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changes to the efficiency of the sparse GP when there are many outputs
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James Hensman
parent
5f1445bf04
commit
0c12641eca
3 changed files with 32 additions and 12 deletions
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@ -63,6 +63,7 @@ class SparseGP(GPBase):
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def _computations(self):
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# factor Kmm
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self.Lm = jitchol(self.Kmm)
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@ -89,17 +90,18 @@ class SparseGP(GPBase):
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self.B = np.eye(self.num_inducing) + self.A
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self.LB = jitchol(self.B)
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# TODO: make a switch for either first compute psi1V, or VV.T
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self.psi1V = np.dot(self.psi1.T, self.likelihood.V)
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#VVT_factor is a matrix such that tdot(VVT_factor) = VVT...this is for efficiency!
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self.psi1Vf = np.dot(self.psi1.T, self.likelihood.VVT_factor)
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# back substutue C into psi1V
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tmp, info1 = dtrtrs(self.Lm, np.asfortranarray(self.psi1V), lower=1, trans=0)
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self._LBi_Lmi_psi1V, _ = dtrtrs(self.LB, np.asfortranarray(tmp), lower=1, trans=0)
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# back substutue C into psi1Vf
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tmp, info1 = dtrtrs(self.Lm, np.asfortranarray(self.psi1Vf), lower=1, trans=0)
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self._LBi_Lmi_psi1Vf, _ = dtrtrs(self.LB, np.asfortranarray(tmp), lower=1, trans=0)
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tmp, info2 = dpotrs(self.LB, tmp, lower=1)
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self.Cpsi1V, info3 = dtrtrs(self.Lm, tmp, lower=1, trans=1)
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self.Cpsi1Vf, info3 = dtrtrs(self.Lm, tmp, lower=1, trans=1)
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# Compute dL_dKmm
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tmp = tdot(self._LBi_Lmi_psi1V)
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tmp = tdot(self._LBi_Lmi_psi1Vf)
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self.data_fit = np.trace(tmp)
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self.DBi_plus_BiPBi = backsub_both_sides(self.LB, self.output_dim * np.eye(self.num_inducing) + tmp)
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tmp = -0.5 * self.DBi_plus_BiPBi
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tmp += -0.5 * self.B * self.output_dim
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@ -108,7 +110,7 @@ class SparseGP(GPBase):
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# Compute dL_dpsi # FIXME: this is untested for the heterscedastic + uncertain inputs case
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self.dL_dpsi0 = -0.5 * self.output_dim * (self.likelihood.precision * np.ones([self.num_data, 1])).flatten()
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self.dL_dpsi1 = np.dot(self.Cpsi1V, self.likelihood.V.T).T
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self.dL_dpsi1 = np.dot(self.likelihood.VVT_factor, self.Cpsi1Vf.T)
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dL_dpsi2_beta = 0.5 * backsub_both_sides(self.Lm, self.output_dim * np.eye(self.num_inducing) - self.DBi_plus_BiPBi)
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if self.likelihood.is_heteroscedastic:
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@ -138,18 +140,18 @@ class SparseGP(GPBase):
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# likelihood is not heterscedatic
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self.partial_for_likelihood = -0.5 * self.num_data * self.output_dim * self.likelihood.precision + 0.5 * self.likelihood.trYYT * self.likelihood.precision ** 2
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self.partial_for_likelihood += 0.5 * self.output_dim * (self.psi0.sum() * self.likelihood.precision ** 2 - np.trace(self.A) * self.likelihood.precision)
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self.partial_for_likelihood += self.likelihood.precision * (0.5 * np.sum(self.A * self.DBi_plus_BiPBi) - np.sum(np.square(self._LBi_Lmi_psi1V)))
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self.partial_for_likelihood += self.likelihood.precision * (0.5 * np.sum(self.A * self.DBi_plus_BiPBi) - self.data_fit)
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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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if self.likelihood.is_heteroscedastic:
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A = -0.5 * self.num_data * self.output_dim * np.log(2.*np.pi) + 0.5 * np.sum(np.log(self.likelihood.precision)) - 0.5 * np.sum(self.likelihood.V * self.likelihood.Y)
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A = -0.5 * self.num_data * self.output_dim * np.log(2.*np.pi) + 0.5 * np.sum(np.log(self.likelihood.precision)) - 0.5 * np.sum(self.likelihood.V*self.likelihood.Y)
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B = -0.5 * self.output_dim * (np.sum(self.likelihood.precision.flatten() * self.psi0) - np.trace(self.A))
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else:
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A = -0.5 * self.num_data * self.output_dim * (np.log(2.*np.pi) - np.log(self.likelihood.precision)) - 0.5 * self.likelihood.precision * self.likelihood.trYYT
