(self, Y):
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self._Ymax = Y.max()
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self._Ymin = Y.min()
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@ -40,27 +46,22 @@ class WarpedGP(GP):
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return (Y + 0.5) * (self._Ymax - self._Ymin) + self._Ymin
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def parameters_changed(self):
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"""
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Notice that we update the warping function gradients here.
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"""
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self.Y[:] = self.transform_data()
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super(WarpedGP, self).parameters_changed()
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Kiy = self.posterior.woodbury_vector.flatten()
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grad_y = self.warping_function.fgrad_y(self.Y_untransformed)
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grad_y_psi, grad_psi = self.warping_function.fgrad_y_psi(self.Y_untransformed,
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return_covar_chain=True)
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djac_dpsi = ((1.0 / grad_y[:, :, None, None]) * grad_y_psi).sum(axis=0).sum(axis=0)
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dquad_dpsi = (Kiy[:, None, None, None] * grad_psi).sum(axis=0).sum(axis=0)
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warping_grads = -dquad_dpsi + djac_dpsi
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self.warping_function.psi.gradient[:] = warping_grads[:, :-1]
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self.warping_function.d.gradient[:] = warping_grads[0, -1]
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self.warping_function.update_grads(self.Y_untransformed, Kiy)
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def transform_data(self):
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Y = self.warping_function.f(self.Y_untransformed.copy()).copy()
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return Y
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def log_likelihood(self):
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"""
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Notice we add the jacobian of the warping function here.
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"""
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ll = GP.log_likelihood(self)
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jacobian = self.warping_function.fgrad_y(self.Y_untransformed)
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return ll + np.log(jacobian).sum()
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@ -73,22 +74,22 @@ class WarpedGP(GP):
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arg2 = np.ones(shape=gh_samples.shape).dot(mean.T)
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return self.warping_function.f_inv(arg1 + arg2, y=pred_init)
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def _get_warped_mean(self, mean, std, pred_init=None, deg_gauss_hermite=100):
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def _get_warped_mean(self, mean, std, pred_init=None, deg_gauss_hermite=20):
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"""
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Calculate the warped mean by using Gauss-Hermite quadrature.
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"""
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gh_samples, gh_weights = np.polynomial.hermite.hermgauss(deg_gauss_hermite)
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gh_samples = gh_samples[:,None]
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gh_weights = gh_weights[None,:]
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gh_samples = gh_samples[:, None]
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gh_weights = gh_weights[None, :]
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return gh_weights.dot(self._get_warped_term(mean, std, gh_samples)) / np.sqrt(np.pi)
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def _get_warped_variance(self, mean, std, pred_init=None, deg_gauss_hermite=100):
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def _get_warped_variance(self, mean, std, pred_init=None, deg_gauss_hermite=20):
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"""
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Calculate the warped variance by using Gauss-Hermite quadrature.
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"""
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gh_samples, gh_weights = np.polynomial.hermite.hermgauss(deg_gauss_hermite)
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gh_samples = gh_samples[:,None]
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gh_weights = gh_weights[None,:]
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gh_samples = gh_samples[:, None]
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gh_weights = gh_weights[None, :]
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arg1 = gh_weights.dot(self._get_warped_term(mean, std, gh_samples,
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pred_init=pred_init) ** 2) / np.sqrt(np.pi)
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arg2 = self._get_warped_mean(mean, std, pred_init=pred_init,
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@ -96,11 +97,14 @@ class WarpedGP(GP):
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return arg1 - (arg2 ** 2)
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def predict(self, Xnew, which_parts='all', pred_init=None, full_cov=False, Y_metadata=None,
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median=False, deg_gauss_hermite=100):
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# normalize X values
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# Xnew = (Xnew.copy() - self._Xoffset) / self._Xscale
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median=False, deg_gauss_hermite=20, likelihood=None):
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"""
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Prediction results depend on:
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- The value of the self.predict_in_warped_space flag
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- The median flag passed as argument
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The likelihood keyword is never used, it is just to follow the plotting API.
