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Broken whilst unlinking GP and sparse_GP, kern not being imported

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Alan Saul 2013-06-04 16:05:33 +01:00
parent 26b4cd6c4f
commit 1302c46ace
16 changed files with 328 additions and 318 deletions
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146
GPy/core/GP.py Normal file
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# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
# Licensed under the BSD 3-clause license (see LICENSE.txt)
import numpy as np
from scipy import linalg
import pylab as pb
from .. import kern
from ..util.linalg import pdinv, mdot, tdot
#from ..util.plot import gpplot, Tango
from ..likelihoods import EP
from gp_base import GPBase
class GP(GPBase):
"""
Gaussian Process model for regression and EP
:param X: input observations
:param kernel: a GPy kernel, defaults to rbf+white
:parm likelihood: a GPy likelihood
:param normalize_X: whether to normalize the input data before computing (predictions will be in original scales)
:type normalize_X: False|True
:rtype: model object
:param epsilon_ep: convergence criterion for the Expectation Propagation algorithm, defaults to 0.1
:param powerep: power-EP parameters [$\eta$,$\delta$], defaults to [1.,1.]
:type powerep: list
.. Note:: Multiple independent outputs are allowed using columns of Y
"""
def __init__(self, X, likelihood, kernel, normalize_X=False):
super(GP, self).__init__(X, likelihood, kernel, normalize_X=normalize_X)
self._set_params(self._get_params())
def _set_params(self, p):
self.kern._set_params_transformed(p[:self.kern.Nparam_transformed()])
self.likelihood._set_params(p[self.kern.Nparam_transformed():])
self.K = self.kern.K(self.X)
self.K += self.likelihood.covariance_matrix
self.Ki, self.L, self.Li, self.K_logdet = pdinv(self.K)
# the gradient of the likelihood wrt the covariance matrix
if self.likelihood.YYT is None:
#alpha = np.dot(self.Ki, self.likelihood.Y)
alpha,_ = linalg.lapack.flapack.dpotrs(self.L, self.likelihood.Y,lower=1)
self.dL_dK = 0.5 * (tdot(alpha) - self.D * self.Ki)
else:
#tmp = mdot(self.Ki, self.likelihood.YYT, self.Ki)
tmp, _ = linalg.lapack.flapack.dpotrs(self.L, np.asfortranarray(self.likelihood.YYT), lower=1)
tmp, _ = linalg.lapack.flapack.dpotrs(self.L, np.asfortranarray(tmp.T), lower=1)
self.dL_dK = 0.5 * (tmp - self.D * self.Ki)
def _get_param_names(self):
return self.kern._get_param_names_transformed() + self.likelihood._get_param_names()
def update_likelihood_approximation(self):
"""
Approximates a non-gaussian likelihood using Expectation Propagation
For a Gaussian likelihood, no iteration is required:
this function does nothing
"""
self.likelihood.fit_full(self.kern.K(self.X))
self._set_params(self._get_params()) # update the GP
def _model_fit_term(self):
"""
Computes the model fit using YYT if it's available
"""
if self.likelihood.YYT is None:
tmp, _ = linalg.lapack.flapack.dtrtrs(self.L, np.asfortranarray(self.likelihood.Y), lower=1)
return -0.5 * np.sum(np.square(tmp))
#return -0.5 * np.sum(np.square(np.dot(self.Li, self.likelihood.Y)))
else:
return -0.5 * np.sum(np.multiply(self.Ki, self.likelihood.YYT))
def log_likelihood(self):
"""
The log marginal likelihood of the GP.
For an EP model, can be written as the log likelihood of a regression
model for a new variable Y* = v_tilde/tau_tilde, with a covariance
matrix K* = K + diag(1./tau_tilde) plus a normalization term.
"""
return -0.5 * self.D * self.K_logdet + self._model_fit_term() + self.likelihood.Z
def _log_likelihood_gradients(self):
"""
The gradient of all parameters.
