diff --git a/GPy/core/sparse_gp.py b/GPy/core/sparse_gp.py index d137ceff..a0b09564 100644 --- a/GPy/core/sparse_gp.py +++ b/GPy/core/sparse_gp.py @@ -31,7 +31,7 @@ class SparseGP(GP): """ - def __init__(self, X, Y, Z, kernel, likelihood, inference_method=None, name='sparse gp'): + def __init__(self, X, Y, Z, kernel, likelihood, inference_method=None, name='sparse gp', Y_metadata=None): #pick a sensible inference method if inference_method is None: @@ -45,7 +45,7 @@ class SparseGP(GP): self.Z = Param('inducing inputs', Z) self.num_inducing = Z.shape[0] - GP.__init__(self, X, Y, kernel, likelihood, inference_method=inference_method, name=name) + GP.__init__(self, X, Y, kernel, likelihood, inference_method=inference_method, name=name, Y_metadata=Y_metadata) self.add_parameter(self.Z, index=0) @@ -53,7 +53,7 @@ class SparseGP(GP): return isinstance(self.X, VariationalPosterior) def parameters_changed(self): - self.posterior, self._log_marginal_likelihood, self.grad_dict = self.inference_method.inference(self.kern, self.X, self.Z, self.likelihood, self.Y) + 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) self.likelihood.update_gradients(self.grad_dict['dL_dthetaL']) if isinstance(self.X, VariationalPosterior): #gradients wrt kernel @@ -75,7 +75,6 @@ class SparseGP(GP): target += self.kern.gradient self.kern.update_gradients_full(self.grad_dict['dL_dKmm'], self.Z, None) self.kern.gradient += target - #gradients wrt Z self.Z.gradient[:,self.kern.active_dims] = self.kern.gradients_X(self.grad_dict['dL_dKmm'], self.Z) self.Z.gradient[:,self.kern.active_dims] += self.kern.gradients_X(self.grad_dict['dL_dKnm'].T, self.Z, self.X) diff --git a/GPy/examples/coreg_example.py b/GPy/examples/coreg_example.py index 967758c6..8f4cfcc6 100644 --- a/GPy/examples/coreg_example.py +++ b/GPy/examples/coreg_example.py @@ -2,6 +2,55 @@ import numpy as np import pylab as pb import GPy pb.ion() +pb.close('all') + +X1 = np.arange(3)[:,None] +X2 = np.arange(4)[:,None] +I1 = np.zeros_like(X1) +I2 = np.ones_like(X2) + +_X = np.vstack([ X1, X2 ]) +_I = np.vstack([ I1, I2 ]) + +X = np.hstack([ _X, _I ]) + +Y1 = np.sin(X1/8.) +Y2 = np.cos(X2/8.) + +Bias = GPy.kern.Bias(1,active_dims=[0]) +Coreg = GPy.kern.Coregionalize(1,2,active_dims=[1]) +K = Bias.prod(Coreg,name='X') + +#K.coregion.W = 0 +#print K.coregion.W + +#print Bias.K(_X,_X) +#print K.K(X,X) + +#pb.matshow(K.K(X,X)) + + +Mlist = [GPy.kern.Matern32(1,lengthscale=20.,name="Mat")] +kern = GPy.util.multioutput.LCM(input_dim=1,num_outputs=2,kernels_list=Mlist,name='H') +kern.B.W = 0 +kern.B.kappa = 1. +#kern.B.W.fix() +#kern.B.kappa.fix() +#m = GPy.models.GPCoregionalizedRegression(X_list=[X1,X2], Y_list=[Y1,Y2], kernel=kern) +m = GPy.models.SparseGPCoregionalizedRegression(X_list=[X1], Y_list=[Y1], kernel=kern) +#m.optimize() +m.checkgrad(verbose=1) + +fig = pb.figure() +ax0 = fig.add_subplot(211) +ax1 = fig.add_subplot(212) +slices = GPy.util.multioutput.get_slices([Y1,Y2]) +m.plot(fixed_inputs=[(1,0)],which_data_rows=slices[0],ax=ax0) +#m.plot(fixed_inputs=[(1,1)],which_data_rows=slices[1],ax=ax1) + + + +""" X1 = 100 * np.random.rand(100)[:,None] X2 = 100 * np.random.rand(100)[:,None] @@ -28,3 +77,4 @@ slices = GPy.util.multioutput.get_slices([Y1,Y2]) m.plot(fixed_inputs=[(1,0)],which_data_rows=slices[0],ax=ax0) m.plot(fixed_inputs=[(1,1)],which_data_rows=slices[1],ax=ax1) +""" diff --git a/GPy/inference/latent_function_inference/dtc.py b/GPy/inference/latent_function_inference/dtc.py index 89140ce2..5ebc5e53 100644 --- a/GPy/inference/latent_function_inference/dtc.py +++ b/GPy/inference/latent_function_inference/dtc.py @@ -91,8 +91,12 @@ class vDTC(object): def __init__(self): self.const_jitter = 1e-6 - def inference(self, kern, X, Z, likelihood, Y): - #assert X_variance is None, "cannot use X_variance with DTC. Try varDTC." + def inference(self, kern, X, X_variance, Z, likelihood, Y): + assert X_variance is None, "cannot use X_variance with DTC. Try varDTC." + + #TODO: MAX! fix this! + from ...util.misc import param_to_array + Y = param_to_array(Y) num_inducing, _ = Z.shape num_data, output_dim = Y.shape @@ -105,14 +109,15 @@ class vDTC(object): Kmm = kern.K(Z) Knn = kern.Kdiag(X) Knm = kern.K(X, Z) - KnmY = np.dot(Knm.T,Y) + U = Knm + Uy = np.dot(U.T,Y) - #factor Kmm + #factor Kmm Kmmi, L, Li, _ = pdinv(Kmm) # Compute A - LiKmnbeta = np.dot(Li, Knm.T)*np.sqrt(beta) - A_ = tdot(LiKmnbeta) + LiUTbeta = np.dot(Li, U.T)*np.sqrt(beta) + A_ = tdot(LiUTbeta) trace_term = -0.5*(np.sum(Knn)*beta - np.trace(A_)) A = A_ + np.eye(num_inducing) @@ -120,7 +125,7 @@ class vDTC(object): LA = jitchol(A) # back substutue to get b, P, v - tmp, _ = dtrtrs(L, KnmY, lower=1) + tmp, _ = dtrtrs(L, Uy, lower=1) b, _ = dtrtrs(LA, tmp*beta, lower=1) tmp, _ = dtrtrs(LA, b, lower=1, trans=1) v, _ = dtrtrs(L, tmp, lower=1, trans=1) @@ -140,18 +145,19 @@ class vDTC(object): LAL = Li.T.dot(A).dot(Li) dL_dK = Kmmi - 0.5*(vvT_P + LAL) - # Compute dL_dKnm + # Compute dL_dU vY = np.dot(v.reshape(-1,1),Y.T) - dL_dKmn = vY - np.dot(vvT_P - Kmmi, Knm.T) - dL_dKmn *= beta + #dL_dU = vY - np.dot(vvT_P, U.T) + dL_dU = vY - np.dot(vvT_P - Kmmi, U.T) + dL_dU *= beta #compute dL_dR - Knmv = np.dot(Knm, v) - dL_dR = 0.5*(np.sum(Knm*np.dot(Knm,P), 1) - 1./beta + np.sum(np.square(Y), 1) - 2.*np.sum(Knmv*Y, 1) + np.sum(np.square(Knmv), 1) )*beta**2 + Uv = np.dot(U, v) + dL_dR = 0.5*(np.sum(U*np.dot(U,P), 1) - 1./beta + np.sum(np.square(Y), 1) - 2.*np.sum(Uv*Y, 1) + np.sum(np.square(Uv), 1) )*beta**2 dL_dR -=beta*trace_term/num_data dL_dthetaL = likelihood.exact_inference_gradients(dL_dR) - grad_dict = {'dL_dKmm': dL_dK, 'dL_dKdiag':np.zeros_like(Knn) + -0.5*beta, 'dL_dKnm':dL_dKmn.T, 'dL_dthetaL':dL_dthetaL} + grad_dict = {'dL_dKmm': dL_dK, 'dL_dKdiag':np.zeros_like(Knn) + -0.5*beta, 'dL_dKnm':dL_dU.T, 'dL_dthetaL':dL_dthetaL} #construct a posterior object post = Posterior(woodbury_inv=Kmmi-P, woodbury_vector=v, K=Kmm, mean=None, cov=None, K_chol=L) diff --git a/GPy/inference/latent_function_inference/exact_gaussian_inference.py