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"""
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mu, var = GP._raw_predict(self, Xnew)
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# now push through likelihood
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mean, var = self.likelihood.predictive_values(mu, var)
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@ -116,13 +120,11 @@ class WarpedGP(GP):
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else:
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wmean = mean
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wvar = var
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if self.scale_data:
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pred = self._unscale_data(pred)
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return wmean, wvar
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def predict_quantiles(self, X, quantiles=(2.5, 97.5), Y_metadata=None):
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def predict_quantiles(self, X, quantiles=(2.5, 97.5), Y_metadata=None, likelihood=None, median=False):
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"""
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Get the predictive quantiles around the prediction at X
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@ -137,15 +139,30 @@ class WarpedGP(GP):
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if self.normalizer is not None:
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m, v = self.normalizer.inverse_mean(m), self.normalizer.inverse_variance(v)
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a, b = self.likelihood.predictive_quantiles(m, v, quantiles, Y_metadata)
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#return [a, b]
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if not self.predict_in_warped_space:
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return [a, b]
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#print a.shape
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new_a = self.warping_function.f_inv(a)
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new_b = self.warping_function.f_inv(b)
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return [new_a, new_b]
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#return self.likelihood.predictive_quantiles(m, v, quantiles, Y_metadata)
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def log_predictive_density(self, x_test, y_test, Y_metadata=None):
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"""
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Calculation of the log predictive density. Notice we add
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the jacobian of the warping function here.
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.. math:
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p(y_{*}|D) = p(y_{*}|f_{*})p(f_{*}|\mu_{*}\\sigma^{2}_{*})
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:param x_test: test locations (x_{*})
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:type x_test: (Nx1) array
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:param y_test: test observations (y_{*})
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:type y_test: (Nx1) array
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:param Y_metadata: metadata associated with the test points
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"""
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mu_star, var_star = self._raw_predict(x_test)
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fy = self.warping_function.f(y_test)
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ll_lpd = self.likelihood.log_predictive_density(fy, mu_star, var_star, Y_metadata=Y_metadata)
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return ll_lpd + np.log(self.warping_function.fgrad_y(y_test))
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if __name__ == '__main__':
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@ -31,6 +31,7 @@
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import numpy as np
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from scipy import sparse
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import itertools
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from ...models import WarpedGP
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def in_ipynb():
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try:
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@ -73,6 +74,9 @@ def helper_predict_with_model(self, Xgrid, plot_raw, apply_link, percentiles, wh
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if 'output_index' not in predict_kw['Y_metadata']:
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predict_kw['Y_metadata']['output_index'] = Xgrid[:,-1:].astype(np.int)
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if isinstance(self, WarpedGP) and self.predict_in_warped_space:
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predict_kw['median'] = True
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mu, _ = self.predict(Xgrid, **predict_kw)
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if percentiles is not None:
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@ -295,6 +299,8 @@ def get_x_y_var(model):
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Y = model.Y.values
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except AttributeError:
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Y = model.Y
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if isinstance(model, WarpedGP) and model.predict_in_warped_space:
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Y = model.Y_untransformed
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if sparse.issparse(Y): Y = Y.todense().view(np.ndarray)
