mirror of
https://github.com/SheffieldML/GPy.git
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kern params adapted: Nparams > num_params and fixes of input_dim
This commit is contained in:
Max Zwiessele
parent
aa7fd122ca
commit
0490861099
42 changed files with 480 additions and 502 deletions
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@ -2,21 +2,14 @@
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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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import pylab as pb
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from ..util.linalg import mdot, jitchol, chol_inv, pdinv, trace_dot
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from ..util.plot import gpplot
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from .. import kern
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from scipy import stats, linalg
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<<<<<<< HEAD:GPy/models/generalized_FITC.py
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from sparse_GP import sparse_GP
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=======
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from ..core import SparseGP
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>>>>>>> 7040b26f41f382edfdca3d3f7b689b9bbfc1a54f:GPy/models/generalized_fitc.py
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from scipy import linalg
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from GPy.core.sparse_gp import SparseGP
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from GPy.util.linalg import mdot
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def backsub_both_sides(L,X):
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def backsub_both_sides(L, X):
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""" Return L^-T * X * L^-1, assumuing X is symmetrical and L is lower cholesky"""
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tmp,_ = linalg.lapack.flapack.dtrtrs(L,np.asfortranarray(X),lower=1,trans=1)
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return linalg.lapack.flapack.dtrtrs(L,np.asfortranarray(tmp.T),lower=1,trans=1)[0].T
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tmp, _ = linalg.lapack.flapack.dtrtrs(L, np.asfortranarray(X), lower=1, trans=1)
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return linalg.lapack.flapack.dtrtrs(L, np.asfortranarray(tmp.T), lower=1, trans=1)[0].T
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class GeneralizedFITC(SparseGP):
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@ -45,17 +38,13 @@ class GeneralizedFITC(SparseGP):
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self.num_inducing = self.Z.shape[0]
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self.true_precision = likelihood.precision
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<<<<<<< HEAD:GPy/models/generalized_FITC.py
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sparse_GP.__init__(self, X, likelihood, kernel=kernel, Z=self.Z, X_variance=None, normalize_X=False)
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=======
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super(GeneralizedFITC, self).__init__(X, likelihood, kernel=kernel, Z=self.Z, X_variance=X_variance, normalize_X=normalize_X)
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self._set_params(self._get_params())
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>>>>>>> 7040b26f41f382edfdca3d3f7b689b9bbfc1a54f:GPy/models/generalized_fitc.py
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def _set_params(self, p):
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self.Z = p[:self.num_inducing*self.input_dim].reshape(self.num_inducing, self.input_dim)
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self.kern._set_params(p[self.Z.size:self.Z.size+self.kern.Nparam])
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self.likelihood._set_params(p[self.Z.size+self.kern.Nparam:])
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self.Z = p[:self.num_inducing * self.input_dim].reshape(self.num_inducing, self.input_dim)
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self.kern._set_params(p[self.Z.size:self.Z.size + self.kern.num_params])
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self.likelihood._set_params(p[self.Z.size + self.kern.num_params:])
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self._compute_kernel_matrices()
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self._computations()
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self._FITC_computations()
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@ -73,9 +62,9 @@ class GeneralizedFITC(SparseGP):
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if self.has_uncertain_inputs:
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raise NotImplementedError, "FITC approximation not implemented for uncertain inputs"
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else:
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self.likelihood.fit_FITC(self.Kmm,self.psi1,self.psi0)
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self.likelihood.fit_FITC(self.Kmm, self.psi1, self.psi0)
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self.true_precision = self.likelihood.precision # Save the true precision
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self.likelihood.precision = self.true_precision/(1. + self.true_precision*self.Diag0[:,None]) # Add the diagonal element of the FITC approximation
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self.likelihood.precision = self.true_precision / (1. + self.true_precision * self.Diag0[:, None]) # Add the diagonal element of the FITC approximation
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self._set_params(self._get_params()) # update the GP
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def _FITC_computations(self):
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@ -87,37 +76,37 @@ class GeneralizedFITC(SparseGP):
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- removes the extra terms computed in the SparseGP approximation
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- computes the likelihood gradients wrt the true precision.
