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Merge branch 'devel' into params
Conflicts: GPy/core/transformations.py GPy/kern/parts/kernpart.py
This commit is contained in:
Max Zwiessele
commit
c2d217e72c
77 changed files with 3608 additions and 807 deletions
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@ -5,7 +5,7 @@ import numpy as np
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import pylab as pb
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from ..util.linalg import mdot, jitchol, tdot, symmetrify, backsub_both_sides, chol_inv, dtrtrs, dpotrs, dpotri
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from scipy import linalg
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from ..likelihoods import Gaussian
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from ..likelihoods import Gaussian, EP,EP_Mixed_Noise
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from gp_base import GPBase
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class SparseGP(GPBase):
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@ -109,7 +109,6 @@ class SparseGP(GPBase):
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tmp, _ = dtrtrs(self._Lm, np.asfortranarray(tmp.T), lower=1)
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self._A = tdot(tmp)
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# factor B
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self.B = np.eye(self.num_inducing) + self._A
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self.LB = jitchol(self.B)
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@ -139,6 +138,7 @@ class SparseGP(GPBase):
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dL_dpsi2_beta = 0.5 * backsub_both_sides(self._Lm, self.output_dim * np.eye(self.num_inducing) - self.DBi_plus_BiPBi)
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if self.likelihood.is_heteroscedastic:
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if self.has_uncertain_inputs:
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self.dL_dpsi2 = self.likelihood.precision.flatten()[:, None, None] * dL_dpsi2_beta[None, :, :]
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else:
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@ -160,9 +160,27 @@ class SparseGP(GPBase):
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# save computation here.
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self.partial_for_likelihood = None
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elif self.likelihood.is_heteroscedastic:
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raise NotImplementedError, "heteroscedatic derivates not implemented"
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if self.has_uncertain_inputs:
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raise NotImplementedError, "heteroscedatic derivates with uncertain inputs not implemented"
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else:
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LBi = chol_inv(self.LB)
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Lmi_psi1, nil = dtrtrs(self._Lm, np.asfortranarray(self.psi1.T), lower=1, trans=0)
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_LBi_Lmi_psi1, _ = dtrtrs(self.LB, np.asfortranarray(Lmi_psi1), lower=1, trans=0)
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self.partial_for_likelihood = -0.5 * self.likelihood.precision + 0.5 * self.likelihood.V**2
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self.partial_for_likelihood += 0.5 * self.output_dim * (self.psi0 - np.sum(Lmi_psi1**2,0))[:,None] * self.likelihood.precision**2
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self.partial_for_likelihood += 0.5*np.sum(mdot(LBi.T,LBi,Lmi_psi1)*Lmi_psi1,0)[:,None]*self.likelihood.precision**2
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self.partial_for_likelihood += -np.dot(self._LBi_Lmi_psi1Vf.T,_LBi_Lmi_psi1).T * self.likelihood.Y * self.likelihood.precision**2
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self.partial_for_likelihood += 0.5*np.dot(self._LBi_Lmi_psi1Vf.T,_LBi_Lmi_psi1).T**2 * self.likelihood.precision**2
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else:
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# likelihood is not heterscedatic
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# likelihood is not heteroscedatic
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self.partial_for_likelihood = -0.5 * self.num_data * self.output_dim * self.likelihood.precision + 0.5 * self.likelihood.trYYT * self.likelihood.precision ** 2
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self.partial_for_likelihood += 0.5 * self.output_dim * (self.psi0.sum() * self.likelihood.precision ** 2 - np.trace(self._A) * self.likelihood.precision)
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self.partial_for_likelihood += self.likelihood.precision * (0.5 * np.sum(self._A * self.DBi_plus_BiPBi) - self.data_fit)
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@ -194,8 +212,8 @@ class SparseGP(GPBase):
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return sum([['iip_%i_%i' % (i, j) for j in range(self.Z.shape[1])] for i in range(self.Z.shape[0])], [])\
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+ self.kern._get_param_names_transformed() + self.likelihood._get_param_names()
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def _get_print_names(self):
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return self.kern._get_param_names_transformed() + self.likelihood._get_param_names()
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#def _get_print_names(self):
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# return self.kern._get_param_names_transformed() + self.likelihood._get_param_names()
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def update_likelihood_approximation(self):
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"""
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@ -240,7 +258,7 @@ class SparseGP(GPBase):
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"""
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The derivative of the bound wrt the inducing inputs Z
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"""
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dL_dZ = 2.*self.kern.dK_dX(self.dL_dKmm, self.Z) # factor of two becase of vertical and horizontal 'stripes' in dKmm_dZ