b/GPy/inference/latent_function_inference/exact_gaussian_inference.py index ca1b92c6..95a15fcc 100644 --- a/GPy/inference/latent_function_inference/exact_gaussian_inference.py +++ b/GPy/inference/latent_function_inference/exact_gaussian_inference.py @@ -52,6 +52,6 @@ class ExactGaussianInference(object): dL_dK = 0.5 * (tdot(alpha) - Y.shape[1] * Wi) - dL_dthetaL = likelihood.exact_inference_gradients(np.diag(dL_dK)) + dL_dthetaL = likelihood.exact_inference_gradients(np.diag(dL_dK),Y_metadata) return Posterior(woodbury_chol=LW, woodbury_vector=alpha, K=K), log_marginal, {'dL_dK':dL_dK, 'dL_dthetaL':dL_dthetaL} diff --git a/GPy/inference/latent_function_inference/var_dtc.py b/GPy/inference/latent_function_inference/var_dtc.py index 97d54624..0401bde2 100644 --- a/GPy/inference/latent_function_inference/var_dtc.py +++ b/GPy/inference/latent_function_inference/var_dtc.py @@ -2,7 +2,7 @@ # Licensed under the BSD 3-clause license (see LICENSE.txt) from posterior import Posterior -from ...util.linalg import jitchol, backsub_both_sides, tdot, dtrtrs, dtrtri, dpotri, dpotrs, symmetrify +from ...util.linalg import mdot, jitchol, backsub_both_sides, tdot, dtrtrs, dtrtri, dpotri, dpotrs, symmetrify from ...util import diag from ...core.parameterization.variational import VariationalPosterior import numpy as np @@ -74,7 +74,7 @@ class VarDTC(object): trYYT = self.get_trYYT(Y) # do the inference: - het_noise = beta.size < 1 + het_noise = beta.size > 1 num_inducing = Z.shape[0] num_data = Y.shape[0] # kernel computations, using BGPLVM notation @@ -134,16 +134,16 @@ class VarDTC(object): # log marginal likelihood log_marginal = _compute_log_marginal_likelihood(likelihood, num_data, output_dim, beta, het_noise, - psi0, A, LB, trYYT, data_fit) + psi0, A, LB, trYYT, data_fit, Y) #put the gradients in the right places dL_dR = _compute_dL_dR(likelihood, het_noise, uncertain_inputs, LB, _LBi_Lmi_psi1Vf, DBi_plus_BiPBi, Lm, A, psi0, psi1, beta, - data_fit, num_data, output_dim, trYYT) + data_fit, num_data, output_dim, trYYT, Y) - dL_dthetaL = likelihood.exact_inference_gradients(dL_dR) + dL_dthetaL = likelihood.exact_inference_gradients(dL_dR,Y_metadata) if uncertain_inputs: grad_dict = {'dL_dKmm': dL_dKmm, @@ -387,7 +387,7 @@ def _compute_dL_dpsi(num_inducing, num_data, output_dim, beta, Lm, VVT_factor, C return dL_dpsi0, dL_dpsi1, dL_dpsi2 -def _compute_dL_dR(likelihood, het_noise, uncertain_inputs, LB, _LBi_Lmi_psi1Vf, DBi_plus_BiPBi, Lm, A, psi0, psi1, beta, data_fit, num_data, output_dim, trYYT): +def _compute_dL_dR(likelihood, het_noise, uncertain_inputs, LB, _LBi_Lmi_psi1Vf, DBi_plus_BiPBi, Lm, A, psi0, psi1, beta, data_fit, num_data, output_dim, trYYT, Y): # the partial derivative vector for the likelihood if likelihood.size == 0: # save computation here. @@ -396,19 +396,20 @@ def _compute_dL_dR(likelihood, het_noise, uncertain_inputs, LB, _LBi_Lmi_psi1Vf, if uncertain_inputs: raise NotImplementedError, "heteroscedatic derivates with uncertain inputs not implemented" else: - from ...util.linalg import