Note, we use the chain rule: dL_dtheta = dL_dK * d_K_dtheta
"""
return np.hstack((self.kern.dK_dtheta(dL_dK=self.dL_dK, X=self.X), self.likelihood._gradients(partial=np.diag(self.dL_dK))))
def _raw_predict(self, _Xnew, which_parts='all', full_cov=False,stop=False):
"""
Internal helper function for making predictions, does not account
for normalization or likelihood
"""
Kx = self.kern.K(_Xnew,self.X,which_parts=which_parts).T
#KiKx = np.dot(self.Ki, Kx)
KiKx, _ = linalg.lapack.flapack.dpotrs(self.L, np.asfortranarray(Kx), lower=1)
mu = np.dot(KiKx.T, self.likelihood.Y)
if full_cov:
Kxx = self.kern.K(_Xnew, which_parts=which_parts)
var = Kxx - np.dot(KiKx.T, Kx)
else:
Kxx = self.kern.Kdiag(_Xnew, which_parts=which_parts)
var = Kxx - np.sum(np.multiply(KiKx, Kx), 0)
var = var[:, None]
if stop:
debug_this
return mu, var
def predict(self, Xnew, which_parts='all', full_cov=False):
"""
Predict the function(s) at the new point(s) Xnew.
Arguments
---------
:param Xnew: The points at which to make a prediction
:type Xnew: np.ndarray, Nnew x self.Q
:param which_parts: specifies which outputs kernel(s) to use in prediction
:type which_parts: ('all', list of bools)
:param full_cov: whether to return the folll covariance matrix, or just the diagonal
:type full_cov: bool
:rtype: posterior mean, a Numpy array, Nnew x self.D
:rtype: posterior variance, a Numpy array, Nnew x 1 if full_cov=False, Nnew x Nnew otherwise
:rtype: lower and upper boundaries of the 95% confidence intervals, Numpy arrays, Nnew x self.D
If full_cov and self.D > 1, the return shape of var is Nnew x Nnew x self.D. If self.D == 1, the return shape is Nnew x Nnew.
This is to allow for different normalizations of the output dimensions.
"""
# normalize X values
Xnew = (Xnew.copy() - self._Xmean) / self._Xstd
mu, var = self._raw_predict(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)
return mean, var, _025pm, _975pm

3
GPy/core/__init__.py
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@ -1,7 +1,8 @@
# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
# Licensed under the BSD 3-clause license (see LICENSE.txt)
from GP import GP
from sparse_GP import sparse_GP
from model import *
from parameterised import *
import priors

129
GPy/core/gp_base.py Normal file
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import numpy as np
import model
from .. import kern
from ..util.plot import gpplot, Tango, x_frame1D, x_frame2D
import pylab as pb
class GPBase(model):
"""
Gaussian Process model for holding shared behaviour between
sprase_GP and GP models
"""
def __init__(self, X, likelihood, kernel, normalize_X=False):
self.X = X
assert len(self.X.shape) == 2
self.N, self.Q = self.X.shape
assert isinstance(kernel, kern.kern)
self.kern = kernel
self.likelihood = likelihood
assert self.X.shape[0] == self.likelihood.data.shape[0]
self.N, self.D = self.likelihood.data.shape
if normalize_X:
self._Xmean = X.mean(0)[None, :]
self._Xstd = X.std(0)[None, :]
self.X = (X.copy() - self._Xmean) / self._Xstd
super(GPBase, self).__init__()
# All leaf nodes should call self._set_params(self._get_params()) at
# the end
def _get_params(self):
return np.hstack((self.kern._get_params_transformed(), self.likelihood._get_params()))
def plot_f(self, samples=0, plot_limits=None, which_data='all', which_parts='all', resolution=None, full_cov=False):
"""
Plot the GP's view of the world, where the data is normalized and the
likelihood is Gaussian.
:param samples: the number of a posteriori samples to plot
:param which_data: which if the training data to plot (default all)
:type which_data: 'all' or a slice object to slice self.X, self.Y
:param plot_limits: The limits of the plot. If 1D [xmin,xmax], if 2D [[xmin,ymin],[xmax,ymax]]. Defaluts to data limits
:param which_parts: which of the kernel functions to plot (additively)
:type which_parts: 'all', or list of bools
:param resolution: the number of intervals to sample the GP on. Defaults to 200 in 1D and 50 (a 50x50 grid) in 2D
Plot the posterior of the GP.
- In one dimension, the function is plotted with a shaded region identifying two standard deviations.