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return X, X_variance, Y
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@ -381,4 +387,4 @@ def x_frame2D(X,plot_limits=None,resolution=None):
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resolution = resolution or 50
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xx, yy = np.mgrid[xmin[0]:xmax[0]:1j*resolution,xmin[1]:xmax[1]:1j*resolution]
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Xnew = np.c_[xx.flat, yy.flat]
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return Xnew, xx, yy, xmin, xmax
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return Xnew, xx, yy, xmin, xmax
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@ -361,51 +361,74 @@ class MiscTests(unittest.TestCase):
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preds = m.predict(self.X)
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warp_k = GPy.kern.RBF(1)
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warp_f = GPy.util.warping_functions.IdentityFunction()
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warp_m = GPy.models.WarpedGP(self.X, self.Y, kernel=warp_k, warping_function=warp_f)
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warp_f = GPy.util.warping_functions.IdentityFunction(closed_inverse=False)
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warp_m = GPy.models.WarpedGP(self.X, self.Y, kernel=warp_k,
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warping_function=warp_f)
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warp_m.optimize()
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warp_preds = warp_m.predict(self.X)
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np.testing.assert_almost_equal(preds, warp_preds)
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warp_k_exact = GPy.kern.RBF(1)
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warp_f_exact = GPy.util.warping_functions.IdentityFunction()
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warp_m_exact = GPy.models.WarpedGP(self.X, self.Y, kernel=warp_k_exact,
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warping_function=warp_f_exact)
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warp_m_exact.optimize()
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warp_preds_exact = warp_m_exact.predict(self.X)
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np.testing.assert_almost_equal(preds, warp_preds, decimal=4)
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np.testing.assert_almost_equal(preds, warp_preds_exact, decimal=4)
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@unittest.skip('Comment this to plot the modified sine function')
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def test_warped_gp_sine(self):
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def test_warped_gp_log(self):
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"""
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A test replicating the sine regression problem from
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Snelson's paper.
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A WarpedGP with the log warping function should be
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equal to a standard GP with log labels.
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Note that we predict the median here.
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"""
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k = GPy.kern.RBF(1)
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Y = np.abs(self.Y)
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logY = np.log(Y)
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m = GPy.models.GPRegression(self.X, logY, kernel=k)
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m.optimize()
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preds = m.predict(self.X)[0]
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warp_k = GPy.kern.RBF(1)
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warp_f = GPy.util.warping_functions.LogFunction(closed_inverse=False)
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warp_m = GPy.models.WarpedGP(self.X, Y, kernel=warp_k,
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warping_function=warp_f)
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warp_m.optimize()
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warp_preds = warp_m.predict(self.X, median=True)[0]
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warp_k_exact = GPy.kern.RBF(1)
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warp_f_exact = GPy.util.warping_functions.LogFunction()
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warp_m_exact = GPy.models.WarpedGP(self.X, Y, kernel=warp_k_exact,
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warping_function=warp_f_exact)
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warp_m_exact.optimize(messages=True)
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warp_preds_exact = warp_m_exact.predict(self.X, median=True)[0]
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np.testing.assert_almost_equal(np.exp(preds), warp_preds, decimal=4)
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np.testing.assert_almost_equal(np.exp(preds), warp_preds_exact, decimal=4)
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def test_warped_gp_cubic_sine(self, max_iters=100):
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"""
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A test replicating the cubic sine regression problem from
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Snelson's paper. This test doesn't have any assertions, it's
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just to ensure coverage of the tanh warping function code.