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B = -0.5 * self.output_dim * (np.sum(self.likelihood.precision * self.psi0) - np.trace(self.A))
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C = -self.output_dim * (np.sum(np.log(np.diag(self.LB)))) # + 0.5 * 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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D = 0.5 * self.data_fit
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return A + B + C + D + self.likelihood.Z
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def _set_params(self, p):
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@ -158,6 +160,7 @@ class SparseGP(GPBase):
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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.Cpsi1V = None
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def _get_params(self):
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return np.hstack([self.Z.flatten(), self.kern._get_params_transformed(), self.likelihood._get_params()])
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@ -224,6 +227,14 @@ class SparseGP(GPBase):
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symmetrify(Bi)
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Kmmi_LmiBLmi = backsub_both_sides(self.Lm, np.eye(self.num_inducing) - Bi)
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if self.Cpsi1V is None:
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psi1V = np.dot(self.psi1.T,self.likelihood.V)
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tmp, _ = dtrtrs(self.Lm, np.asfortranarray(psi1V), lower=1, trans=0)
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tmp, _ = dpotrs(self.LB, tmp, lower=1)
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self.Cpsi1V, _ = dtrtrs(self.Lm, tmp, lower=1, trans=1)
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if X_variance_new is None:
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Kx = self.kern.K(self.Z, Xnew, which_parts=which_parts)
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mu = np.dot(Kx.T, self.Cpsi1V)
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@ -34,6 +34,8 @@ class EP(likelihood):
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self.Z = 0
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self.YYT = None
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self.V = self.precision * self.Y
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self.VVT_factor = self.V
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self.trYYT = 0.
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def restart(self):
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self.tau_tilde = np.zeros(self.N)
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@ -44,6 +46,8 @@ class EP(likelihood):
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self.Z = 0
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self.YYT = None
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self.V = self.precision * self.Y
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self.VVT_factor = self.V
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self.trYYT = 0.
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def predictive_values(self,mu,var,full_cov):
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if full_cov:
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@ -71,6 +75,8 @@ class EP(likelihood):
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self.covariance_matrix = np.diag(1./self.tau_tilde)
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self.precision = self.tau_tilde[:,None]
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self.V = self.precision * self.Y
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self.VVT_factor = self.V
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self.trYYT = np.trace(self.YYT)
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def fit_full(self,K):
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"""
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@ -40,9 +40,11 @@ class Gaussian(likelihood):
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if D > self.N:
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self.YYT = np.dot(self.Y, self.Y.T)
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self.trYYT = np.trace(self.YYT)
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self.YYT_factor = jitchol(self.YYT)
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else:
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self.YYT = None
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self.trYYT = np.sum(np.square(self.Y))
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self.YYT_factor = self.Y
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def _get_params(self):
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return np.asarray(self._variance)
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@ -53,12 +55,13 @@ class Gaussian(likelihood):
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def _set_params(self, x):
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x = np.float64(x)
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if np.all(self._variance != x):
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if x == 0.:
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if x == 0.:#special case of zero noise
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self.precision = np.inf
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self.V = None
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else:
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self.precision = 1. / x
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self.V = (self.precision) * self.Y
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self.VVT_factor = self.precision * self.YYT_factor
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self.covariance_matrix = np.eye(self.N) * x
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self._variance = x
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