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dL_dZ = self.kern.dK_dX(self.dL_dKmm, self.Z)
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if self.has_uncertain_inputs:
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dL_dZ += self.kern.dpsi1_dZ(self.dL_dpsi1, self.Z, self.X, self.X_variance)
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dL_dZ += self.kern.dpsi2_dZ(self.dL_dpsi2, self.Z, self.X, self.X_variance)
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@ -298,7 +316,7 @@ class SparseGP(GPBase):
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:type X_variance_new: np.ndarray, Nnew x self.input_dim
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:param which_parts: specifies which outputs kernel(s) to use in prediction
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:type which_parts: ('all', list of bools)
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:param full_cov: whether to return the folll covariance matrix, or just the diagonal
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:param full_cov: whether to return the full covariance matrix, or just the diagonal
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:type full_cov: bool
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:rtype: posterior mean, a Numpy array, Nnew x self.input_dim
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:rtype: posterior variance, a Numpy array, Nnew x 1 if full_cov=False, Nnew x Nnew otherwise
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@ -322,26 +340,133 @@ class SparseGP(GPBase):
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return mean, var, _025pm, _975pm
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def plot(self, samples=0, plot_limits=None, which_data='all', which_parts='all', resolution=None, levels=20, fignum=None, ax=None):
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def plot(self, samples=0, plot_limits=None, which_data='all', which_parts='all', resolution=None, levels=20, fignum=None, ax=None, output=None):
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if ax is None:
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fig = pb.figure(num=fignum)
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ax = fig.add_subplot(111)
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if which_data is 'all':
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which_data = slice(None)
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GPBase.plot(self, samples=0, plot_limits=None, which_data='all', which_parts='all', resolution=None, levels=20, ax=ax)
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GPBase.plot(self, samples=0, plot_limits=plot_limits, which_data='all', which_parts='all', resolution=None, levels=20, ax=ax, output=output)
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# add the inducing inputs and some errorbars
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if self.X.shape[1] == 1:
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if self.has_uncertain_inputs:
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Xu = self.X * self._Xscale + self._Xoffset # NOTE self.X are the normalized values now
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ax.errorbar(Xu[which_data, 0], self.likelihood.data[which_data, 0],
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xerr=2 * np.sqrt(self.X_variance[which_data, 0]),
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ecolor='k', fmt=None, elinewidth=.5, alpha=.5)
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Zu = self.Z * self._Xscale + self._Xoffset
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ax.plot(Zu, np.zeros_like(Zu) + ax.get_ylim()[0], 'r|', mew=1.5, markersize=12)
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if not hasattr(self,'multioutput'):
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elif self.X.shape[1] == 2:
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Zu = self.Z * self._Xscale + self._Xoffset
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ax.plot(Zu[:, 0], Zu[:, 1], 'wo')
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if self.X.shape[1] == 1:
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if self.has_uncertain_inputs:
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Xu = self.X * self._Xscale + self._Xoffset # NOTE self.X are the normalized values now
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ax.errorbar(Xu[which_data, 0], self.likelihood.data[which_data, 0],
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xerr=2 * np.sqrt(self.X_variance[which_data, 0]),
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ecolor='k', fmt=None, elinewidth=.5, alpha=.5)
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Zu = self.Z * self._Xscale + self._Xoffset
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ax.plot(Zu, np.zeros_like(Zu) + ax.get_ylim()[0], 'r|', mew=1.5, markersize=12)
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elif self.X.shape[1] == 2:
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Zu = self.Z * self._Xscale + self._Xoffset
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ax.plot(Zu[:, 0], Zu[:, 1], 'wo')
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else:
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pass
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"""
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if self.X.shape[1] == 2 and hasattr(self,'multioutput'):
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Xu = self.X[self.X[:,-1]==output,:]
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if self.has_uncertain_inputs:
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Xu = self.X * self._Xscale + self._Xoffset # NOTE self.X are the normalized values now
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Xu = self.X[self.X[:,-1]==output ,0:1] #??
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ax.errorbar(Xu[which_data, 0], self.likelihood.data[which_data, 0],
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xerr=2 * np.sqrt(self.X_variance[which_data, 0]),
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ecolor='k', fmt=None, elinewidth=.5, alpha=.5)
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Zu = self.Z[self.Z[:,-1]==output,:]
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Zu = self.Z * self._Xscale + self._Xoffset
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Zu = self.Z[self.Z[:,-1]==output ,0:1] #??
