diff --git a/GPy/core/__init__.py b/GPy/core/__init__.py index 37c95ee8..39887284 100644 --- a/GPy/core/__init__.py +++ b/GPy/core/__init__.py @@ -6,6 +6,5 @@ from parameterization import priors from parameterization.parameterized import * from gp import GP from sparse_gp import SparseGP -from ..inference.latent_function_inference.fitc import FITC from svigp import SVIGP from mapping import * diff --git a/GPy/core/sparse_gp.py b/GPy/core/sparse_gp.py index 6c4da1af..2c0e7547 100644 --- a/GPy/core/sparse_gp.py +++ b/GPy/core/sparse_gp.py @@ -4,12 +4,12 @@ import numpy as np import pylab as pb from ..util.linalg import mdot, tdot, symmetrify, backsub_both_sides, chol_inv, dtrtrs, dpotrs, dpotri -from gp_base import GPBase -from GPy.core import Param +from gp import GP +from parameterization.param import Param -class SparseGP(GPBase): +class SparseGP(GP): """ - Variational sparse GP model + A general purpose Sparse GP model :param X: inputs :type X: np.ndarray (num_data x input_dim) @@ -19,17 +19,25 @@ class SparseGP(GPBase): :type kernel: a GPy.kern.kern instance :param X_variance: The uncertainty in the measurements of X (Gaussian variance) :type X_variance: np.ndarray (num_data x input_dim) | None - :param Z: inducing inputs (optional, see note) - :type Z: np.ndarray (num_inducing x input_dim) | None + :param Z: inducing inputs + :type Z: np.ndarray (num_inducing x input_dim) :param num_inducing: Number of inducing points (optional, default 10. Ignored if Z is not None) :type num_inducing: 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, name='sparse gp'): - GPBase.__init__(self, X, likelihood, kernel, normalize_X=normalize_X, name=name) + def __init__(self, X, Y, Z, kernel, likelihood, inference_method=None, X_variance=None, name='sparse gp'): + + #pick a sensible inference method + if inference_method is None: + if isinstance(likelihood, likelihoods.Gaussian): + inference_method = varDTC.Gaussian_inference() + else: + #inference_method = ?? + raise NotImplementedError, "what to do what to do?" + print "defaulting to ", inference_method, "for latent function inference" + + GP.__init__(self, X, Y, likelihood, inference_method, kernel, name) self.Z = Z self.num_inducing = Z.shape[0] @@ -42,39 +50,13 @@ class SparseGP(GPBase): self.has_uncertain_inputs = True self.X_variance = X_variance - if normalize_X: - self.Z = (self.Z.copy() - self._Xoffset) / self._Xscale - - # normalize X uncertainty also - if self.has_uncertain_inputs: - self.X_variance /= np.square(self._Xscale) - - self._const_jitter = None - self.Z = Param('inducing inputs', self.Z) self.add_parameter(self.Z, gradient=self.dL_dZ, index=0) self.add_parameter(self.kern, gradient=self.dL_dtheta) self.add_parameter(self.likelihood, gradient=lambda:self.likelihood._gradients(partial=self.partial_for_likelihood)) - #self.Z.add_observer(self, lambda Z: self._compute_kernel_matrices() or self._computations()) - def getstate(self): - """ - Get the current state of the class, - here just all the indices, rest can get recomputed - """ - return GPBase.getstate(self) + [self.Z, - self.num_inducing, - self.has_uncertain_inputs, - self.X_variance] - def setstate(self, state): - self.X_variance = state.pop() - self.has_uncertain_inputs = state.pop() - self.num_inducing = state.pop() - self.Z = state.pop() - GPBase.setstate(self, state) - - def _compute_kernel_matrices(self): + def parameters_changed(self): # kernel computations, using BGPLVM notation self.Kmm = self.kern.K(self.Z) if self.has_uncertain_inputs: @@ -85,35 +67,11 @@ class SparseGP(GPBase): self.psi0 = self.kern.Kdiag(self.X) self.psi1 = self.kern.K(self.X, self.Z) self.psi2 = None - def parameters_changed(self): - self._compute_kernel_matrices() - self._computations() - self.Cpsi1V = None - self.dL_dK = self.dL_dKmm + + self.posterior = self.inference_method.inference(??) super(SparseGP, self).parameters_changed() - def update_likelihood_approximation(self, **kwargs): - """ - 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() - 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.T, diag_tr_psi2Kmmi, **kwargs) # 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.T, **kwargs) - # self.likelihood.fit_FITC(self.Kmm,self.psi1,self.psi0) - self._set_params(self._get_params()) # update the GP - def