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"""
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#NOTE the true precison is now 'true_precision' not 'precision'
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# NOTE the true precison is now 'true_precision' not 'precision'
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if self.likelihood.is_heteroscedastic:
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# Compute generalized FITC's diagonal term of the covariance
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self.Lmi,info = linalg.lapack.flapack.dtrtrs(self.Lm,np.eye(self.num_inducing),lower=1)
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Lmipsi1 = np.dot(self.Lmi,self.psi1)
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self.Qnn = np.dot(Lmipsi1.T,Lmipsi1)
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#self.Kmmi, Lm, Lmi, Kmm_logdet = pdinv(self.Kmm)
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#self.Qnn = mdot(self.psi1.T,self.Kmmi,self.psi1)
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#a = kj
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self.Lmi, info = linalg.lapack.flapack.dtrtrs(self.Lm, np.eye(self.num_inducing), lower=1)
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Lmipsi1 = np.dot(self.Lmi, self.psi1)
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self.Qnn = np.dot(Lmipsi1.T, Lmipsi1)
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# self.Kmmi, Lm, Lmi, Kmm_logdet = pdinv(self.Kmm)
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# self.Qnn = mdot(self.psi1.T,self.Kmmi,self.psi1)
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# a = kj
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self.Diag0 = self.psi0 - np.diag(self.Qnn)
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Iplus_Dprod_i = 1./(1.+ self.Diag0 * self.true_precision.flatten())
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Iplus_Dprod_i = 1. / (1. + self.Diag0 * self.true_precision.flatten())
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self.Diag = self.Diag0 * Iplus_Dprod_i
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self.P = Iplus_Dprod_i[:,None] * self.psi1.T
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self.RPT0 = np.dot(self.Lmi,self.psi1)
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self.L = np.linalg.cholesky(np.eye(self.num_inducing) + np.dot(self.RPT0,((1. - Iplus_Dprod_i)/self.Diag0)[:,None]*self.RPT0.T))
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self.R,info = linalg.flapack.dtrtrs(self.L,self.Lmi,lower=1)
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self.RPT = np.dot(self.R,self.P.T)
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self.Sigma = np.diag(self.Diag) + np.dot(self.RPT.T,self.RPT)
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self.P = Iplus_Dprod_i[:, None] * self.psi1.T
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self.RPT0 = np.dot(self.Lmi, self.psi1)
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self.L = np.linalg.cholesky(np.eye(self.num_inducing) + np.dot(self.RPT0, ((1. - Iplus_Dprod_i) / self.Diag0)[:, None] * self.RPT0.T))
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self.R, info = linalg.lapack.dtrtrs(self.L, self.Lmi, lower=1)
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self.RPT = np.dot(self.R, self.P.T)
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self.Sigma = np.diag(self.Diag) + np.dot(self.RPT.T, self.RPT)
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self.w = self.Diag * self.likelihood.v_tilde
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self.Gamma = np.dot(self.R.T, np.dot(self.RPT,self.likelihood.v_tilde))
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self.mu = self.w + np.dot(self.P,self.Gamma)
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self.Gamma = np.dot(self.R.T, np.dot(self.RPT, self.likelihood.v_tilde))
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self.mu = self.w + np.dot(self.P, self.Gamma)
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# Remove extra term from dL_dpsi1
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self.dL_dpsi1 -= mdot(self.Lmi.T,Lmipsi1*self.likelihood.precision.flatten().reshape(1,self.N))
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#self.Kmmi, Lm, Lmi, Kmm_logdet = pdinv(self.Kmm)
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#self.dL_dpsi1 -= mdot(self.Kmmi,self.psi1*self.likelihood.precision.flatten().reshape(1,self.N)) #dB
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self.dL_dpsi1 -= mdot(self.Lmi.T, Lmipsi1 * self.likelihood.precision.flatten().reshape(1, self.N))
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# self.Kmmi, Lm, Lmi, Kmm_logdet = pdinv(self.Kmm)
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# self.dL_dpsi1 -= mdot(self.Kmmi,self.psi1*self.likelihood.precision.flatten().reshape(1,self.N)) #dB
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#########333333
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#self.Bi, self.LB, self.LBi, self.B_logdet = pdinv(self.B)
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# self.Bi, self.LB, self.LBi, self.B_logdet = pdinv(self.B)
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#########333333
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@ -125,54 +114,54 @@ class GeneralizedFITC(SparseGP):
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else:
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raise NotImplementedError, "homoscedastic fitc not implemented"
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# Remove extra term from dL_dpsi1
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#self.dL_dpsi1 += -mdot(self.Kmmi,self.psi1*self.likelihood.precision) #dB
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# self.dL_dpsi1 += -mdot(self.Kmmi,self.psi1*self.likelihood.precision) #dB
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sf = self.scale_factor
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sf2 = sf**2
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sf2 = sf ** 2
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# Remove extra term from dL_dKmm
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self.dL_dKmm += 0.5 * self.input_dim * mdot(self.Lmi.T, self.A, self.Lmi)*sf2 # dB
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self.dL_dKmm += 0.5 * self.input_dim * mdot(self.Lmi.T, self.A, self.Lmi) * sf2 # dB
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self.dL_dpsi0 = None
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#the partial derivative vector for the likelihood
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# the partial derivative vector for the likelihood