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ax.plot(Zu, np.zeros_like(Zu) + ax.get_ylim()[0], 'r|', mew=1.5, markersize=12)
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#ax.set_ylim(ax.get_ylim()[0],)
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else:
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raise NotImplementedError, "Cannot define a frame with more than two input dimensions"
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"""
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def predict_single_output(self, Xnew, output=0, which_parts='all', full_cov=False):
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"""
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For a specific output, predict the function at the new point(s) Xnew.
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Arguments
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---------
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:param Xnew: The points at which to make a prediction
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:type Xnew: np.ndarray, Nnew x self.input_dim
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:param output: output to predict
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:type output: integer in {0,..., num_outputs-1}
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:param which_parts: specifies which outputs kernel(s) to use in prediction
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:type which_parts: ('all', list of bools)
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:param full_cov: whether to return the full covariance matrix, or just the diagonal
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:type full_cov: bool
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:rtype: posterior mean, a Numpy array, Nnew x self.input_dim
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:rtype: posterior variance, a Numpy array, Nnew x 1 if full_cov=False, Nnew x Nnew otherwise
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:rtype: lower and upper boundaries of the 95% confidence intervals, Numpy arrays, Nnew x self.input_dim
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.. Note:: For multiple output models only
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"""
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assert hasattr(self,'multioutput')
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index = np.ones_like(Xnew)*output
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Xnew = np.hstack((Xnew,index))
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# normalize X values
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Xnew = (Xnew.copy() - self._Xoffset) / self._Xscale
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mu, var = self._raw_predict(Xnew, full_cov=full_cov, which_parts=which_parts)
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# now push through likelihood
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mean, var, _025pm, _975pm = self.likelihood.predictive_values(mu, var, full_cov, noise_model = output)
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return mean, var, _025pm, _975pm
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def _raw_predict_single_output(self, _Xnew, output=0, X_variance_new=None, which_parts='all', full_cov=False,stop=False):
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"""
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Internal helper function for making predictions for a specific output,
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does not account for normalization or likelihood
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---------
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:param Xnew: The points at which to make a prediction
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:type Xnew: np.ndarray, Nnew x self.input_dim
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:param output: output to predict
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:type output: integer in {0,..., num_outputs-1}
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:param which_parts: specifies which outputs kernel(s) to use in prediction
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:type which_parts: ('all', list of bools)
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:param full_cov: whether to return the full covariance matrix, or just the diagonal
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.. Note:: For multiple output models only
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"""
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Bi, _ = dpotri(self.LB, lower=0) # WTH? this lower switch should be 1, but that doesn't work!
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symmetrify(Bi)
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Kmmi_LmiBLmi = backsub_both_sides(self._Lm, np.eye(self.num_inducing) - Bi)
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if self.Cpsi1V is None:
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psi1V = np.dot(self.psi1.T,self.likelihood.V)
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tmp, _ = dtrtrs(self._Lm, np.asfortranarray(psi1V), lower=1, trans=0)
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tmp, _ = dpotrs(self.LB, tmp, lower=1)
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self.Cpsi1V, _ = dtrtrs(self._Lm, tmp, lower=1, trans=1)
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assert hasattr(self,'multioutput')
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index = np.ones_like(_Xnew)*output
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_Xnew = np.hstack((_Xnew,index))
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if X_variance_new is None:
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Kx = self.kern.K(self.Z, _Xnew, which_parts=which_parts)
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mu = np.dot(Kx.T, self.Cpsi1V)
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if full_cov:
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Kxx = self.kern.K(_Xnew, which_parts=which_parts)
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var = Kxx - mdot(Kx.T, Kmmi_LmiBLmi, Kx) # NOTE this won't work for plotting
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else:
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Kxx = self.kern.Kdiag(_Xnew, which_parts=which_parts)
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var = Kxx - np.sum(Kx * np.dot(Kmmi_LmiBLmi, Kx), 0)
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else:
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Kx = self.kern.psi1(self.Z, _Xnew, X_variance_new)
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mu = np.dot(Kx, self.Cpsi1V)
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if full_cov:
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raise NotImplementedError, "TODO"
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else:
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Kxx = self.kern.psi0(self.Z, _Xnew, X_variance_new)
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psi2 = self.kern.psi2(self.Z, _Xnew, X_variance_new)
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var = Kxx - np.sum(np.sum(psi2 * Kmmi_LmiBLmi[None, :, :], 1), 1)
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return mu, var[:, None]
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