- In two dimsensions, a contour-plot shows the mean predicted function
- In higher dimensions, we've no implemented this yet !TODO!
Can plot only part of the data and part of the posterior functions
using which_data and which_functions
"""
if which_data == 'all':
which_data = slice(None)
if self.X.shape[1] == 1:
Xnew, xmin, xmax = x_frame1D(self.X, plot_limits=plot_limits)
if samples == 0:
m, v = self._raw_predict(Xnew, which_parts=which_parts)
gpplot(Xnew, m, m - 2 * np.sqrt(v), m + 2 * np.sqrt(v))
pb.plot(self.X[which_data], self.likelihood.Y[which_data], 'kx', mew=1.5)
else:
m, v = self._raw_predict(Xnew, which_parts=which_parts, full_cov=True)
Ysim = np.random.multivariate_normal(m.flatten(), v, samples)
gpplot(Xnew, m, m - 2 * np.sqrt(np.diag(v)[:, None]), m + 2 * np.sqrt(np.diag(v))[:, None])
for i in range(samples):
pb.plot(Xnew, Ysim[i, :], Tango.colorsHex['darkBlue'], linewidth=0.25)
pb.plot(self.X[which_data], self.likelihood.Y[which_data], 'kx', mew=1.5)
pb.xlim(xmin, xmax)
ymin, ymax = min(np.append(self.likelihood.Y, m - 2 * np.sqrt(np.diag(v)[:, None]))), max(np.append(self.likelihood.Y, m + 2 * np.sqrt(np.diag(v)[:, None])))
ymin, ymax = ymin - 0.1 * (ymax - ymin), ymax + 0.1 * (ymax - ymin)
pb.ylim(ymin, ymax)
if hasattr(self, 'Z'):
pb.plot(self.Z, self.Z * 0 + pb.ylim()[0], 'r|', mew=1.5, markersize=12)
elif self.X.shape[1] == 2:
resolution = resolution or 50
Xnew, xmin, xmax, xx, yy = x_frame2D(self.X, plot_limits, resolution)
m, v = self._raw_predict(Xnew, which_parts=which_parts)
m = m.reshape(resolution, resolution).T
pb.contour(xx, yy, m, vmin=m.min(), vmax=m.max(), cmap=pb.cm.jet)
pb.scatter(self.X[:, 0], self.X[:, 1], 40, self.likelihood.Y, linewidth=0, cmap=pb.cm.jet, vmin=m.min(), vmax=m.max())
pb.xlim(xmin[0], xmax[0])
pb.ylim(xmin[1], xmax[1])
else:
raise NotImplementedError, "Cannot define a frame with more than two input dimensions"
def plot(self, samples=0, plot_limits=None, which_data='all', which_parts='all', resolution=None, levels=20):
"""
TODO: Docstrings!
:param levels: for 2D plotting, the number of contour levels to use
"""
# TODO include samples
if which_data == 'all':
which_data = slice(None)
if self.X.shape[1] == 1:
Xu = self.X * self._Xstd + self._Xmean # NOTE self.X are the normalized values now
Xnew, xmin, xmax = x_frame1D(Xu, plot_limits=plot_limits)
m, var, lower, upper = self.predict(Xnew, which_parts=which_parts)
for d in range(m.shape[1]):
gpplot(Xnew, m[:,d], lower[:,d], upper[:,d])
pb.plot(Xu[which_data], self.likelihood.data[which_data,d], 'kx', mew=1.5)
ymin, ymax = min(np.append(self.likelihood.data, lower)), max(np.append(self.likelihood.data, upper))
ymin, ymax = ymin - 0.1 * (ymax - ymin), ymax + 0.1 * (ymax - ymin)
pb.xlim(xmin, xmax)
pb.ylim(ymin, ymax)
elif self.X.shape[1] == 2: # FIXME
resolution = resolution or 50
Xnew, xx, yy, xmin, xmax = x_frame2D(self.X, plot_limits, resolution)
x, y = np.linspace(xmin[0], xmax[0], resolution), np.linspace(xmin[1], xmax[1], resolution)
m, var, lower, upper = self.predict(Xnew, which_parts=which_parts)
m = m.reshape(resolution, resolution).T
pb.contour(x, y, m, levels, vmin=m.min(), vmax=m.max(), cmap=pb.cm.jet)
Yf = self.likelihood.Y.flatten()
pb.scatter(self.X[:, 0], self.X[:, 1], 40, Yf, cmap=pb.cm.jet, vmin=m.min(), vmax=m.max(), linewidth=0.)