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"""
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X = (2 * np.pi) * np.random.random(151) - np.pi
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Y = np.sin(X) + np.random.normal(0,0.1,151)
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Y = np.exp(Y) - 5
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#Y = np.array([np.power(abs(y),float(1)/3) * (1,-1)[y<0] for y in Y]) + 0
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Y = np.sin(X) + np.random.normal(0,0.2,151)
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Y = np.array([np.power(abs(y),float(1)/3) * (1,-1)[y<0] for y in Y])
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X = X[:, None]
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Y = Y[:, None]
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#np.seterr(over='raise')
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import matplotlib.pyplot as plt
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warp_k = GPy.kern.RBF(1)
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warp_f = GPy.util.warping_functions.TanhWarpingFunction_d(n_terms=2)
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warp_m = GPy.models.WarpedGP(X[:, None], Y[:, None], kernel=warp_k, warping_function=warp_f)
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#warp_m['.*variance.*'].constrain_fixed(0.25)
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#warp_m['.*lengthscale.*'].constrain_fixed(1)
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#warp_m['warp_tanh.d'].constrain_fixed(1)
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#warp_m.randomize()
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#warp_m['.*warp_tanh.psi*'][:,0:2].constrain_bounded(0,100)
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#warp_m['.*warp_tanh.psi*'][:,0:1].constrain_fixed(1)
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#print(warp_m.checkgrad())
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#warp_m.plot()
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#plt.show()
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warp_m.optimize_restarts(parallel=True, robust=True)
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#print(warp_m.checkgrad())
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print(warp_m)
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print(warp_m['.*warp.*'])
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warp_m = GPy.models.WarpedGP(X, Y)#, kernel=warp_k)#, warping_function=warp_f)
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warp_m['.*\.d'].constrain_fixed(1.0)
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warp_m.optimize_restarts(parallel=False, robust=False, num_restarts=5,
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max_iters=max_iters)
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warp_m.predict(X)
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warp_m.predict_quantiles(X)
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warp_m.log_predictive_density(X, Y)
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warp_m.predict_in_warped_space = False
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warp_m.plot()
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warp_m.predict_in_warped_space = True
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warp_m.plot()
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warp_f.plot(X.min()-10, X.max()+10)
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plt.show()
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warp_m.predict(X)
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warp_m.predict_quantiles(X)
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class GradientTests(np.testing.TestCase):
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@ -4,6 +4,7 @@
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import numpy as np
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from ..core.parameterization import Parameterized, Param
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from paramz.transformations import Logexp
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import sys
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class WarpingFunction(Parameterized):
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@ -14,6 +15,7 @@ class WarpingFunction(Parameterized):
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def __init__(self, name):
|
||||
super(WarpingFunction, self).__init__(name=name)
|
||||
self.rate = 0.1
|
||||
|
||||
def f(self, y, psi):
|
||||
"""function transformation
|
||||
|
|
@ -29,15 +31,35 @@ class WarpingFunction(Parameterized):
|
|||
"""gradient of f w.r.t to y"""
|
||||
raise NotImplementedError
|
||||
|
||||
def f_inv(self, z, psi):
|
||||
"""inverse function transformation"""
|
||||
raise NotImplementedError
|
||||
def f_inv(self, z, max_iterations=100, y=None):
|
||||
"""
|
||||
Calculate the numerical inverse of f. This should be
|
||||
overwritten for specific warping functions where the
|
||||
inverse can be found in closed form.
|
||||
|
||||
:param max_iterations: maximum number of N.R. iterations
|
||||
"""
|
||||
|
||||
z = z.copy()
|
||||
y = np.ones_like(z)
|
||||
|
||||
it = 0
|
||||
update = np.inf
|
||||
while np.abs(update).sum() > 1e-10 and it < max_iterations:
|
||||
fy = self.f(y)
|
||||
fgrady = self.fgrad_y(y)
|
||||
update = (fy - z) / fgrady
|
||||
y -= self.rate * update
|
||||
it += 1
|
||||
if it == max_iterations:
|
||||
print("WARNING!!! Maximum number of iterations reached in f_inv ")
|
||||
print("Sum of roots: %.4f" % np.sum(fy - z))
|
||||
return y
|
||||
|
||||
def _get_param_names(self):
|
||||
raise NotImplementedError
|
||||
|
||||
def plot(self, xmin, xmax):
|
||||
psi = self.psi
|
||||
y = np.arange(xmin, xmax, 0.01)
|
||||
f_y = self.f(y)
|
||||
from matplotlib import pyplot as plt
|
||||
|
|
@ -49,183 +71,59 @@ class WarpingFunction(Parameterized):
|
|||
plt.show()
|
||||
|
||||
|
||||
class TanhWarpingFunction(WarpingFunction):
|
||||
|
||||
def __init__(self, n_terms=3):
|
||||
"""n_terms specifies the number of tanh terms to be used"""
|
||||
self.n_terms = n_terms
|
||||
self.num_parameters = 3 * self.n_terms
|
||||
super(TanhWarpingFunction, self).__init__(name='warp_tanh')
|
||||
|
||||
def f(self, y, psi):
|
||||
class TanhFunction(WarpingFunction):
|
||||
"""
|
||||
This is the function proposed in Snelson et al.:
|
||||
A sum of tanh functions with linear trends outside
|
||||
the range. Notice the term 'd', which scales the
|
||||
linear trend.
