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Merge branch 'devel' of github.com:SheffieldML/GPy into devel
This commit is contained in:
Ricardo
commit
afcb30dfbe
12 changed files with 186 additions and 202 deletions
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@ -16,9 +16,9 @@ class sparse_GP(GP):
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:param X: inputs
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:type X: np.ndarray (N x Q)
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:param likelihood: a likelihood instance, containing the observed data
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:type likelihood: GPy.likelihood.(Gaussian | EP)
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:param kernel : the kernel/covariance function. See link kernels
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:type kernel: a GPy kernel
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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 (N x Q) | None
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:param Z: inducing inputs (optional, see note)
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@ -30,8 +30,6 @@ class sparse_GP(GP):
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"""
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def __init__(self, X, likelihood, kernel, Z, X_variance=None, normalize_X=False):
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# self.scale_factor = 100.0 # a scaling factor to help keep the algorithm stable
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# self.auto_scale_factor = False
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self.Z = Z
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self.M = Z.shape[0]
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self.likelihood = likelihood
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@ -63,49 +61,29 @@ class sparse_GP(GP):
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self.psi2 = None
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def _computations(self):
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# sf = self.scale_factor
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# sf2 = sf ** 2
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# factor Kmm
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self.Lm = jitchol(self.Kmm)
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# The rather complex computations of self.A
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if self.likelihood.is_heteroscedastic:
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assert self.likelihood.D == 1 # TODO: what if the likelihood is heterscedatic and there are multiple independent outputs?
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if self.has_uncertain_inputs:
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# psi2_beta_scaled = (self.psi2 * (self.likelihood.precision.flatten().reshape(self.N, 1, 1) / sf2)).sum(0)
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psi2_beta_scaled = (self.psi2 * (self.likelihood.precision.flatten().reshape(self.N, 1, 1))).sum(0)
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evals, evecs = linalg.eigh(psi2_beta_scaled)
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clipped_evals = np.clip(evals, 0., 1e6) # TODO: make clipping configurable
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if not np.allclose(evals, clipped_evals):
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print "Warning: clipping posterior eigenvalues"
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tmp = evecs * np.sqrt(clipped_evals)
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tmp, _ = linalg.lapack.flapack.dtrtrs(self.Lm, np.asfortranarray(tmp), lower=1)
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self.A = tdot(tmp)
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if self.has_uncertain_inputs:
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if self.likelihood.is_heteroscedastic:
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psi2_beta = (self.psi2 * (self.likelihood.precision.flatten().reshape(self.N, 1, 1))).sum(0)
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else:
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# tmp = self.psi1 * (np.sqrt(self.likelihood.precision.flatten().reshape(1, self.N)) / sf)
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tmp = self.psi1 * (np.sqrt(self.likelihood.precision.flatten().reshape(1, self.N)))
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tmp, _ = linalg.lapack.flapack.dtrtrs(self.Lm, np.asfortranarray(tmp), lower=1)
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self.A = tdot(tmp)
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psi2_beta = self.psi2.sum(0) * self.likelihood.precision
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evals, evecs = linalg.eigh(psi2_beta)
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clipped_evals = np.clip(evals, 0., 1e6) # TODO: make clipping configurable
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tmp = evecs * np.sqrt(clipped_evals)
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else:
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if self.has_uncertain_inputs:
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# psi2_beta_scaled = (self.psi2 * (self.likelihood.precision / sf2)).sum(0)
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psi2_beta_scaled = (self.psi2 * (self.likelihood.precision)).sum(0)
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evals, evecs = linalg.eigh(psi2_beta_scaled)
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clipped_evals = np.clip(evals, 0., 1e15) # TODO: make clipping configurable
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if not np.allclose(evals, clipped_evals):
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print "Warning: clipping posterior eigenvalues"
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tmp = evecs * np.sqrt(clipped_evals)
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tmp, _ = linalg.lapack.flapack.dtrtrs(self.Lm, np.asfortranarray(tmp), lower=1)
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self.A = tdot(tmp)
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if self.likelihood.is_heteroscedastic:
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tmp = self.psi1 * (np.sqrt(self.likelihood.precision.flatten().reshape(1, self.N)))
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else:
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# tmp = self.psi1 * (np.sqrt(self.likelihood.precision) / sf)
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tmp = self.psi1 * (np.sqrt(self.likelihood.precision))
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tmp, _ = linalg.lapack.flapack.dtrtrs(self.Lm, np.asfortranarray(tmp), lower=1)
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self.A = tdot(tmp)
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tmp, _ = linalg.lapack.flapack.dtrtrs(self.Lm, np.asfortranarray(tmp), lower=1)
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self.A = tdot(tmp)
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# factor B
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# self.B = np.eye(self.M) / sf2 + self.A
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self.B = np.eye(self.M) + self.A
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self.LB = jitchol(self.B)
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@ -121,8 +99,6 @@ class sparse_GP(GP):
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# Compute dL_dKmm
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tmp = tdot(self._LBi_Lmi_psi1V)
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self.DBi_plus_BiPBi = backsub_both_sides(self.LB, self.D * np.eye(self.M) + tmp)
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# tmp = -0.5 * self.DBi_plus_BiPBi / sf2
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# tmp += -0.5 * self.B * sf2 * self.D
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tmp = -0.5 * self.DBi_plus_BiPBi
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tmp += -0.5 * self.B * self.D
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tmp += self.D * np.eye(self.M)
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@ -132,6 +108,7 @@ class sparse_GP(GP):
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self.dL_dpsi0 = -0.5 * self.D * (self.likelihood.precision * np.ones([self.N, 1])).flatten()
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self.dL_dpsi1 = np.dot(self.Cpsi1V, self.likelihood.V.T)
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dL_dpsi2_beta = 0.5 * backsub_both_sides(self.Lm, self.D * np.eye(self.M) - self.DBi_plus_BiPBi)
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if self.likelihood.is_heteroscedastic:
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if self.has_uncertain_inputs:
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self.dL_dpsi2 = self.likelihood.precision.flatten()[:, None, None] * dL_dpsi2_beta[None, :, :]
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@ -158,7 +135,6 @@ class sparse_GP(GP):
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else:
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# likelihood is not heterscedatic
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self.partial_for_likelihood = -0.5 * self.N * self.D * self.likelihood.precision + 0.5 * self.likelihood.trYYT * self.likelihood.precision ** 2
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# self.partial_for_likelihood += 0.5 * self.D * (self.psi0.sum() * self.likelihood.precision ** 2 - np.trace(self.A) * self.likelihood.precision * sf2)
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self.partial_for_likelihood += 0.5 * self.D * (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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@ -166,16 +142,12 @@ class sparse_GP(GP):
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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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if self.likelihood.is_heteroscedastic:
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A = -0.5 * self.N * self.D * 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.D * (np.sum(self.likelihood.precision.flatten() * self.psi0) - np.trace(self.A) * sf2)
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B = -0.5 * self.D * (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.N * self.D * (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.D * (np.sum(self.likelihood.precision * self.psi0) - np.trace(self.A) * sf2)
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B = -0.5 * self.D * (np.sum(self.likelihood.precision * self.psi0) - np.trace(self.A))
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# C = -self.D * (np.sum(np.log(np.diag(self.LB))) + 0.5 * self.M * np.log(sf2))
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C = -self.D * (np.sum(np.log(np.diag(self.LB)))) # + 0.5 * self.M * np.log(sf2))
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D = 0.5 * np.sum(np.square(self._LBi_Lmi_psi1V))
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return A + B + C + D
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@ -185,14 +157,6 @@ class sparse_GP(GP):
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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._compute_kernel_matrices()
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# if self.auto_scale_factor:
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# self.scale_factor = np.sqrt(self.psi2.sum(0).mean()*self.likelihood.precision)
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# if self.auto_scale_factor:
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# if self.likelihood.is_heteroscedastic:
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# self.scale_factor = max(100,np.sqrt(self.psi2_beta_scaled.sum(0).mean()))
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# else:
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# self.scale_factor = np.sqrt(self.psi2.sum(0).mean()*self.likelihood.precision)
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# self.scale_factor = 100.
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self._computations()
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def _get_params(self):
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@ -205,7 +169,7 @@ class sparse_GP(GP):
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"""
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Approximates a non-gaussian likelihood using Expectation Propagation
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For a Gaussian (or direct: TODO) likelihood, no iteration is required:
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For a Gaussian likelihood, no iteration is required:
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this function does nothing
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"""
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if self.has_uncertain_inputs:
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