pb.xlim(xmin[0], xmax[0])
pb.ylim(xmin[1], xmax[1])
else:
raise NotImplementedError, "Cannot define a frame with more than two input dimensions"

2
GPy/core/model.py
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@ -22,8 +22,8 @@ class model(parameterised):
self.priors = [None for i in range(self._get_params().size)]
self.optimization_runs = []
self.sampling_runs = []
self._set_params(self._get_params())
self.preferred_optimizer = 'tnc'
#self._set_params(self._get_params()) has been taken out as it should only be called on leaf nodes
def _get_params(self):
raise NotImplementedError, "this needs to be implemented to use the model class"
def _set_params(self, x):

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GPy/core/sparse_GP.py Normal file
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# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
# Licensed under the BSD 3-clause license (see LICENSE.txt)
import numpy as np
import pylab as pb
from ..util.linalg import mdot, jitchol, tdot, symmetrify, backsub_both_sides, chol_inv
from GP import GP
from scipy import linalg
from ..likelihoods import Gaussian
from gp_base import GPBase
class sparse_GP(GPBase):
"""
Variational sparse GP model
:param X: inputs
:type X: np.ndarray (N x Q)
:param likelihood: a likelihood instance, containing the observed data
:type likelihood: GPy.likelihood.(Gaussian | EP | Laplace)
:param kernel : the kernel (covariance function). See link kernels
:type kernel: a GPy.kern.kern instance
:param X_variance: The uncertainty in the measurements of X (Gaussian variance)
:type X_variance: np.ndarray (N x Q) | None
:param Z: inducing inputs (optional, see note)
:type Z: np.ndarray (M x Q) | None
:param M : Number of inducing points (optional, default 10. Ignored if Z is not None)
:type M: int
:param normalize_(X|Y) : whether to normalize the data before computing (predictions will be in original scales)
:type normalize_(X|Y): bool
"""
def __init__(self, X, likelihood, kernel, Z, X_variance=None, normalize_X=False):
super(sparse_GP, self).__init__(X, likelihood, kernel, normalize_X=normalize_X)
self.Z = Z
self.M = Z.shape[0]
self.likelihood = likelihood
if X_variance is None:
self.has_uncertain_inputs = False
else:
assert X_variance.shape == X.shape
self.has_uncertain_inputs = True
self.X_variance = X_variance
if normalize_X:
self.Z = (self.Z.copy() - self._Xmean) / self._Xstd
# normalize X uncertainty also
if self.has_uncertain_inputs:
self.X_variance /= np.square(self._Xstd)
def _compute_kernel_matrices(self):
# kernel computations, using BGPLVM notation
self.Kmm = self.kern.K(self.Z)
if self.has_uncertain_inputs:
self.psi0 = self.kern.psi0(self.Z, self.X, self.X_variance)
self.psi1 = self.kern.psi1(self.Z, self.X, self.X_variance).T
self.psi2 = self.kern.psi2(self.Z, self.X, self.X_variance)
else:
self.psi0 = self.kern.Kdiag(self.X)
self.psi1 = self.kern.K(self.Z, self.X)
self.psi2 = None
def _computations(self):
# factor Kmm
self.Lm = jitchol(self.Kmm)
# The rather complex computations of self.A
if self.has_uncertain_inputs:
if self.likelihood.is_heteroscedastic:
psi2_beta = (self.psi2 * (self.likelihood.precision.flatten().reshape(self.N, 1, 1))).sum(0)
else:
psi2_beta = self.psi2.sum(0) * self.likelihood.precision
evals, evecs = linalg.eigh(psi2_beta)