|
||||
"""
|
||||
def __init__(self, n_terms=3, initial_y=None):
|
||||
"""
|
||||
transform y with f using parameter vector psi
|
||||
psi = [[a,b,c]]
|
||||
::math::`f = \\sum_{terms} a * tanh(b*(y+c))`
|
||||
n_terms specifies the number of tanh terms to be used
|
||||
"""
|
||||
#1. check that number of params is consistent
|
||||
assert psi.shape[0] == self.n_terms, 'inconsistent parameter dimensions'
|
||||
assert psi.shape[1] == 3, 'inconsistent parameter dimensions'
|
||||
|
||||
#2. exponentiate the a and b (positive!)
|
||||
mpsi = psi.copy()
|
||||
|
||||
#3. transform data
|
||||
z = y.copy()
|
||||
for i in range(len(mpsi)):
|
||||
a,b,c = mpsi[i]
|
||||
z += a*np.tanh(b*(y+c))
|
||||
return z
|
||||
|
||||
def f_inv(self, y, psi, iterations=10):
|
||||
"""
|
||||
calculate the numerical inverse of f
|
||||
:param iterations: number of N.R. iterations
|
||||
"""
|
||||
|
||||
y = y.copy()
|
||||
z = np.ones_like(y)
|
||||
for i in range(iterations):
|
||||
z -= (self.f(z, psi) - y)/self.fgrad_y(z,psi)
|
||||
return z
|
||||
|
||||
def fgrad_y(self, y, psi, return_precalc=False):
|
||||
"""
|
||||
gradient of f w.r.t to y ([N x 1])
|
||||
returns: Nx1 vector of derivatives, unless return_precalc is true,
|
||||
then it also returns the precomputed stuff
|
||||
"""
|
||||
|
||||
mpsi = psi.copy()
|
||||
|
||||
# vectorized version
|
||||
|
||||
# S = (mpsi[:,1]*(y + mpsi[:,2])).T
|
||||
S = (mpsi[:,1]*(y[:,:,None] + mpsi[:,2])).T
|
||||
R = np.tanh(S)
|
||||
D = 1-R**2
|
||||
|
||||
# GRAD = (1+(mpsi[:,0:1]*mpsi[:,1:2]*D).sum(axis=0))[:,np.newaxis]
|
||||
GRAD = (1+(mpsi[:,0:1][:,:,None]*mpsi[:,1:2][:,:,None]*D).sum(axis=0)).T
|
||||
|
||||
if return_precalc:
|
||||
# return GRAD,S.sum(axis=1),R.sum(axis=1),D.sum(axis=1)
|
||||
return GRAD, S, R, D
|
||||
|
||||
return GRAD
|
||||
|
||||
def fgrad_y_psi(self, y, psi, return_covar_chain=False):
|
||||
"""
|
||||
gradient of f w.r.t to y and psi
|
||||
returns: NxIx3 tensor of partial derivatives
|
||||
"""
