mirror of
https://github.com/SheffieldML/GPy.git
synced 2026-05-24 14:15:14 +02:00
everything is broken
This commit is contained in:
James Hensman
parent
de51ad638a
commit
d636c8c30c
13 changed files with 325 additions and 323 deletions
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@ -1,7 +1,7 @@
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from _src.rbf import RBF
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from _src.white import White
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from _src.kern import Kern
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Linear = 'foo'
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from _src.linear import Linear
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#import bias
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#import Brownian
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#import coregionalize
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@ -34,7 +34,7 @@ class Add(Kern):
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:param X: the first set of inputs to the kernel
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:param X2: (optional) the second set of arguments to the kernel. If X2
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is None, this is passed throgh to the 'part' object, which
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handles this as X2 == X.
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handLes this as X2 == X.
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"""
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assert X.shape[1] == self.input_dim
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if X2 is None:
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@ -48,9 +48,6 @@ class Add(Kern):
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def update_gradients_sparse(self, dL_dKmm, dL_dKnm, dL_dKdiag, X, Z):
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[p.update_gradients_sparse(dL_dKmm, dL_dKnm, dL_dKdiag, X[:,i_s], Z[:,i_s]) for p, i_s in zip(self._parameters_, self.input_slices)]
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def update_gradients_variational(self, dL_dKmm, dL_dpsi0, dL_dpsi1, dL_dpsi2, mu, S, Z):
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[p.update_gradients_variational(dL_dKmm, dL_dpsi0, dL_dpsi1, dL_dpsi2, mu, S, Z) for p in self._parameters_]
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def gradients_X(self, dL_dK, X, X2=None):
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"""Compute the gradient of the objective function with respect to X.
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@ -69,123 +66,125 @@ class Add(Kern):
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return target
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def Kdiag(self, X):
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"""Compute the diagonal of the covariance function for inputs X."""
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assert X.shape[1] == self.input_dim
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return sum([p.Kdiag(X[:, i_s]) for p, i_s in zip(self._parameters_, self.input_slices)])
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def psi0(self, Z, mu, S):
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target = np.zeros(mu.shape[0])
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[p.psi0(Z[:, i_s], mu[:, i_s], S[:, i_s], target) for p, i_s in zip(self._parameters_, self.input_slices)]
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return target
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def dpsi0_dtheta(self, dL_dpsi0, Z, mu, S):
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target = np.zeros(self.size)
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[p.dpsi0_dtheta(dL_dpsi0, Z[:, i_s], mu[:, i_s], S[:, i_s], target[ps]) for p, ps, i_s in zip(self._parameters_, self._param_slices_, self.input_slices)]
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return self._transform_gradients(target)
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def dpsi0_dmuS(self, dL_dpsi0, Z, mu, S):
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target_mu, target_S = np.zeros_like(mu), np.zeros_like(S)
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[p.dpsi0_dmuS(dL_dpsi0, Z[:, i_s], mu[:, i_s], S[:, i_s], target_mu[:, i_s], target_S[:, i_s]) for p, i_s in zip(self._parameters_, self.input_slices)]
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return target_mu, target_S
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return np.sum([p.psi0(Z[:, i_s], mu[:, i_s], S[:, i_s]) for p, i_s in zip(self._parameters_, self.input_slices))],0)
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def psi1(self, Z, mu, S):
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target = np.zeros((mu.shape[0], Z.shape[0]))
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[p.psi1(Z[:, i_s], mu[:, i_s], S[:, i_s], target) for p, i_s in zip(self._parameters_, self.input_slices)]
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return target
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def dpsi1_dtheta(self, dL_dpsi1, Z, mu, S):
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target = np.zeros((self.size))
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[p.dpsi1_dtheta(dL_dpsi1, Z[:, i_s], mu[:, i_s], S[:, i_s], target[ps]) for p, ps, i_s in zip(self._parameters_, self._param_slices_, self.input_slices)]
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return self._transform_gradients(target)
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def dpsi1_dZ(self, dL_dpsi1, Z, mu, S):
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target = np.zeros_like(Z)
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[p.dpsi1_dZ(dL_dpsi1, Z[:, i_s], mu[:, i_s], S[:, i_s], target[:, i_s]) for p, i_s in zip(self._parameters_, self.input_slices)]
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return target
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def dpsi1_dmuS(self, dL_dpsi1, Z, mu, S):
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"""return shapes are num_samples,num_inducing,input_dim"""
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target_mu, target_S = np.zeros((2, mu.shape[0], mu.shape[1]))
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[p.dpsi1_dmuS(dL_dpsi1, Z[:, i_s], mu[:, i_s], S[:, i_s], target_mu[:, i_s], target_S[:, i_s]) for p, i_s in zip(self._parameters_, self.input_slices)]
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return target_mu, target_S
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return np.sum([p.psi1(Z[:, i_s], mu[:, i_s], S[:, i_s]) for p, i_s in zip(self._parameters_, self.input_slices)], 0)
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def psi2(self, Z, mu, S):
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"""
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Computer the psi2 statistics for the covariance function.