chol_inv - LBi = chol_inv(LB) + #from ...util.linalg import chol_inv + #LBi = chol_inv(LB) + LBi, _ = dtrtrs(LB,np.eye(LB.shape[0])) + Lmi_psi1, nil = dtrtrs(Lm, psi1.T, lower=1, trans=0) _LBi_Lmi_psi1, _ = dtrtrs(LB, Lmi_psi1, lower=1, trans=0) - dL_dR = -0.5 * beta + 0.5 * likelihood.V**2 + dL_dR = -0.5 * beta + 0.5 * (beta*Y)**2 dL_dR += 0.5 * output_dim * (psi0 - np.sum(Lmi_psi1**2,0))[:,None] * beta**2 dL_dR += 0.5*np.sum(mdot(LBi.T,LBi,Lmi_psi1)*Lmi_psi1,0)[:,None]*beta**2 - dL_dR += -np.dot(_LBi_Lmi_psi1Vf.T,_LBi_Lmi_psi1).T * likelihood.Y * beta**2 + dL_dR += -np.dot(_LBi_Lmi_psi1Vf.T,_LBi_Lmi_psi1).T * Y * beta**2 dL_dR += 0.5*np.dot(_LBi_Lmi_psi1Vf.T,_LBi_Lmi_psi1).T**2 * beta**2 - else: # likelihood is not heteroscedatic dL_dR = -0.5 * num_data * output_dim * beta + 0.5 * trYYT * beta ** 2 @@ -416,11 +417,11 @@ def _compute_dL_dR(likelihood, het_noise, uncertain_inputs, LB, _LBi_Lmi_psi1Vf, dL_dR += beta * (0.5 * np.sum(A * DBi_plus_BiPBi) - data_fit) return dL_dR -def _compute_log_marginal_likelihood(likelihood, num_data, output_dim, beta, het_noise, psi0, A, LB, trYYT, data_fit): -#compute log marginal likelihood +def _compute_log_marginal_likelihood(likelihood, num_data, output_dim, beta, het_noise, psi0, A, LB, trYYT, data_fit,Y): + #compute log marginal likelihood if het_noise: - lik_1 = -0.5 * num_data * output_dim * np.log(2. * np.pi) + 0.5 * np.sum(np.log(beta)) - 0.5 * np.sum(likelihood.V * likelihood.Y) - lik_2 = -0.5 * output_dim * (np.sum(beta * psi0) - np.trace(A)) + lik_1 = -0.5 * num_data * output_dim * np.log(2. * np.pi) + 0.5 * np.sum(np.log(beta)) - 0.5 * np.sum(beta * Y**2) + lik_2 = -0.5 * output_dim * (np.sum(beta.flatten() * psi0) - np.trace(A)) else: lik_1 = -0.5 * num_data * output_dim * (np.log(2. * np.pi) - np.log(beta)) - 0.5 * beta * trYYT lik_2 = -0.5 * output_dim * (np.sum(beta * psi0) - np.trace(A)) diff --git a/GPy/likelihoods/gaussian.py b/GPy/likelihoods/gaussian.py index 79d62bb7..89ad4486 100644 --- a/GPy/likelihoods/gaussian.py +++ b/GPy/likelihoods/gaussian.py @@ -50,7 +50,11 @@ class Gaussian(Likelihood): if isinstance(gp_link, link_functions.Identity): self.log_concave = True - def gaussian_variance(self, Y, Y_metadata=None): + def betaY(self,Y,Y_metadata=None): + #TODO: ~Ricardo this does not live here + return Y/self.gaussian_variance(Y_metadata) + + def gaussian_variance(self, Y_metadata=None): return self.variance def update_gradients(self, grad): diff --git a/GPy/likelihoods/mixed_noise.py b/GPy/likelihoods/mixed_noise.py index bfcb5916..b4960f3a 100644 --- a/GPy/likelihoods/mixed_noise.py +++ b/GPy/likelihoods/mixed_noise.py @@ -18,6 +18,17 @@ class MixedNoise(Likelihood): self.likelihoods_list = likelihoods_list self.log_concave = False + def gaussian_variance(self, Y_metadata): + assert all([isinstance(l, Gaussian) for l in self.likelihoods_list]) + ind = Y_metadata['output_index'].flatten() + variance = np.zeros(ind.size) + for lik, j in zip(self.likelihoods_list, range(len(self.likelihoods_list))): + variance[ind==j] = lik.variance + return variance[:,None] + + def betaY(self,Y,Y_metadata): + return Y/self.gaussian_variance(Y_metadata=Y_metadata) + def update_gradients(self, gradients): self.gradient = gradients @@ -32,13 +43,9 @@ class MixedNoise(Likelihood): _variance = np.array([self.likelihoods_list[j].variance for j in ind ]) if full_cov: var += np.eye(var.shape[0])*_variance - #d = 2*np.sqrt(np.diag(var)) - #low, up = mu - d, mu + d else: var += _variance - #d = 2*np.sqrt(var) - #low, up = mu - d, mu + d - return mu, var#, low, up + return mu, var else: raise NotImplementedError @@ -51,12 +58,13 @@ class MixedNoise(Likelihood): def covariance_matrix(self, Y, Y_metadata): - assert all([isinstance(l, Gaussian) for l in self.likelihoods_list]) - ind = Y_metadata['output_index'].flatten() - variance = np.zeros(Y.shape[0]) - for lik, j in zip(self.likelihoods_list, range(len(self.likelihoods_list))): - variance[ind==j] = lik.variance - return np.diag(variance) + #assert all([isinstance(l, Gaussian) for l in self.likelihoods_list]) + #ind = Y_metadata['output_index'].flatten() + #variance = np.zeros(Y.shape[0]) + #for lik, j in zip(self.likelihoods_list, range(len(self.likelihoods_list))): + # variance[ind==j] = lik.variance + #return np.diag(variance) + return np.diag(self.gaussian_variance(Y_metadata).flatten()) def samples(self, gp, Y_metadata): diff --git a/GPy/models/__init__.py b/GPy/models/__init__.py index 34e5a17e..d0988c9e 100644 --- a/GPy/models/__init__.py +++ b/GPy/models/__init__.py @@ -15,4 +15,5 @@ from mrd import MRD from gradient_checker import GradientChecker from ss_gplvm import SSGPLVM from gp_coregionalized_regression import GPCoregionalizedRegression +from sparse_gp_coregionalized_regression import SparseGPCoregionalizedRegression #.py file not included!!! #from sparse_gp_coregionalized_regression import SparseGPCoregionalizedRegression diff --git a/GPy/models/sparse_gp_coregionalized_regression.py b/GPy/models/sparse_gp_coregionalized_regression.py new file mode 100644 index 00000000..a97696d2 --- /dev/null +++ b/GPy/models/sparse_gp_coregionalized_regression.py @@ -0,0 +1,66 @@ +# Copyright (c) 2012 - 2014 the GPy Austhors (see AUTHORS.txt) +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +import numpy as np +from ..core import SparseGP +from ..inference.latent_function_inference import VarDTC +from .. import likelihoods +from .. import kern +from .. import util + +class SparseGPCoregionalizedRegression(SparseGP): + """ + Sparse Gaussian Process model for heteroscedastic multioutput regression + + This is a thin wrapper around the SparseGP class, with a set of sensible defaults + + :param X_list: list of input observations corresponding to each output + :type X_list: list of numpy arrays + :param Y_list: list of observed values related to the different noise models + :type Y_list: list of numpy arrays + :param Z_list: list of inducing inputs (optional) + :type Z_list: empty list | list of numpy arrays + :param kernel: a GPy kernel, defaults to RBF ** Coregionalized + :type kernel: None | GPy.kernel defaults + :likelihoods_list: a list of likelihoods, defaults to list of Gaussian likelihoods + :type likelihoods_list: None | a list GPy.likelihoods + :param num_inducing: number of inducing inputs, defaults to 10 per output (ignored if Z_list is not empty) + :type num_inducing: integer | list of integers + + :param name: model name + :type name: string + :param W_rank: number tuples of the corregionalization parameters 'W' (see coregionalize kernel documentation) + :type W_rank: integer + :param kernel_name: name of the kernel + :type kernel_name: string + """ + + def __init__(self, X_list, Y_list, Z_list=[], kernel=None, likelihoods_list=None, num_inducing=10, X_variance=None, name='SGPCR',W_rank=1,kernel_name='X'): + + #Input and Output + X,Y,self.output_index = util.multioutput.build_XY(X_list,Y_list) + Ny = len(Y_list) + + #Kernel + if kernel is None: + kernel = util.multioutput.ICM(input_dim=X.shape[1]-1, num_outputs=Ny, kernel=GPy.kern.rbf(X.shape[1]-1), W_rank=1,name=kernel_name) + + #Likelihood + likelihood = util.multioutput.build_likelihood(Y_list,self.output_index,likelihoods_list) + + #Inducing inputs list + if len(Z_list): + assert len(Z_list) == self.output_dim, 'Number of outputs do not match length of inducing inputs list.' + else: + if isinstance(num_inducing,np.int): + num_inducing = [num_inducing] * Ny + num_inducing = np.asarray(num_inducing) + assert num_inducing.size == Ny, 'Number of outputs do not match length of inducing inputs list.' + for ni,Xi in zip(num_inducing,X_list): + i = np.random.permutation(Xi.shape[0])[:ni] + Z_list.append(Xi[i].copy()) + + Z, _, Iz = util.multioutput.build_XY(Z_list) + + super(SparseGPCoregionalizedRegression, self).__init__(X, Y, Z, kernel, likelihood, inference_method=VarDTC(), Y_metadata={'output_index':self.output_index}) + self['.*inducing'][:,-1].fix() diff --git a/GPy/plotting/matplot_dep/models_plots.py b/GPy/plotting/matplot_dep/models_plots.py index ae79569b..cbb213b1 100644 --- a/GPy/plotting/matplot_dep/models_plots.py +++ b/GPy/plotting/matplot_dep/models_plots.py @@ -7,6 +7,7 @@ import Tango from base_plots import gpplot, x_frame1D, x_frame2D from ...util.misc import param_to_array from ...models.gp_coregionalized_regression import GPCoregionalizedRegression +from ...models.sparse_gp_coregionalized_regression import SparseGPCoregionalizedRegression def plot_fit(model, plot_limits=None, which_data_rows='all', @@ -86,7 +87,10 @@ def plot_fit(model, plot_limits=None, which_data_rows='all', lower = m - 2*np.sqrt(v) upper = m + 2*np.sqrt(v) else: - meta = {'output_index': Xgrid[:,-1:].astype(np.int)} if isinstance(model,GPCoregionalizedRegression) else None + if isinstance(model,GPCoregionalizedRegression) or isinstance(model,SparseGPCoregionalizedRegression): + meta = {'output_index': Xgrid[:,-1:].astype(np.int)} + else: + meta = None m, v = model.predict(Xgrid, full_cov=False, Y_metadata=meta) lower, upper = model.predict_quantiles(Xgrid, Y_metadata=meta)