|
||||
|
||||
# 1. exponentiate the a and b (positive!)
|
||||
mpsi = psi.copy()
|
||||
w, s, r, d = self.fgrad_y(y, psi, return_precalc = True)
|
||||
|
||||
gradients = np.zeros((y.shape[0], y.shape[1], len(mpsi), 3))
|
||||
for i in range(len(mpsi)):
|
||||
a,b,c = mpsi[i]
|
||||
gradients[:,:,i,0] = (b*(1.0/np.cosh(s[i]))**2).T
|
||||
gradients[:,:,i,1] = a*(d[i] - 2.0*s[i]*r[i]*(1.0/np.cosh(s[i]))**2).T
|
||||
gradients[:,:,i,2] = (-2.0*a*(b**2)*r[i]*((1.0/np.cosh(s[i]))**2)).T
|
||||
|
||||
if return_covar_chain:
|
||||
covar_grad_chain = np.zeros((y.shape[0], y.shape[1], len(mpsi), 3))
|
||||
|
||||
for i in range(len(mpsi)):
|
||||
a,b,c = mpsi[i]
|
||||
covar_grad_chain[:, :, i, 0] = (r[i]).T
|
||||
covar_grad_chain[:, :, i, 1] = (a*(y + c) * ((1.0/np.cosh(s[i]))**2).T)
|
||||
covar_grad_chain[:, :, i, 2] = a*b*((1.0/np.cosh(s[i]))**2).T
|
||||
|
||||
return gradients, covar_grad_chain
|
||||
|
||||
return gradients
|
||||
|
||||
def _get_param_names(self):
|
||||
variables = ['a', 'b', 'c']
|
||||
names = sum([['warp_tanh_%s_t%i' % (variables[n],q) for n in range(3)] for q in range(self.n_terms)],[])
|
||||
return names
|
||||
|
||||
|
||||
class TanhWarpingFunction_d(WarpingFunction):
|
||||
|
||||
def __init__(self, n_terms=3):
|
||||
"""n_terms specifies the number of tanh terms to be used"""
|
||||
self.n_terms = n_terms
|
||||
self.num_parameters = 3 * self.n_terms + 1
|
||||
self.psi = np.ones((self.n_terms, 3))
|
||||
|
||||
super(TanhWarpingFunction_d, self).__init__(name='warp_tanh')
|
||||
super(TanhFunction, self).__init__(name='warp_tanh')
|
||||
self.psi = Param('psi', self.psi)
|
||||
self.psi[:, :2].constrain_positive()
|
||||
|
||||
self.d = Param('%s' % ('d'), 1.0, Logexp())
|
||||
self.link_parameter(self.psi)
|
||||
self.link_parameter(self.d)
|
||||
self.initial_y = initial_y
|
||||
|
||||
def f(self, y):
|
||||
"""
|
||||
Transform y with f using parameter vector psi
|
||||
psi = [[a,b,c]]
|
||||
|
||||
:math:`f = \\sum_{terms} a * tanh(b*(y+c))`
|
||||
:math:`f = (y * d) + \\sum_{terms} a * tanh(b *(y + c))`
|
||||
"""
|
||||
#1. check that number of params is consistent
|
||||
# assert psi.shape[0] == self.n_terms, 'inconsistent parameter dimensions'
|
||||
# assert psi.shape[1] == 4, 'inconsistent parameter dimensions'
|
||||
|
||||
d = self.d
|
||||
mpsi = self.psi
|
||||
|
||||
#3. transform data
|
||||
z = d*y.copy()
|
||||
z = d * y.copy()
|
||||
for i in range(len(mpsi)):
|
||||
a,b,c = mpsi[i]
|
||||
z += a*np.tanh(b*(y+c))
|
||||
a, b, c = mpsi[i]
|
||||
z += a * np.tanh(b * (y + c))
|
||||
return z
|
||||
|
||||
def f_inv(self, z, max_iterations=1000, y=None):
|
||||
"""
|
||||
calculate the numerical inverse of f
|
||||
|
||||
:param max_iterations: maximum number of N.R. iterations
|
||||
"""
|
||||
|
||||
z = z.copy()