clipped_evals = np.clip(evals, 0., 1e6) # TODO: make clipping configurable
tmp = evecs * np.sqrt(clipped_evals)
else:
if self.likelihood.is_heteroscedastic:
tmp = self.psi1 * (np.sqrt(self.likelihood.precision.flatten().reshape(1, self.N)))
else:
tmp = self.psi1 * (np.sqrt(self.likelihood.precision))
tmp, _ = linalg.lapack.flapack.dtrtrs(self.Lm, np.asfortranarray(tmp), lower=1)
self.A = tdot(tmp)
# factor B
self.B = np.eye(self.M) + self.A
self.LB = jitchol(self.B)
# TODO: make a switch for either first compute psi1V, or VV.T
self.psi1V = np.dot(self.psi1, self.likelihood.V)
# back substutue C into psi1V
tmp, info1 = linalg.lapack.flapack.dtrtrs(self.Lm, np.asfortranarray(self.psi1V), lower=1, trans=0)
self._LBi_Lmi_psi1V, _ = linalg.lapack.flapack.dtrtrs(self.LB, np.asfortranarray(tmp), lower=1, trans=0)
tmp, info2 = linalg.lapack.flapack.dpotrs(self.LB, tmp, lower=1)
self.Cpsi1V, info3 = linalg.lapack.flapack.dtrtrs(self.Lm, tmp, lower=1, trans=1)
# Compute dL_dKmm
tmp = tdot(self._LBi_Lmi_psi1V)
self.DBi_plus_BiPBi = backsub_both_sides(self.LB, self.D * np.eye(self.M) + tmp)
tmp = -0.5 * self.DBi_plus_BiPBi
tmp += -0.5 * self.B * self.D
tmp += self.D * np.eye(self.M)
self.dL_dKmm = backsub_both_sides(self.Lm, tmp)
# Compute dL_dpsi # FIXME: this is untested for the heterscedastic + uncertain inputs case
self.dL_dpsi0 = -0.5 * self.D * (self.likelihood.precision * np.ones([self.N, 1])).flatten()
self.dL_dpsi1 = np.dot(self.Cpsi1V, self.likelihood.V.T)
dL_dpsi2_beta = 0.5 * backsub_both_sides(self.Lm, self.D * np.eye(self.M) - self.DBi_plus_BiPBi)
if self.likelihood.is_heteroscedastic:
if self.has_uncertain_inputs:
self.dL_dpsi2 = self.likelihood.precision.flatten()[:, None, None] * dL_dpsi2_beta[None, :, :]
else:
self.dL_dpsi1 += 2.*np.dot(dL_dpsi2_beta, self.psi1 * self.likelihood.precision.reshape(1, self.N))
self.dL_dpsi2 = None
else:
dL_dpsi2 = self.likelihood.precision * dL_dpsi2_beta
if self.has_uncertain_inputs:
# repeat for each of the N psi_2 matrices
self.dL_dpsi2 = np.repeat(dL_dpsi2[None, :, :], self.N, axis=0)
else:
# subsume back into psi1 (==Kmn)
self.dL_dpsi1 += 2.*np.dot(dL_dpsi2, self.psi1)
self.dL_dpsi2 = None
# the partial derivative vector for the likelihood
if self.likelihood.Nparams == 0:
# save computation here.
self.partial_for_likelihood = None
elif self.likelihood.is_heteroscedastic:
raise NotImplementedError, "heteroscedatic derivates not implemented"
else:
# likelihood is not heterscedatic
self.partial_for_likelihood = -0.5 * self.N * self.D * self.likelihood.precision + 0.5 * self.likelihood.trYYT * self.likelihood.precision ** 2
self.partial_for_likelihood += 0.5 * self.D * (self.psi0.sum() * self.likelihood.precision ** 2 - np.trace(self.A) * self.likelihood.precision)
self.partial_for_likelihood += self.likelihood.precision * (0.5 * np.sum(self.A * self.DBi_plus_BiPBi) - np.sum(np.square(self._LBi_Lmi_psi1V)))
def log_likelihood(self):
""" Compute the (lower bound on the) log marginal likelihood """
if self.likelihood.is_heteroscedastic:
A = -0.5 * self.N * self.D * np.log(2.*np.pi) + 0.5 * np.sum(np.log(self.likelihood.precision)) - 0.5 * np.sum(self.likelihood.V * self.likelihood.Y)
B = -0.5 * self.D * (np.sum(self.likelihood.precision.flatten() * self.psi0) - np.trace(self.A))
else:
A = -0.5 * self.N * self.D * (np.log(2.*np.pi) - np.log(self.likelihood.precision)) - 0.5 * self.likelihood.precision * self.likelihood.trYYT
B = -0.5 * self.D * (np.sum(self.likelihood.precision * self.psi0) - np.trace(self.A))
C = -self.D * (np.sum(np.log(np.diag(self.LB)))) # + 0.5 * self.M * np.log(sf2))
D = 0.5 * np.sum(np.square(self._LBi_Lmi_psi1V))
return A + B + C + D + self.likelihood.Z
def _set_params(self, p):
self.Z = p[:self.M * self.Q].reshape(self.M, self.Q)
self.kern._set_params(p[self.Z.size:self.Z.size + self.kern.Nparam])
self.likelihood._set_params(p[self.Z.size + self.kern.Nparam:])
self._compute_kernel_matrices()
self._computations()
def _get_params(self):
return np.hstack([self.Z.flatten(), GP._get_params(self)])
def _get_param_names(self):
return sum([['iip_%i_%i' % (i, j) for j in range(self.Z.shape[1])] for i in range(self.Z.shape[0])], []) + GP._get_param_names(self)
def update_likelihood_approximation(self):
"""
Approximates a non-gaussian likelihood using Expectation Propagation
For a Gaussian likelihood, no iteration is required:
this function does nothing
"""
if not isinstance(self.likelihood, Gaussian): # Updates not needed for Gaussian likelihood
self.likelihood.restart() # TODO check consistency with pseudo_EP
if self.has_uncertain_inputs:
Lmi = chol_inv(self.Lm)
Kmmi = tdot(Lmi.T)
diag_tr_psi2Kmmi = np.array([np.trace(psi2_Kmmi) for psi2_Kmmi in np.dot(self.psi2, Kmmi)])
self.likelihood.fit_FITC(self.Kmm, self.psi1, diag_tr_psi2Kmmi) # This uses the fit_FITC code, but does not perfomr a FITC-EP.#TODO solve potential confusion
# raise NotImplementedError, "EP approximation not implemented for uncertain inputs"
else:
self.likelihood.fit_DTC(self.Kmm, self.psi1)
# self.likelihood.fit_FITC(self.Kmm,self.psi1,self.psi0)
self._set_params(self._get_params()) # update the GP
def _log_likelihood_gradients(self):
return np.hstack((self.dL_dZ().flatten(), self.dL_dtheta(), self.likelihood._gradients(partial=self.partial_for_likelihood)))
def dL_dtheta(self):
"""
Compute and return the derivative of the log marginal likelihood wrt the parameters of the kernel
"""
dL_dtheta = self.kern.dK_dtheta(self.dL_dKmm, self.Z)
if self.has_uncertain_inputs:
dL_dtheta += self.kern.dpsi0_dtheta(self.dL_dpsi0, self.Z, self.X, self.X_variance)
dL_dtheta += self.kern.dpsi1_dtheta(self.dL_dpsi1.T, self.Z, self.X, self.X_variance)
dL_dtheta += self.kern.dpsi2_dtheta(self.dL_dpsi2, self.Z, self.X, self.X_variance)
else:
dL_dtheta += self.kern.dK_dtheta(self.dL_dpsi1, self.Z, self.X)
dL_dtheta += self.kern.dKdiag_dtheta(self.dL_dpsi0, self.X)
return dL_dtheta
def dL_dZ(self):
"""
The derivative of the bound wrt the inducing inputs Z
"""
dL_dZ = 2.*self.kern.dK_dX(self.dL_dKmm, self.Z) # factor of two becase of vertical and horizontal 'stripes' in dKmm_dZ
if self.has_uncertain_inputs:
dL_dZ += self.kern.dpsi1_dZ(self.dL_dpsi1, self.Z, self.X, self.X_variance)
dL_dZ += self.kern.dpsi2_dZ(self.dL_dpsi2, self.Z, self.X, self.X_variance)
else:
dL_dZ += self.kern.dK_dX(self.dL_dpsi1, self.Z, self.X)
return dL_dZ
def _raw_predict(self, Xnew, X_variance_new=None, which_parts='all', full_cov=False):
"""Internal helper function for making predictions, does not account for normalization"""
Bi, _ = linalg.lapack.flapack.dpotri(self.LB, lower=0) # WTH? this lower switch should be 1, but that doesn't work!
symmetrify(Bi)
Kmmi_LmiBLmi = backsub_both_sides(self.Lm, np.eye(self.M) - Bi)
if X_variance_new is None:
Kx = self.kern.K(self.Z, Xnew, which_parts=which_parts)
mu = np.dot(Kx.T, self.Cpsi1V)
if full_cov:
Kxx = self.kern.K(Xnew, which_parts=which_parts)
var = Kxx - mdot(Kx.T, Kmmi_LmiBLmi, Kx) # NOTE this won't work for plotting
else:
Kxx = self.kern.Kdiag(Xnew, which_parts=which_parts)
var = Kxx - np.sum(Kx * np.dot(Kmmi_LmiBLmi, Kx), 0)
else:
# assert which_parts=='all', "swithching out parts of variational kernels is not implemented"
Kx = self.kern.psi1(self.Z, Xnew, X_variance_new) # , which_parts=which_parts) TODO: which_parts
mu = np.dot(Kx, self.Cpsi1V)
if full_cov:
raise NotImplementedError, "TODO"
else:
Kxx = self.kern.psi0(self.Z, Xnew, X_variance_new)
psi2 = self.kern.psi2(self.Z, Xnew, X_variance_new)
var = Kxx - np.sum(np.sum(psi2 * Kmmi_LmiBLmi[None, :, :], 1), 1)
return mu, var[:, None]
def predict(self, Xnew, X_variance_new=None, which_parts='all', full_cov=False):
"""
Predict the function(s) at the new point(s) Xnew.
Arguments
---------
:param Xnew: The points at which to make a prediction
:type Xnew: np.ndarray, Nnew x self.Q
:param X_variance_new: The uncertainty in the prediction points
:type X_variance_new: np.ndarray, Nnew x self.Q
:param which_parts: specifies which outputs kernel(s) to use in prediction
:type which_parts: ('all', list of bools)
:param full_cov: whether to return the folll covariance matrix, or just the diagonal
:type full_cov: bool
:rtype: posterior mean, a Numpy array, Nnew x self.D
:rtype: posterior variance, a Numpy array, Nnew x 1 if full_cov=False, Nnew x Nnew otherwise
:rtype: lower and upper boundaries of the 95% confidence intervals, Numpy arrays, Nnew x self.D
If full_cov and self.D > 1, the return shape of var is Nnew x Nnew x self.D. If self.D == 1, the return shape is Nnew x Nnew.
This is to allow for different normalizations of the output dimensions.
"""
# normalize X values
Xnew = (Xnew.copy() - self._Xmean) / self._Xstd
if X_variance_new is not None:
X_variance_new = X_variance_new / self._Xstd ** 2
# here's the actual prediction by the GP model
mu, var = self._raw_predict(Xnew, X_variance_new, full_cov=full_cov, which_parts=which_parts)
# now push through likelihood
mean, var, _025pm, _975pm = self.likelihood.predictive_values(mu, var, full_cov)
return mean, var, _025pm, _975pm
def plot(self, samples=0, plot_limits=None, which_data='all', which_parts='all', resolution=None, levels=20):
super(sparse_GP, self).plot(samples=0, plot_limits=None, which_data='all', which_parts='all', resolution=None, levels=20)
if self.X.shape[1] == 1:
Xu = self.X * self._Xstd + self._Xmean # NOTE self.X are the normalized values now
if self.has_uncertain_inputs:
pb.errorbar(Xu[which_data, 0], self.likelihood.data[which_data, 0],
xerr=2 * np.sqrt(self.X_variance[which_data, 0]),
ecolor='k', fmt=None, elinewidth=.5, alpha=.5)
Zu = self.Z * self._Xstd + self._Xmean
pb.plot(Zu, Zu * 0 + pb.ylim()[0], 'r|', mew=1.5, markersize=12)
# pb.errorbar(self.X[:,0], pb.ylim()[0]+np.zeros(self.N), xerr=2*np.sqrt(self.X_variance.flatten()))
elif self.X.shape[1] == 2: # FIXME
pb.plot(self.Z[:, 0], self.Z[:, 1], 'wo')