dL_dtheta(self): """ Compute and return the derivative of the log marginal likelihood wrt the parameters of the kernel @@ -143,82 +101,14 @@ class SparseGP(GPBase): 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 or likelihood function + Make a prediction for the latent function values """ - - Bi, _ = 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.num_inducing) - Bi) - - if self.Cpsi1V is None: - psi1V = np.dot(self.psi1.T, self.likelihood.V) - tmp, _ = dtrtrs(self._Lm, np.asfortranarray(psi1V), lower=1, trans=0) - tmp, _ = dpotrs(self.LB, tmp, lower=1) - self.Cpsi1V, _ = dtrtrs(self._Lm, tmp, lower=1, trans=1) - - 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, **likelihood_args): - """ - 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.input_dim - :param X_variance_new: The uncertainty in the prediction points - :type X_variance_new: np.ndarray, Nnew x self.input_dim - :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 full covariance matrix, or just the diagonal - :type full_cov: bool - :rtype: posterior mean, a Numpy array, Nnew x self.input_dim - :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.input_dim - - - If full_cov and self.input_dim > 1, the return shape of var is Nnew x Nnew x self.input_dim. If self.input_dim == 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._Xoffset) / self._Xscale - if X_variance_new is not None: - X_variance_new = X_variance_new / self._Xscale ** 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, **likelihood_args) - - return mean, var, _025pm, _975pm + #TODO!!! def plot_f(self, samples=0, plot_limits=None, which_data='all', which_parts='all', resolution=None, full_cov=False, fignum=None, ax=None): """ - Plot the GP's view of the world, where the data is normalized and the + Plot the belief in the latent function, the "GP's view of the world" - 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 - Not implemented in higher dimensions @@ -249,12 +139,11 @@ class SparseGP(GPBase): if which_data is 'all': which_data = slice(None) - GPBase.plot_f(self, samples=samples, plot_limits=plot_limits, which_data='all', which_parts='all', resolution=resolution, full_cov=full_cov, fignum=fignum, ax=ax) + GP.plot_f(self, samples=samples, plot_limits=plot_limits, which_data='all', which_parts='all', resolution=resolution, full_cov=full_cov, fignum=fignum, ax=ax) if self.X.shape[1] == 1: if self.has_uncertain_inputs: - Xu = self.X * self._Xscale + self._Xoffset # NOTE self.X are the normalized values now - ax.errorbar(Xu[which_data, 0], self.likelihood.data[which_data, 0], + ax.errorbar(self.X[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._Xscale + self._Xoffset @@ -264,7 +153,6 @@ class SparseGP(GPBase): Zu = self.Z * self._Xscale + self._Xoffset ax.plot(Zu[:, 0], Zu[:, 1], 'wo') - else: raise NotImplementedError, "Cannot define a frame with more than two input dimensions" @@ -277,12 +165,11 @@ class SparseGP(GPBase): if which_data is 'all': which_data = slice(None) - GPBase.plot(self, samples=samples, plot_limits=plot_limits, which_data='all', which_parts='all', resolution=resolution, levels=20, fignum=fignum, ax=ax) + GP.plot(self, samples=samples, plot_limits=plot_limits, which_data='all', which_parts='all', resolution=resolution, levels=20, fignum=fignum, ax=ax) if self.X.shape[1] == 1: if self.has_uncertain_inputs: - Xu = self.X * self._Xscale + self._Xoffset # NOTE self.X are the normalized values now - ax.errorbar(Xu[which_data, 0], self.likelihood.data[which_data, 0], + ax.errorbar(self.X[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._Xscale + self._Xoffset @@ -296,145 +183,20 @@ class SparseGP(GPBase): else: raise NotImplementedError, "Cannot define a frame with more than two input dimensions" - def predict_single_output(self, Xnew, output=0, which_parts='all', full_cov=False): + def getstate(self): """ - For a specific output, predict the function at the new point(s) Xnew. - - :param Xnew: The points at which to make a prediction - :type Xnew: np.ndarray, Nnew x self.input_dim - :param output: output to predict - :type output: integer in {0,..., num_outputs-1} - :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 full covariance matrix, or just the diagonal - :type full_cov: bool - :rtype: posterior mean, a Numpy array, Nnew x