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:param Z: np.ndarray of inducing inputs (num_inducing x input_dim)
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:param mu, S: np.ndarrays of means and variances (each num_samples x input_dim)
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:returns psi2: np.ndarray (num_samples,num_inducing,num_inducing)
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"""
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target = np.zeros((mu.shape[0], Z.shape[0], Z.shape[0]))
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[p.psi2(Z[:, i_s], mu[:, i_s], S[:, i_s], target) for p, i_s in zip(self._parameters_, self.input_slices)]
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psi2 = np.sum([p.psi2(Z[:, i_s], mu[:, i_s], S[:, i_s]) for p, i_s in zip(self._parameters_, self.input_slices)], 0)
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# compute the "cross" terms
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# TODO: input_slices needed
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crossterms = 0
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from white import White
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from rbf import RBF
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#from rbf_inv import RBFInv
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#from bias import Bias
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from linear import Linear
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#ffrom fixed import Fixed
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for [p1, i_s1], [p2, i_s2] in itertools.combinations(zip(self._parameters_, self.input_slices), 2):
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if i_s1 == i_s2:
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# TODO psi1 this must be faster/better/precached/more nice
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tmp1 = np.zeros((mu.shape[0], Z.shape[0]))
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p1.psi1(Z[:, i_s1], mu[:, i_s1], S[:, i_s1], tmp1)
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tmp2 = np.zeros((mu.shape[0], Z.shape[0]))
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p2.psi1(Z[:, i_s2], mu[:, i_s2], S[:, i_s2], tmp2)
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for (p1, i1), (p2, i2) in itertools.combinations(itertools.izip(self._parameters_, self.input_slices), 2):
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# white doesn;t combine with anything
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if isinstance(p1, White) or isinstance(p2, White):
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pass
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# rbf X bias
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#elif isinstance(p1, (Bias, Fixed)) and isinstance(p2, (RBF, RBFInv)):
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elif isinstance(p1, Bias) and isinstance(p2, (RBF, Linear))):
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tmp = p2.psi1(Z[:,i2], mu[:,i2], S[:,i2])
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psi2 += p1.variance * (tmp[:, :, None] + tmp[:, None, :])
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#elif isinstance(p2, (Bias, Fixed)) and isinstance(p1, (RBF, RBFInv)):
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elif isinstance(p2, Bias) and isinstance(p1, (RBF, Linear)):
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tmp = p1.psi1(Z[:,i1], mu[:,i1], S[:,i1])
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psi2 += p2.variance * (tmp[:, :, None] + tmp[:, None, :])
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else:
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raise NotImplementedError, "psi2 cannot be computed for this kernel"
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return psi2
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prod = np.multiply(tmp1, tmp2)
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crossterms += prod[:, :, None] + prod[:, None, :]
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def update_gradients_variational(self, dL_dKmm, dL_dpsi0, dL_dpsi1, dL_dpsi2, mu, S, Z):
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from white import White
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from rbf import RBF
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#from rbf_inv import RBFInv
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#from bias import Bias
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from linear import Linear
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#ffrom fixed import Fixed
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target += crossterms
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for p1, is1 in zip(self._parameters_, self.input_slices):
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#compute the effective dL_dpsi1. Extra terms appear becaue of the cross terms in psi2!
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eff_dL_dpsi1 = dL_dpsi1.copy()
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for p2, is2 in zip(self._parameters_, self.input_slices):
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if p2 is p1:
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continue
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if isinstance(p2, White):
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continue
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elif isinstance(p2, Bias):
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eff_dL_dpsi1 += dL_dpsi2.sum(1) * p2.variance * 2.
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else:
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eff_dL_dpsi1 += dL_dpsi2.sum(1) * p2.psi1(Z[:,is2], mu[:,is2], S[:,is2]) * 2.
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p1.update_gradients_variational(dL_dKmm, dL_dpsi0, eff_dL_dpsi1, dL_dpsi2, mu[:,is1], S[:,is1], Z[:,is1])
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def gradients_Z_variational(self, dL_dKmm, dL_dpsi0, dL_dpsi1, dL_dpsi2, mu, S, Z):
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from white import white
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from rbf import rbf
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#from rbf_inv import rbfinv
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#from bias import bias
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from linear import linear
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#ffrom fixed import fixed
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target = np.zeros(Z.shape)
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for p1, is1 in zip(self._parameters_, self.input_slices):
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#compute the effective dL_dpsi1. extra terms appear becaue of the cross terms in psi2!
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eff_dL_dpsi1 = dL_dpsi1.copy()
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for p2, is2 in zip(self._parameters_, self.input_slices):
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if p2 is p1:
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continue
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if isinstance(p2, white):
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continue
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elif isinstance(p2, bias):
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eff_dL_dpsi1 += dL_dpsi2.sum(1) * p2.variance * 2.
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else:
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eff_dL_dpsi1 += dL_dpsi2.sum(1) * p2.psi1(z[:,is2], mu[:,is2], s[:,is2]) * 2.
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target += p1.gradients_z_variational(dL_dkmm, dL_dpsi0, eff_dL_dpsi1, dL_dpsi2, mu[:,is1], s[:,is1], z[:,is1])
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return target
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def dpsi2_dtheta(self, dL_dpsi2, Z, mu, S):
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"""Gradient of the psi2 statistics with respect to the parameters."""
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target = np.zeros(self.size)
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[p.dpsi2_dtheta(dL_dpsi2, Z[:, i_s], mu[:, i_s], S[:, i_s], target[ps]) for p, i_s, ps in zip(self._parameters_, self.input_slices, self._param_slices_)]
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def gradients_muS_variational(self, dL_dKmm, dL_dpsi0, dL_dpsi1, dL_dpsi2, mu, S, Z):
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from white import white
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from rbf import rbf
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#from rbf_inv import rbfinv
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#from bias import bias
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from linear import linear
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#ffrom fixed import fixed
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# compute the "cross" terms
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# TODO: better looping, input_slices
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for i1, i2 in itertools.permutations(range(len(self._parameters_)), 2):
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p1, p2 = self._parameters_[i1], self._parameters_[i2]
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# ipsl1, ipsl2 = self.input_slices[i1], self.input_slices[i2]
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ps1, ps2 = self._param_slices_[i1], self._param_slices_[i2]
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target_mu = np.zeros(mu.shape)
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target_S = np.zeros(S.shape)
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for p1, is1 in zip(self._parameters_, self.input_slices):
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tmp = np.zeros((mu.shape[0], Z.shape[0]))
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p1.psi1(Z, mu, S, tmp)
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p2.dpsi1_dtheta((tmp[:, None, :] * dL_dpsi2).sum(1) * 2., Z, mu, S, target[ps2])
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#compute the effective dL_dpsi1. extra terms appear becaue of the cross terms in psi2!
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eff_dL_dpsi1 = dL_dpsi1.copy()
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for p2, is2 in zip(self._parameters_, self.input_slices):
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if p2 is p1:
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continue
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if isinstance(p2, white):
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continue
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elif isinstance(p2, bias):
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eff_dL_dpsi1 += dL_dpsi2.sum(1) * p2.variance * 2.
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else:
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eff_dL_dpsi1 += dL_dpsi2.sum(1) * p2.psi1(z[:,is2], mu[:,is2], s[:,is2]) * 2.
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return self._transform_gradients(target)
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def dpsi2_dZ(self, dL_dpsi2, Z, mu, S):
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target = np.zeros_like(Z)
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[p.dpsi2_dZ(dL_dpsi2, Z[:, i_s], mu[:, i_s], S[:, i_s], target[:, i_s]) for p, i_s in zip(self._parameters_, self.input_slices)]
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# target *= 2
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# compute the "cross" terms
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# TODO: we need input_slices here.
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for p1, p2 in itertools.permutations(self._parameters_, 2):
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# if p1.name == 'linear' and p2.name == 'linear':
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# raise NotImplementedError("We don't handle linear/linear cross-terms")
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tmp = np.zeros((mu.shape[0], Z.shape[0]))
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p1.psi1(Z, mu, S, tmp)
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p2.dpsi1_dZ((tmp[:, None, :] * dL_dpsi2).sum(1), Z, mu, S, target)
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return target * 2
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def dpsi2_dmuS(self, dL_dpsi2, Z, mu, S):
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target_mu, target_S = np.zeros((2, mu.shape[0], mu.shape[1]))
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[p.dpsi2_dmuS(dL_dpsi2, Z[:, i_s], mu[:, i_s], S[:, i_s], target_mu[:, i_s], target_S[:, i_s]) for p, i_s in zip(self._parameters_, self.input_slices)]
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# compute the "cross" terms
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# TODO: we need input_slices here.
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for p1, p2 in itertools.permutations(self._parameters_, 2):
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# if p1.name == 'linear' and p2.name == 'linear':
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# raise NotImplementedError("We don't handle linear/linear cross-terms")
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tmp = np.zeros((mu.shape[0], Z.shape[0]))
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p1.psi1(Z, mu, S, tmp)
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p2.dpsi1_dmuS((tmp[:, None, :] * dL_dpsi2).sum(1) * 2., Z, mu, S, target_mu, target_S)
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a, b = p1.gradients_muS_variational(dL_dkmm, dL_dpsi0, eff_dL_dpsi1, dL_dpsi2, mu[:,is1], s[:,is1], z[:,is1])
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target_mu += a
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target_S += b
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return target_mu, target_S
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def plot(self, *args, **kwargs):
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@ -9,7 +9,7 @@ from ...core.parameterization.param import Param
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class Kern(Parameterized):
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def __init__(self,input_dim,name):
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def __init__(self, input_dim, name):
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"""
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The base class for a kernel: a positive definite function
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which forms of a covariance function (kernel).
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@ -22,21 +22,15 @@ class Kern(Parameterized):
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super(Kern, self).__init__(name)
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self.input_dim = input_dim
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def K(self,X,X2,target):
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def K(self, X, X2, target):
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raise NotImplementedError
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def Kdiag(self,X,target):
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def Kdiag(self, Xa ,target):
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raise NotImplementedError
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def _param_grad_helper(self,dL_dK,X,X2,target):
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def _param_grad_helper(self, dL_dK,X, X2, target):
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raise NotImplementedError
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def dKdiag_dtheta(self,dL_dKdiag,X,target): # TODO: Max??
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# In the base case compute this by calling _param_grad_helper. Need to
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# override for stationary covariances (for example) to save
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# time.
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for i in range(X.shape[0]):
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self._param_grad_helper(dL_dKdiag[i], X[i, :][None, :], X2=None, target=target)
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def psi0(self,Z,mu,S,target):
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raise NotImplementedError
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def dpsi0_dtheta(self,dL_dpsi0,Z,mu,S,target):
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def dpsi0_dtheta(self,dL_dpsi0, Z,mu,S,target):
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raise NotImplementedError
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def dpsi0_dmuS(self,dL_dpsi0,Z,mu,S,target_mu,target_S):
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raise NotImplementedError
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@ -9,6 +9,7 @@ from ...util.linalg import tdot
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from ...util.misc import fast_array_equal, param_to_array
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from ...core.parameterization import Param
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from ...core.parameterization.transformations import Logexp
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from ...util.caching import Cacher, cache_this
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class Linear(Kern):
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"""
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@ -45,22 +46,35 @@ class Linear(Kern):
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variances = np.ones(self.input_dim)
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self.variances = Param('variances', variances, Logexp())
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#TODO: remove?self.variances.gradient = np.zeros(self.variances.shape)
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self.add_parameter(self.variances)
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self.variances.add_observer(self, self.update_variance)
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self.variances.add_observer(self, self._on_changed)
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# initialize cache
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self._Z, self._mu, self._S = np.empty(shape=(3, 1))
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self._X, self._X2 = np.empty(shape=(2, 1))
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def _on_changed(self, obj):
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self._notify_observers()
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def update_variance(self, v):
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self.variances2 = np.square(self.variances)
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@cache_this(limit=3, reset_on_self=True)
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def K(self, X, X2=None):
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if self.ARD:
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if X2 is None:
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return tdot(X*np.sqrt(self.variances))
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else:
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rv = np.sqrt(self.variances)
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return np.dot(X*rv, (X2*rv).T)
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else:
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return self._dot_product(X, X2) * self.variances
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def on_input_change(self, X):
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self._K_computations(X, None)
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@cache_this(limit=3, reset_on_self=False)
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def _dot_product(self, X, X2=None):
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if X2 is None:
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return tdot(X)
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else:
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return np.dot(X, X2.T)
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def Kdiag(self, X):
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return np.sum(self.variances * np.square(X), -1)
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def update_gradients_full(self, dL_dK, X):
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self.variances.gradient[:] = 0
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self.variances.gradient = np.zeros(self.variances.size)
|
||||
self._param_grad_helper(dL_dK, X, None, self.variances.gradient)
|
||||
|
||||
def update_gradients_sparse(self, dL_dKmm, dL_dKnm, dL_dKdiag, X, Z):
|
||||
|
|
@ -68,7 +82,7 @@ class Linear(Kern):
|
|||
if self.ARD:
|
||||
self.variances.gradient = tmp.sum(0)
|
||||
else:
|
||||
self.variances.gradient = tmp.sum()
|
||||
self.variances.gradient = np.atleast_1d(tmp.sum())
|
||||
self._param_grad_helper(dL_dKmm, Z, None, self.variances.gradient)
|
||||
self._param_grad_helper(dL_dKnm, X, Z, self.variances.gradient)
|
||||
|
||||
|
|
@ -85,25 +99,8 @@ class Linear(Kern):
|
|||
if self.ARD: self.variances.gradient += tmp.sum(0).sum(0).sum(0)
|
||||
else: self.variances.gradient += tmp.sum()
|
||||
#from Kmm
|
||||
self._K_computations(Z, None)
|
||||
self._param_grad_helper(dL_dKmm, Z, None, self.variances.gradient)
|
||||
|
||||
def K(self, X, X2, target):
|
||||
if self.ARD:
|
||||
XX = X * np.sqrt(self.variances)
|
||||
if X2 is None:
|
||||
target += tdot(XX)
|
||||
else:
|
||||
XX2 = X2 * np.sqrt(self.variances)
|
||||
target += np.dot(XX, XX2.T)
|
||||
else:
|
||||
if X is not self._X or X2 is not None:
|
||||
self._K_computations(X, X2)
|
||||
target += self.variances * self._dot_product
|
||||
|
||||
def Kdiag(self, X, target):
|
||||
np.add(target, np.sum(self.variances * np.square(X), -1), target)
|
||||
|
||||
def _param_grad_helper(self, dL_dK, X, X2, target):
|
||||
if self.ARD:
|
||||
if X2 is None:
|
||||
|
|
@ -112,18 +109,16 @@ class Linear(Kern):
|
|||
product = X[:, None, :] * X2[None, :, :]
|
||||
target += (dL_dK[:, :, None] * product).sum(0).sum(0)
|
||||
else:
|
||||
if X is not self._X or X2 is not None:
|
||||
self._K_computations(X, X2)
|
||||
target += np.sum(self._dot_product * dL_dK)
|
||||
target += np.sum(self._dot_product(X, X2) * dL_dK)
|
||||
|
||||
def gradients_X(self, dL_dK, X, X2, target):
|
||||
def gradients_X(self, dL_dK, X, X2=None):
|
||||
if X2 is None:
|
||||
target += 2*(((X[None,:, :] * self.variances)) * dL_dK[:, :, None]).sum(1)
|
||||
return 2.*(((X[None,:, :] * self.variances)) * dL_dK[:, :, None]).sum(1)
|
||||
else:
|
||||
target += (((X2[None,:, :] * self.variances)) * dL_dK[:, :, None]).sum(1)
|
||||
return (((X2[None,:, :] * self.variances)) * dL_dK[:, :, None]).sum(1)
|
||||
|
||||
def dKdiag_dX(self,dL_dKdiag,X,target):
|
||||
target += 2.*self.variances*dL_dKdiag[:,None]*X
|
||||
def gradients_X_diag(self, dL_dKdiag, X):
|
||||
return 2.*self.variances*dL_dKdiag[:,None]*X
|
||||
|
||||
#---------------------------------------#
|
||||
# PSI statistics #
|
||||
|
|
@ -273,15 +268,15 @@ class Linear(Kern):
|
|||
# Precomputations #
|
||||
#---------------------------------------#
|
||||
|
||||
def _K_computations(self, X, X2):
|
||||
if not (fast_array_equal(X, self._X) and fast_array_equal(X2, self._X2)):
|
||||
self._X = X.copy()
|
||||
if X2 is None:
|
||||
self._dot_product = tdot(param_to_array(X))
|
||||
self._X2 = None
|
||||
else:
|
||||
self._X2 = X2.copy()
|
||||
self._dot_product = np.dot(param_to_array(X), param_to_array(X2.T))
|
||||
#def _K_computations(self, X, X2):
|
||||
#if not (fast_array_equal(X, self._X) and fast_array_equal(X2, self._X2)):
|
||||
#self._X = X.copy()
|
||||
#if X2 is None:
|
||||
##self._dot_product = tdot(param_to_array(X))
|
||||
#self._X2 = None
|
||||
#else:
|
||||
#self._X2 = X2.copy()
|
||||
#self._dot_product = np.dot(param_to_array(X), param_to_array(X2.T))
|
||||
|
||||
def _psi_computations(self, Z, mu, S):
|
||||
# here are the "statistics" for psi1 and psi2
|
||||
|
|
|
|||
|
|
@ -2,9 +2,7 @@
|
|||
# Licensed under the BSD 3-clause license (see LICENSE.txt)
|
||||
|
||||
from kern import Kern
|
||||
from coregionalize import Coregionalize
|
||||
import numpy as np
|
||||
import hashlib
|
||||
|
||||
class Prod(Kern):
|
||||
"""
|
||||
|
|
@ -17,7 +15,7 @@ class Prod(Kern):
|
|||
:rtype: kernel object
|
||||
|
||||
"""
|
||||
def __init__(self,k1,k2,tensor=False):
|
||||
def __init__(self, k1, k2, tensor=False):
|
||||
if tensor:
|
||||
super(Prod, self).__init__(k1.input_dim + k2.input_dim, k1.name + '_xx_' + k2.name)
|
||||
self.slice1 = slice(0,k1.input_dim)
|
||||
|
|
@ -25,64 +23,43 @@ class Prod(Kern):
|
|||
else:
|
||||
assert k1.input_dim == k2.input_dim, "Error: The input spaces of the kernels to multiply don't have the same dimension."
|
||||
super(Prod, self).__init__(k1.input_dim, k1.name + '_x_' + k2.name)
|
||||
self.slice1 = slice(0,self.input_dim)
|
||||
self.slice2 = slice(0,self.input_dim)
|
||||
self.slice1 = slice(0, self.input_dim)
|
||||
self.slice2 = slice(0, self.input_dim)
|
||||
self.k1 = k1
|
||||
self.k2 = k2
|
||||
self.add_parameters(self.k1, self.k2)
|
||||
|
||||
#initialize cache
|
||||
self._X, self._X2 = np.empty(shape=(2,1))
|
||||
self._params = None
|
||||
|
||||
def K(self, X, X2=None):
|
||||
self._K_computations(X, X2)
|
||||
return self._K1 * self._K2
|
||||
if X2 is None:
|
||||
return self.k1.K(X[:,self.slice1], None) * self.k2.K(X[:,self.slice2], None)
|
||||
else:
|
||||
return self.k1.K(X[:,self.slice1], X2[:,self.slice1]) * self.k2.K(X[:,self.slice2], X2[:,self.slice2])
|
||||
|
||||
def Kdiag(self, X):
|
||||
return self.k1.Kdiag(X[:,self.slice1]) * self.k2.Kdiag(X[:,self.slice2])
|
||||
|
||||
def update_gradients_full(self, dL_dK, X):
|
||||
self._K_computations(X, None)
|
||||
self.k1.update_gradients_full(dL_dK*self._K2, X[:,self.slice1])
|
||||
self.k2.update_gradients_full(dL_dK*self._K1, X[:,self.slice2])
|
||||
self.k1.update_gradients_full(dL_dK*self.k2(X[:,self.slice2]), X[:,self.slice1])
|
||||
self.k2.update_gradients_full(dL_dK*self.k1(X[:,self.slice1]), X[:,self.slice2])
|
||||
|
||||
def update_gradients_sparse(self, dL_dKmm, dL_dKnm, dL_dKdiag, X, Z):
|
||||
self.k1.update_gradients_sparse(dL_dKmm * self.k2.K(Z[:,self.slice2]), dL_dKnm * self.k2(X[:,self.slice2], Z[:,self.slice2]), dL_dKdiag * self.k2.Kdiag(X[:,self.slice2]), X[:,self.slice1], Z[:,self.slice1] )
|
||||
self.k2.update_gradients_sparse(dL_dKmm * self.k1.K(Z[:,self.slice1]), dL_dKnm * self.k1(X[:,self.slice1], Z[:,self.slice1]), dL_dKdiag * self.k1.Kdiag(X[:,self.slice1]), X[:,self.slice2], Z[:,self.slice2] )
|
||||
|
||||
def gradients_X(self, dL_dK, X, X2=None):
|
||||
"""derivative of the covariance matrix with respect to X."""
|
||||
self._K_computations(X, X2)
|
||||
target = np.zeros(X.shape)
|
||||
if X2 is None:
|
||||
target[:,self.slice1] += self.k1.gradients_X(dL_dK*self._K2, X[:,self.slice1], None)
|
||||
target[:,self.slice2] += self.k2.gradients_X(dL_dK*self._K1, X[:,self.slice2], None)
|
||||
target[:,self.slice1] += self.k1.gradients_X(dL_dK*self.k2(X[:,self.slice2]), X[:,self.slice1], None)
|
||||
target[:,self.slice2] += self.k2.gradients_X(dL_dK*self.k1(X[:,self.slice1]), X[:,self.slice2], None)
|
||||
else:
|
||||
target[:,self.slice1] += self.k1.gradients_X(dL_dK*self._K2, X[:,self.slice1], X2[:,self.slice1])
|
||||
target[:,self.slice2] += self.k2.gradients_X(dL_dK*self._K1, X[:,self.slice2], X2[:,self.slice2])
|
||||
|
||||
target[:,self.slice1] += self.k1.gradients_X(dL_dK*self.k2(X[:,self.slice2], X2[:,self.slice2]), X[:,self.slice1], X2[:,self.slice1])
|
||||
target[:,self.slice2] += self.k2.gradients_X(dL_dK*self.k1(X[:,self.slice1], X2[:,self.slice1]), X[:,self.slice2], X2[:,self.slice2])
|
||||
return target
|
||||
|
||||
def dKdiag_dX(self, dL_dKdiag, X, target):
|
||||
K1 = np.zeros(X.shape[0])
|
||||
K2 = np.zeros(X.shape[0])
|
||||
self.k1.Kdiag(X[:,self.slice1],K1)
|
||||
self.k2.Kdiag(X[:,self.slice2],K2)
|
||||
def gradients_X_diag(self, dL_dKdiag, X):
|
||||
target = np.zeros(X.shape)
|
||||
target[:,self.slice1] = self.k1.gradients_X(dL_dKdiag*self.k2.Kdiag(X[:,self.slice2]), X[:,self.slice1])
|
||||
target[:,self.slice2] += self.k2.gradients_X(dL_dKdiag*self.k1.Kdiag(X[:,self.slice1]), X[:,self.slice2])
|
||||
return target
|
||||
|
||||
self.k1.gradients_X(dL_dKdiag*K2, X[:,self.slice1], target[:,self.slice1])
|
||||
self.k2.gradients_X(dL_dKdiag*K1, X[:,self.slice2], target[:,self.slice2])
|
||||
|
||||
def _K_computations(self, X, X2):
|
||||
if not (np.array_equal(X,self._X) and np.array_equal(X2,self._X2) and np.array_equal(self._params , self._get_params())):
|
||||
self._X = X.copy()
|
||||
self._params == self._get_params().copy()
|
||||
if X2 is None:
|
||||
self._X2 = None
|
||||
self._K1 = self.k1.K(X[:,self.slice1],None)
|
||||
self._K2 = self.k2.K(X[:,self.slice2],None)
|
||||
else:
|
||||
self._X2 = X2.copy()
|
||||
self._K1 = self.k1.K(X[:,self.slice1],X2[:,self.slice1])
|
||||
self._K2 = self.k2.K(X[:,self.slice2],X2[:,self.slice2])
|
||||
|
||||
|
|
|
|||
|
|
@ -79,17 +79,18 @@ class RBF(Kern):
|
|||
ret[:] = self.variance
|
||||
return ret
|
||||
|
||||
#TODO: remove TARGET!
|
||||
def psi0(self, Z, mu, S, target):
|
||||
target += self.variance
|
||||
def psi0(self, Z, mu, S):
|
||||
ret = np.empty(mu.shape[0], dtype=np.float64)
|
||||
ret[:] = self.variance
|
||||
return ret
|
||||
|
||||
def psi1(self, Z, mu, S, target):
|
||||
def psi1(self, Z, mu, S):
|
||||
self._psi_computations(Z, mu, S)
|
||||
target += self._psi1
|
||||
return self._psi1
|
||||
|
||||
def psi2(self, Z, mu, S, target):
|
||||
def psi2(self, Z, mu, S):
|
||||
self._psi_computations(Z, mu, S)
|
||||
target += self._psi2
|
||||
return self._psi2
|
||||
|
||||
def update_gradients_full(self, dL_dK, X):
|
||||
self._K_computations(X, None)
|
||||
|
|
@ -154,6 +155,37 @@ class RBF(Kern):
|
|||
else:
|
||||
self.lengthscale.gradient += (self.variance / self.lengthscale) * np.sum(self._K_dvar * self._K_dist2 * dL_dKmm)
|
||||
|
||||
def gradients_Z_variational(self, dL_dKmm, dL_dpsi0, dL_dpsi1, dL_dpsi2, mu, S, Z):
|
||||
self._psi_computations(Z, mu, S)
|
||||
|
||||
#psi1
|
||||
denominator = (self.lengthscale2 * (self._psi1_denom))
|
||||
dpsi1_dZ = -self._psi1[:, :, None] * ((self._psi1_dist / denominator))
|
||||
grad = np.sum(dL_dpsi1[:, :, None] * dpsi1_dZ, 0)
|
||||
|
||||
#psi2
|
||||
term1 = self._psi2_Zdist / self.lengthscale2 # num_inducing, num_inducing, input_dim
|
||||
term2 = self._psi2_mudist / self._psi2_denom / self.lengthscale2 # N, num_inducing, num_inducing, input_dim
|
||||
dZ = self._psi2[:, :, :, None] * (term1[None] + term2)
|
||||
grad += (dL_dpsi2[:, :, :, None] * dZ).sum(0).sum(0)
|
||||
|
||||
return grad
|
||||
|
||||
def gradients_muS_variational(self, dL_dKmm, dL_dpsi0, dL_dpsi1, dL_dpsi2, mu, S, Z):
|
||||
self._psi_computations(Z, mu, S)
|
||||
#psi1
|
||||
tmp = self._psi1[:, :, None] / self.lengthscale2 / self._psi1_denom
|
||||
grad_mu = np.sum(dL_dpsi1[:, :, None] * tmp * self._psi1_dist, 1)
|
||||
grad_S = np.sum(dL_dpsi1[:, :, None] * 0.5 * tmp * (self._psi1_dist_sq - 1), 1)
|
||||
|
||||
tmp = self._psi2[:, :, :, None] / self.lengthscale2 / self._psi2_denom
|
||||
grad_mu += -2.*(dL_dpsi2[:, :, :, None] * tmp * self._psi2_mudist).sum(1).sum(1)
|
||||
grad_S += (dL_dpsi2[:, :, :, None] * tmp * (2.*self._psi2_mudist_sq - 1)).sum(1).sum(1)
|
||||
|
||||
return grad_mu, grad_S
|
||||
|
||||
|
||||
|
||||
def gradients_X(self, dL_dK, X, X2=None):
|
||||
#if self._X is None or X.base is not self._X.base or X2 is not None:
|
||||
self._K_computations(X, X2)
|
||||
|
|
@ -171,36 +203,7 @@ class RBF(Kern):
|
|||
# PSI statistics #
|
||||
#---------------------------------------#
|
||||
|
||||
def dpsi0_dmuS(self, dL_dpsi0, Z, mu, S, target_mu, target_S):
|
||||
pass
|
||||
|
||||
def dpsi1_dZ(self, dL_dpsi1, Z, mu, S, target):
|
||||
self._psi_computations(Z, mu, S)
|
||||
denominator = (self.lengthscale2 * (self._psi1_denom))
|
||||
dpsi1_dZ = -self._psi1[:, :, None] * ((self._psi1_dist / denominator))
|
||||
target += np.sum(dL_dpsi1[:, :, None] * dpsi1_dZ, 0)
|
||||
|
||||
def dpsi1_dmuS(self, dL_dpsi1, Z, mu, S, target_mu, target_S):
|
||||
self._psi_computations(Z, mu, S)
|
||||
tmp = self._psi1[:, :, None] / self.lengthscale2 / self._psi1_denom
|
||||
target_mu += np.sum(dL_dpsi1[:, :, None] * tmp * self._psi1_dist, 1)
|
||||
target_S += np.sum(dL_dpsi1[:, :, None] * 0.5 * tmp * (self._psi1_dist_sq - 1), 1)
|
||||
|
||||
def dpsi2_dZ(self, dL_dpsi2, Z, mu, S, target):
|
||||
self._psi_computations(Z, mu, S)
|
||||
term1 = self._psi2_Zdist / self.lengthscale2 # num_inducing, num_inducing, input_dim
|
||||
term2 = self._psi2_mudist / self._psi2_denom / self.lengthscale2 # N, num_inducing, num_inducing, input_dim
|
||||
dZ = self._psi2[:, :, :, None] * (term1[None] + term2)
|
||||
target += (dL_dpsi2[:, :, :, None] * dZ).sum(0).sum(0)
|
||||
|
||||
def dpsi2_dmuS(self, dL_dpsi2, Z, mu, S, target_mu, target_S):
|
||||
"""Think N,num_inducing,num_inducing,input_dim """
|
||||
self._psi_computations(Z, mu, S)
|
||||
tmp = self._psi2[:, :, :, None] / self.lengthscale2 / self._psi2_denom
|
||||
target_mu += -2.*(dL_dpsi2[:, :, :, None] * tmp * self._psi2_mudist).sum(1).sum(1)
|
||||
target_S += (dL_dpsi2[:, :, :, None] * tmp * (2.*self._psi2_mudist_sq - 1)).sum(1).sum(1)
|
||||
|
||||
#---------------------------------------#
|
||||
#---------------------------------------#
|
||||
# Precomputations #
|
||||
#---------------------------------------#
|
||||
|
||||
|
|
@ -362,6 +365,7 @@ class RBF(Kern):
|
|||
#include <omp.h>
|
||||
#include <math.h>
|
||||
"""
|
||||
mu = param_to_array(mu)
|
||||
weave.inline(code, support_code=support_code, libraries=['gomp'],
|
||||
arg_names=['N', 'num_inducing', 'input_dim', 'mu', 'Zhat', 'mudist_sq', 'mudist', 'lengthscale2', '_psi2_denom', 'psi2_Zdist_sq', 'psi2_exponent', 'half_log_psi2_denom', 'psi2', 'variance_sq'],
|
||||
type_converters=weave.converters.blitz, **self.weave_options)
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue