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161 lines
7.4 KiB
Python
161 lines
7.4 KiB
Python
# Copyright (c) 2012-2014, GPy authors (see AUTHORS.txt).
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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 gp import GP
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from parameterization.param import Param
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from ..inference.latent_function_inference import var_dtc
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from .. import likelihoods
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from parameterization.variational import VariationalPosterior, NormalPosterior
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from ..util.linalg import mdot
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import logging
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from GPy.inference.latent_function_inference.posterior import Posterior
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from GPy.inference.optimization.stochastics import SparseGPStochastics,\
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SparseGPMissing
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#no stochastics.py file added! from GPy.inference.optimization.stochastics import SparseGPStochastics,\
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#SparseGPMissing
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logger = logging.getLogger("sparse gp")
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class SparseGP(GP):
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"""
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A general purpose Sparse GP model
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This model allows (approximate) inference using variational DTC or FITC
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(Gaussian likelihoods) as well as non-conjugate sparse methods based on
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these.
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:param X: inputs
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:type X: np.ndarray (num_data x input_dim)
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:param likelihood: a likelihood instance, containing the observed data
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:type likelihood: GPy.likelihood.(Gaussian | EP | Laplace)
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:param kernel: the kernel (covariance function). See link kernels
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:type kernel: a GPy.kern.kern instance
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:param X_variance: The uncertainty in the measurements of X (Gaussian variance)
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:type X_variance: np.ndarray (num_data x input_dim) | None
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:param Z: inducing inputs
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:type Z: np.ndarray (num_inducing x input_dim)
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:param num_inducing: Number of inducing points (optional, default 10. Ignored if Z is not None)
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:type num_inducing: int
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"""
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def __init__(self, X, Y, Z, kernel, likelihood, inference_method=None,
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name='sparse gp', Y_metadata=None, normalizer=False):
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#pick a sensible inference method
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if inference_method is None:
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if isinstance(likelihood, likelihoods.Gaussian):
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inference_method = var_dtc.VarDTC(limit=1 if not self.missing_data else Y.shape[1])
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else:
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#inference_method = ??
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raise NotImplementedError, "what to do what to do?"
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print "defaulting to ", inference_method, "for latent function inference"
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self.Z = Param('inducing inputs', Z)
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self.num_inducing = Z.shape[0]
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GP.__init__(self, X, Y, kernel, likelihood, inference_method=inference_method, name=name, Y_metadata=Y_metadata, normalizer=normalizer)
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logger.info("Adding Z as parameter")
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self.link_parameter(self.Z, index=0)
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self.posterior = None
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def has_uncertain_inputs(self):
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return isinstance(self.X, VariationalPosterior)
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def parameters_changed(self):
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self.posterior, self._log_marginal_likelihood, self.grad_dict = self.inference_method.inference(self.kern, self.X, self.Z, self.likelihood, self.Y, self.Y_metadata)
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self.likelihood.update_gradients(self.grad_dict['dL_dthetaL'])
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if isinstance(self.X, VariationalPosterior):
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#gradients wrt kernel
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dL_dKmm = self.grad_dict['dL_dKmm']
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self.kern.update_gradients_full(dL_dKmm, self.Z, None)
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kerngrad = self.kern.gradient.copy()
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self.kern.update_gradients_expectations(variational_posterior=self.X,
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Z=self.Z,
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dL_dpsi0=self.grad_dict['dL_dpsi0'],
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dL_dpsi1=self.grad_dict['dL_dpsi1'],
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dL_dpsi2=self.grad_dict['dL_dpsi2'])
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self.kern.gradient += kerngrad
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#gradients wrt Z
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self.Z.gradient = self.kern.gradients_X(dL_dKmm, self.Z)
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self.Z.gradient += self.kern.gradients_Z_expectations(
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self.grad_dict['dL_dpsi0'],
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self.grad_dict['dL_dpsi1'],
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self.grad_dict['dL_dpsi2'],
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Z=self.Z,
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variational_posterior=self.X)
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else:
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#gradients wrt kernel
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self.kern.update_gradients_diag(self.grad_dict['dL_dKdiag'], self.X)
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kerngrad = self.kern.gradient.copy()
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self.kern.update_gradients_full(self.grad_dict['dL_dKnm'], self.X, self.Z)
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kerngrad += self.kern.gradient
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self.kern.update_gradients_full(self.grad_dict['dL_dKmm'], self.Z, None)
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self.kern.gradient += kerngrad
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#gradients wrt Z
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self.Z.gradient = self.kern.gradients_X(self.grad_dict['dL_dKmm'], self.Z)
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self.Z.gradient += self.kern.gradients_X(self.grad_dict['dL_dKnm'].T, self.Z, self.X)
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def _raw_predict(self, Xnew, full_cov=False, kern=None):
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"""
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Make a prediction for the latent function values.
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For certain inputs we give back a full_cov of shape NxN,
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if there is missing data, each dimension has its own full_cov of shape NxNxD, and if full_cov is of,
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we take only the diagonal elements across N.
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For uncertain inputs, the SparseGP bound produces a full covariance structure across D, so for full_cov we
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return a NxDxD matrix and in the not full_cov case, we return the diagonal elements across D (NxD).
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This is for both with and without missing data.
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"""
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if kern is None: kern = self.kern
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if not isinstance(Xnew, VariationalPosterior):
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Kx = kern.K(self.Z, Xnew)
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mu = np.dot(Kx.T, self.posterior.woodbury_vector)
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if full_cov:
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Kxx = kern.K(Xnew)
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if self.posterior.woodbury_inv.ndim == 2:
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var = Kxx - np.dot(Kx.T, np.dot(self.posterior.woodbury_inv, Kx))
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elif self.posterior.woodbury_inv.ndim == 3:
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var = Kxx[:,:,None] - np.tensordot(np.dot(np.atleast_3d(self.posterior.woodbury_inv).T, Kx).T, Kx, [1,0]).swapaxes(1,2)
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var = var
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else:
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Kxx = kern.Kdiag(Xnew)
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var = (Kxx - np.sum(np.dot(np.atleast_3d(self.posterior.woodbury_inv).T, Kx) * Kx[None,:,:], 1)).T
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else:
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psi0_star = self.kern.psi0(self.Z, Xnew)
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psi1_star = self.kern.psi1(self.Z, Xnew)
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#psi2_star = self.kern.psi2(self.Z, Xnew) # Only possible if we get NxMxM psi2 out of the code.
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la = self.posterior.woodbury_vector
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mu = np.dot(psi1_star, la) # TODO: dimensions?
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if full_cov:
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var = np.empty((Xnew.shape[0], la.shape[1], la.shape[1]))
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di = np.diag_indices(la.shape[1])
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else:
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var = np.empty((Xnew.shape[0], la.shape[1]))
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for i in range(Xnew.shape[0]):
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_mu, _var = Xnew.mean.values[[i]], Xnew.variance.values[[i]]
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psi2_star = self.kern.psi2(self.Z, NormalPosterior(_mu, _var))
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tmp = (psi2_star[:, :] - psi1_star[[i]].T.dot(psi1_star[[i]]))
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var_ = mdot(la.T, tmp, la)
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p0 = psi0_star[i]
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t = np.atleast_3d(self.posterior.woodbury_inv)
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t2 = np.trace(t.T.dot(psi2_star), axis1=1, axis2=2)
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if full_cov:
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var_[di] += p0
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var_[di] += -t2
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var[i] = var_
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else:
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var[i] = np.diag(var_)+p0-t2
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return mu, var
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