self.input_dim - :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.input_dim - - .. Note:: For multiple output models only + Get the current state of the class, + here just all the indices, rest can get recomputed """ + return GP.getstate(self) + [self.Z, + self.num_inducing, + self.has_uncertain_inputs, + self.X_variance] - assert hasattr(self,'multioutput') - index = np.ones_like(Xnew)*output - Xnew = np.hstack((Xnew,index)) + def setstate(self, state): + self.X_variance = state.pop() + self.has_uncertain_inputs = state.pop() + self.num_inducing = state.pop() + self.Z = state.pop() + GP.setstate(self, state) - # normalize X values - Xnew = (Xnew.copy() - self._Xoffset) / self._Xscale - 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, noise_model = output) - return mean, var, _025pm, _975pm - - def _raw_predict_single_output(self, _Xnew, output=0, X_variance_new=None, which_parts='all', full_cov=False,stop=False): - """ - Internal helper function for making predictions for a specific output, - does not account for normalization or likelihood - --------- - - :param Xnew: The points at which to make a prediction - :type Xnew: np.ndarray, Nnew x self.input_dim - :param output: output to predict - :type output: integer in {0,..., num_outputs-1} - :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 full covariance matrix, or just the diagonal - - .. Note:: For multiple output models only - """ - Bi, _ = 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.num_inducing) - Bi) - - if self.Cpsi1V is None: - psi1V = np.dot(self.psi1.T,self.likelihood.V) - tmp, _ = dtrtrs(self._Lm, np.asfortranarray(psi1V), lower=1, trans=0) - tmp, _ = dpotrs(self.LB, tmp, lower=1) - self.Cpsi1V, _ = dtrtrs(self._Lm, tmp, lower=1, trans=1) - - assert hasattr(self,'multioutput') - index = np.ones_like(_Xnew)*output - _Xnew = np.hstack((_Xnew,index)) - - 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: - Kx = self.kern.psi1(self.Z, _Xnew, X_variance_new) - 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 plot_single_output_f(self, output=None, samples=0, plot_limits=None, which_data='all', which_parts='all', resolution=None, full_cov=False, fignum=None, ax=None): - - if ax is None: - fig = pb.figure(num=fignum) - ax = fig.add_subplot(111) - if fignum is None and ax is None: - fignum = fig.num - if which_data is 'all': - which_data = slice(None) - - GPBase.plot_single_output_f(self, output=output, samples=samples, plot_limits=plot_limits, which_data='all', which_parts='all', resolution=resolution, full_cov=full_cov, fignum=fignum, ax=ax) - - if self.X.shape[1] == 2: - if self.has_uncertain_inputs: - Xu = self.X * self._Xscale + self._Xoffset # NOTE self.X are the normalized values now - ax.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._Xscale + self._Xoffset - Zu = Zu[Zu[:,1]==output,0:1] - ax.plot(Zu[:,0], np.zeros_like(Zu[:,0]) + ax.get_ylim()[0], 'r|', mew=1.5, markersize=12) - - elif self.X.shape[1] == 2: - Zu = self.Z * self._Xscale + self._Xoffset - Zu = Zu[Zu[:,1]==output,0:2] - ax.plot(Zu[:, 0], Zu[:, 1], 'wo') - - - else: - raise NotImplementedError, "Cannot define a frame with more than two input dimensions" - - def plot_single_output(self, output=None, samples=0, plot_limits=None, which_data='all', which_parts='all', resolution=None, levels=20, fignum=None, ax=None): - if ax is None: - fig = pb.figure(num=fignum) - ax = fig.add_subplot(111) - if fignum is None and ax is None: - fignum = fig.num - if which_data is 'all': - which_data = slice(None) - - GPBase.plot_single_output(self, samples=samples, plot_limits=plot_limits, which_data='all', which_parts='all', resolution=resolution, levels=20, fignum=fignum, ax=ax, output=output) - - if self.X.shape[1] == 2: - if self.has_uncertain_inputs: - Xu = self.X * self._Xscale + self._Xoffset # NOTE self.X are the normalized values now - ax.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._Xscale + self._Xoffset - Zu = Zu[Zu[:,1]==output,0:1] - ax.plot(Zu, np.zeros_like(Zu) + ax.get_ylim()[0], 'r|', mew=1.5, markersize=12) - - elif self.X.shape[1] == 3: - Zu = self.Z * self._Xscale + self._Xoffset - Zu = Zu[Zu[:,1]==output,0:1] - ax.plot(Zu[:, 0], Zu[:, 1], 'wo') - - else: - raise NotImplementedError, "Cannot define a frame with more than two input dimensions"