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if self.likelihood.Nparams == 0:
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self.partial_for_likelihood = None
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elif self.likelihood.is_heteroscedastic:
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raise NotImplementedError, "heteroscedastic derivates not implemented"
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else:
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raise NotImplementedError, "homoscedastic derivatives not implemented"
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#likelihood is not heterscedatic
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#self.partial_for_likelihood = - 0.5 * self.N*self.input_dim*self.likelihood.precision + 0.5 * np.sum(np.square(self.likelihood.Y))*self.likelihood.precision**2
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#self.partial_for_likelihood += 0.5 * self.input_dim * trace_dot(self.Bi,self.A)*self.likelihood.precision
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#self.partial_for_likelihood += self.likelihood.precision*(0.5*trace_dot(self.psi2_beta_scaled,self.E*sf2) - np.trace(self.Cpsi1VVpsi1))
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#TODO partial derivative vector for the likelihood not implemented
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# likelihood is not heterscedatic
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# self.partial_for_likelihood = - 0.5 * self.N*self.input_dim*self.likelihood.precision + 0.5 * np.sum(np.square(self.likelihood.Y))*self.likelihood.precision**2
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# self.partial_for_likelihood += 0.5 * self.input_dim * trace_dot(self.Bi,self.A)*self.likelihood.precision
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# self.partial_for_likelihood += self.likelihood.precision*(0.5*trace_dot(self.psi2_beta_scaled,self.E*sf2) - np.trace(self.Cpsi1VVpsi1))
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# TODO partial derivative vector for the likelihood not implemented
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def dL_dtheta(self):
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"""
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Compute and return the derivative of the log marginal likelihood wrt the parameters of the kernel
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"""
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dL_dtheta = self.kern.dK_dtheta(self.dL_dKmm,self.Z)
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dL_dtheta = self.kern.dK_dtheta(self.dL_dKmm, self.Z)
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if self.has_uncertain_inputs:
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raise NotImplementedError, "heteroscedatic derivates not implemented"
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else:
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#NOTE in SparseGP this would include the gradient wrt psi0
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dL_dtheta += self.kern.dK_dtheta(self.dL_dpsi1,self.Z,self.X)
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# NOTE in SparseGP this would include the gradient wrt psi0
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dL_dtheta += self.kern.dK_dtheta(self.dL_dpsi1, self.Z, self.X)
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return dL_dtheta
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def log_likelihood(self):
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""" Compute the (lower bound on the) log marginal likelihood """
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sf2 = self.scale_factor**2
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sf2 = self.scale_factor ** 2
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if self.likelihood.is_heteroscedastic:
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A = -0.5*self.N*self.input_dim*np.log(2.*np.pi) +0.5*np.sum(np.log(self.likelihood.precision)) -0.5*np.sum(self.V*self.likelihood.Y)
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A = -0.5 * self.N * self.input_dim * np.log(2.*np.pi) + 0.5 * np.sum(np.log(self.likelihood.precision)) - 0.5 * np.sum(self.V * self.likelihood.Y)
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else:
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A = -0.5*self.N*self.input_dim*(np.log(2.*np.pi) + np.log(self.likelihood._variance)) -0.5*self.likelihood.precision*self.likelihood.trYYT
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C = -self.input_dim * (np.sum(np.log(np.diag(self.LB))) + 0.5*self.num_inducing*np.log(sf2))
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#C = -0.5*self.input_dim * (self.B_logdet + self.num_inducing*np.log(sf2))
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D = 0.5*np.sum(np.square(self._LBi_Lmi_psi1V))
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#self.Cpsi1VVpsi1 = np.dot(self.Cpsi1V,self.psi1V.T)
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#D_ = 0.5*np.trace(self.Cpsi1VVpsi1)
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return A+C+D
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A = -0.5 * self.N * self.input_dim * (np.log(2.*np.pi) + np.log(self.likelihood._variance)) - 0.5 * self.likelihood.precision * self.likelihood.trYYT
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C = -self.input_dim * (np.sum(np.log(np.diag(self.LB))) + 0.5 * self.num_inducing * np.log(sf2))
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# C = -0.5*self.input_dim * (self.B_logdet + self.num_inducing*np.log(sf2))
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D = 0.5 * np.sum(np.square(self._LBi_Lmi_psi1V))
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# self.Cpsi1VVpsi1 = np.dot(self.Cpsi1V,self.psi1V.T)
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# D_ = 0.5*np.trace(self.Cpsi1VVpsi1)
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return A + C + D
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def _raw_predict(self, Xnew, which_parts, full_cov=False):
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if self.likelihood.is_heteroscedastic:
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@ -191,30 +180,30 @@ class GeneralizedFITC(SparseGP):
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# = I - [RPT0] * (U*U.T)^-1 * [RPT0].T
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# = I - V.T * V
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U = np.linalg.cholesky(np.diag(self.Diag0) + self.Qnn)
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V,info = linalg.flapack.dtrtrs(U,self.RPT0.T,lower=1)
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C = np.eye(self.num_inducing) - np.dot(V.T,V)
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mu_u = np.dot(C,self.RPT0)*(1./self.Diag0[None,:])
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#self.C = C
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#self.RPT0 = np.dot(self.R0,self.Knm.T) P0.T
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#self.mu_u = mu_u
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#self.U = U
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V, info = linalg.lapack.dtrtrs(U, self.RPT0.T, lower=1)
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C = np.eye(self.num_inducing) - np.dot(V.T, V)
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mu_u = np.dot(C, self.RPT0) * (1. / self.Diag0[None, :])
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# self.C = C
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# self.RPT0 = np.dot(self.R0,self.Knm.T) P0.T
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# self.mu_u = mu_u
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# self.U = U
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# q(u|y) = N(u| R0i*mu_H,R0i*Sigma_H*R0i.T)
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mu_H = np.dot(mu_u,self.mu)
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mu_H = np.dot(mu_u, self.mu)
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self.mu_H = mu_H
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Sigma_H = C + np.dot(mu_u,np.dot(self.Sigma,mu_u.T))
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Sigma_H = C + np.dot(mu_u, np.dot(self.Sigma, mu_u.T))
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# q(f_star|y) = N(f_star|mu_star,sigma2_star)
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Kx = self.kern.K(self.Z, Xnew, which_parts=which_parts)
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KR0T = np.dot(Kx.T,self.Lmi.T)
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mu_star = np.dot(KR0T,mu_H)
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KR0T = np.dot(Kx.T, self.Lmi.T)
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mu_star = np.dot(KR0T, mu_H)
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if full_cov:
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Kxx = self.kern.K(Xnew,which_parts=which_parts)
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var = Kxx + np.dot(KR0T,np.dot(Sigma_H - np.eye(self.num_inducing),KR0T.T))
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Kxx = self.kern.K(Xnew, which_parts=which_parts)
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var = Kxx + np.dot(KR0T, np.dot(Sigma_H - np.eye(self.num_inducing), KR0T.T))
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else:
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Kxx = self.kern.Kdiag(Xnew,which_parts=which_parts)
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Kxx_ = self.kern.K(Xnew,which_parts=which_parts) # TODO: RA, is this line needed?
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var_ = Kxx_ + np.dot(KR0T,np.dot(Sigma_H - np.eye(self.num_inducing),KR0T.T)) # TODO: RA, is this line needed?
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var = (Kxx + np.sum(KR0T.T*np.dot(Sigma_H - np.eye(self.num_inducing),KR0T.T),0))[:,None]
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return mu_star[:,None],var
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Kxx = self.kern.Kdiag(Xnew, which_parts=which_parts)
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Kxx_ = self.kern.K(Xnew, which_parts=which_parts) # TODO: RA, is this line needed?
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var_ = Kxx_ + np.dot(KR0T, np.dot(Sigma_H - np.eye(self.num_inducing), KR0T.T)) # TODO: RA, is this line needed?
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var = (Kxx + np.sum(KR0T.T * np.dot(Sigma_H - np.eye(self.num_inducing), KR0T.T), 0))[:, None]
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return mu_star[:, None], var
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else:
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raise NotImplementedError, "homoscedastic fitc not implemented"
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"""
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@ -6,7 +6,7 @@ import numpy as np
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import pylab as pb
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import sys, pdb
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from .. import kern
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from ..core import model
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from ..core import Model
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from ..util.linalg import pdinv, PCA
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from ..core import GP
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from ..likelihoods import Gaussian
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@ -3,7 +3,7 @@ Created on 10 Apr 2013
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@author: Max Zwiessele
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'''
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from GPy.core import model
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from GPy.core import Model
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from GPy.core import SparseGP
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from GPy.util.linalg import PCA
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import numpy
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@ -12,7 +12,7 @@ import pylab
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from GPy.kern.kern import kern
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from GPy.models.bayesian_gplvm import BayesianGPLVM
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class MRD(model):
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class MRD(Model):
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"""
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Do MRD on given Datasets in Ylist.
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All Ys in likelihood_list are in [N x Dn], where Dn can be different per Yn,
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@ -78,7 +78,7 @@ class MRD(model):
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self.NQ = self.N * self.input_dim
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self.MQ = self.num_inducing * self.input_dim
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model.__init__(self) # @UndefinedVariable
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Model.__init__(self) # @UndefinedVariable
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self._set_params(self._get_params())
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@property
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