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110 lines
4.6 KiB
Python
110 lines
4.6 KiB
Python
# Copyright (c) 2012, 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 ..util.linalg import mdot
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from gp import GP
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from parameterization.param import Param
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from GPy.inference.latent_function_inference import var_dtc
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from .. import likelihoods
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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, X_variance=None, name='sparse gp'):
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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()
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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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self.X_variance = X_variance
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if self.has_uncertain_inputs():
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assert X_variance.shape == X.shape
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GP.__init__(self, X, Y, kernel, likelihood, inference_method=inference_method, name=name)
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self.add_parameter(self.Z, index=0)
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self.parameters_changed()
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def has_uncertain_inputs(self):
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return not (self.X_variance is None)
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def parameters_changed(self):
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if self.has_uncertain_inputs():
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self.posterior, self._log_marginal_likelihood, self.grad_dict = self.inference_method.inference_latent(self.kern, self.q, self.Z, self.likelihood, self.Y)
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else:
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self.posterior, self._log_marginal_likelihood, self.grad_dict = self.inference_method.inference(self.kern, self.X, self.X_variance, self.Z, self.likelihood, self.Y)
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self.likelihood.update_gradients(self.grad_dict.pop('partial_for_likelihood'))
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if self.has_uncertain_inputs():
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self.kern.update_gradients_variational(posterior_variational=self.q, Z=self.Z, **self.grad_dict)
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self.Z.gradient = self.kern.gradients_Z_variational(posterior_variational=self.q, Z=self.Z, **self.grad_dict)
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else:
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self.kern.update_gradients_sparse(X=self.X, Z=self.Z, **self.grad_dict)
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self.Z.gradient = self.kern.gradients_Z_sparse(X=self.X, Z=self.Z, **self.grad_dict)
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def _raw_predict(self, Xnew, X_variance_new=None, full_cov=False):
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"""
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Make a prediction for the latent function values
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"""
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if X_variance_new is None:
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Kx = self.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 = self.kern.K(Xnew)
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var = Kxx - mdot(Kx.T, self.posterior.woodbury_inv, Kx)
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else:
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Kxx = self.kern.Kdiag(Xnew)
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var = Kxx - np.sum(Kx * np.dot(self.posterior.woodbury_inv, 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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def _getstate(self):
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"""
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Get the current state of the class,
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here just all the indices, rest can get recomputed
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"""
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return GP._getstate(self) + [self.Z,
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self.num_inducing,
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self.X_variance]
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def _setstate(self, state):
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self.X_variance = state.pop()
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self.num_inducing = state.pop()
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self.Z = state.pop()
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GP._setstate(self, state)
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