|
||||
if y is None:
|
||||
y = np.ones_like(z)
|
||||
|
||||
it = 0
|
||||
update = np.inf
|
||||
|
||||
while it == 0 or (np.abs(update).sum() > 1e-10 and it < max_iterations):
|
||||
fy = self.f(y)
|
||||
fgrady = self.fgrad_y(y)
|
||||
update = (fy - z)/fgrady
|
||||
y -= update
|
||||
it += 1
|
||||
if it == max_iterations:
|
||||
print("WARNING!!! Maximum number of iterations reached in f_inv ")
|
||||
return y
|
||||
|
||||
def fgrad_y(self, y, return_precalc=False):
|
||||
"""
|
||||
gradient of f w.r.t to y ([N x 1])
|
||||
|
||||
:returns: Nx1 vector of derivatives, unless return_precalc is true, then it also returns the precomputed stuff
|
||||
:returns: Nx1 vector of derivatives, unless return_precalc is true,
|
||||
then it also returns the precomputed stuff
|
||||
"""
|
||||
d = self.d
|
||||
mpsi = self.psi
|
||||
|
||||
# vectorized version
|
||||
S = (mpsi[:,1]*(y[:,:,None] + mpsi[:,2])).T
|
||||
S = (mpsi[:,1] * (y[:,:,None] + mpsi[:,2])).T
|
||||
R = np.tanh(S)
|
||||
D = 1-R**2
|
||||
D = 1 - (R ** 2)
|
||||
|
||||
GRAD = (d + (mpsi[:,0:1][:,:,None]*mpsi[:,1:2][:,:,None]*D).sum(axis=0)).T
|
||||
GRAD = (d + (mpsi[:,0:1][:,:,None] * mpsi[:,1:2][:,:,None] * D).sum(axis=0)).T
|
||||
|
||||
if return_precalc:
|
||||
return GRAD, S, R, D
|
||||
|
|
@ -244,45 +142,86 @@ class TanhWarpingFunction_d(WarpingFunction):
|
|||
gradients = np.zeros((y.shape[0], y.shape[1], len(mpsi), 4))
|
||||
for i in range(len(mpsi)):
|
||||
a,b,c = mpsi[i]
|
||||
gradients[:,:,i,0] = (b*(1.0/np.cosh(s[i]))**2).T
|
||||
gradients[:,:,i,1] = a*(d[i] - 2.0*s[i]*r[i]*(1.0/np.cosh(s[i]))**2).T
|
||||
gradients[:,:,i,2] = (-2.0*a*(b**2)*r[i]*((1.0/np.cosh(s[i]))**2)).T
|
||||
gradients[:,:,0,3] = 1.0
|
||||
gradients[:, :, i, 0] = (b * (1.0/np.cosh(s[i])) ** 2).T
|
||||
gradients[:, :, i, 1] = a * (d[i] - 2.0 * s[i] * r[i] * (1.0/np.cosh(s[i])) ** 2).T
|
||||
gradients[:, :, i, 2] = (-2.0 * a * (b ** 2) * r[i] * ((1.0 / np.cosh(s[i])) ** 2)).T
|
||||
gradients[:, :, 0, 3] = 1.0
|
||||
|
||||
if return_covar_chain:
|
||||
covar_grad_chain = np.zeros((y.shape[0], y.shape[1], len(mpsi), 4))
|
||||
|
||||
for i in range(len(mpsi)):
|
||||
a,b,c = mpsi[i]
|
||||
covar_grad_chain[:, :, i, 0] = (r[i]).T
|
||||
covar_grad_chain[:, :, i, 1] = (a*(y + c) * ((1.0/np.cosh(s[i]))**2).T)
|
||||
covar_grad_chain[:, :, i, 2] = a*b*((1.0/np.cosh(s[i]))**2).T
|
||||
covar_grad_chain[:, :, i, 1] = (a * (y + c) * ((1.0 / np.cosh(s[i])) ** 2).T)
|
||||
covar_grad_chain[:, :, i, 2] = a * b * ((1.0 / np.cosh(s[i])) ** 2).T
|
||||
covar_grad_chain[:, :, 0, 3] = y
|
||||
|
||||
return gradients, covar_grad_chain
|
||||
|
||||
return gradients
|
||||
|
||||
def _get_param_names(self):
|
||||
variables = ['a', 'b', 'c', 'd']
|
||||
names = sum([['warp_tanh_%s_t%i' % (variables[n],q) for n in range(3)] for q in range(self.n_terms)],[])
|
||||
names.append('warp_tanh_d')
|
||||
names = sum([['warp_tanh_%s_t%i' % (variables[n],q) for n in range(3)]
|
||||
for q in range(self.n_terms)],[])
|
||||
names.append('warp_tanh')
|
||||
return names
|
||||
|
||||
def update_grads(self, Y_untransformed, Kiy):
|
||||
grad_y = self.fgrad_y(Y_untransformed)
|
||||
grad_y_psi, grad_psi = self.fgrad_y_psi(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.psi.gradient[:] = warping_grads[:, :-1]
|
||||
self.d.gradient[:] = warping_grads[0, -1]
|
||||
|
||||
|
||||
class LogFunction(WarpingFunction):
|
||||
"""
|
||||
Easy wrapper for applying a fixed log warping function to
|
||||
positive-only values.
|
||||
The closed_inverse flag should only be set to False for
|
||||
debugging and testing purposes.
|
||||
"""
|
||||
def __init__(self, closed_inverse=True):
|
||||
self.num_parameters = 0
|
||||
super(LogFunction, self).__init__(name='log')
|
||||
if closed_inverse:
|
||||
self.f_inv = self._f_inv
|
||||
|
||||
def f(self, y):
|
||||
return np.log(y)
|
||||
|
||||
def fgrad_y(self, y):
|
||||
return 1. / y
|
||||
|
||||
def update_grads(self, Y_untransformed, Kiy):
|
||||
pass
|
||||
|
||||
def fgrad_y_psi(self, y, return_covar_chain=False):
|
||||
if return_covar_chain:
|
||||
return 0, 0
|
||||
return 0
|
||||
|
||||
def _f_inv(self, z, y=None):
|
||||
return np.exp(z)
|
||||
|
||||
|
||||
class IdentityFunction(WarpingFunction):
|
||||
"""
|
||||
Identity warping function. This is for testing and sanity check purposes
|
||||
and should not be used in practice.
|
||||
The closed_inverse flag should only be set to False for
|
||||
debugging and testing purposes.
|
||||
"""
|
||||
def __init__(self):
|
||||
self.num_parameters = 4
|
||||
self.psi = Param('psi', np.zeros((1,3)))
|
||||
self.d = Param('%s' % ('d'), 1.0, Logexp())
|
||||
def __init__(self, closed_inverse=True):
|
||||
self.num_parameters = 0
|
||||
super(IdentityFunction, self).__init__(name='identity')
|
||||
self.link_parameter(self.psi)
|
||||
self.link_parameter(self.d)
|
||||
|
||||
if closed_inverse:
|
||||
self.f_inv = self._f_inv
|
||||
|
||||
def f(self, y):
|
||||
return y
|
||||
|
|
@ -290,11 +229,14 @@ class IdentityFunction(WarpingFunction):
|
|||
def fgrad_y(self, y):
|
||||
return np.ones(y.shape)
|
||||
|
||||
def update_grads(self, Y_untransformed, Kiy):
|
||||
pass
|
||||
|
||||
def fgrad_y_psi(self, y, return_covar_chain=False):
|
||||
gradients = np.zeros((y.shape[0], y.shape[1], len(self.psi), 4))
|
||||
if return_covar_chain:
|
||||
return gradients, gradients
|
||||
return gradients
|
||||
return 0, 0
|
||||
return 0
|
||||
|
||||
def f_inv(self, z, y=None):
|
||||
def _f_inv(self, z, y=None):
|
||||
return z
|
||||
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue