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https://github.com/SheffieldML/GPy.git
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Update function kern.gradients_XX() to compute cross-covariance terms
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alessandratosi
parent
1a3e6c3ea3
commit
a9c8ef817a
4 changed files with 69 additions and 42 deletions
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@ -85,13 +85,20 @@ class Add(CombinationKernel):
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[target.__iadd__(p.gradients_X_diag(dL_dKdiag, X)) for p in self.parts]
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return target
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def gradients_XX(self, dL_dK, X, X2):
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if X2 is None:
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target = np.zeros((X.shape[0], X.shape[0], X.shape[1]))
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else:
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target = np.zeros((X.shape[0], X2.shape[0], X.shape[1]))
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[target.__iadd__(p.gradients_XX(dL_dK, X, X2)) for p in self.parts]
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return target
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# def gradients_XX(self, dL_dK, X, X2, cov=True):
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# if cov==True: # full covarance
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# if X2 is None:
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# target = np.zeros((X.shape[0], X.shape[0], X.shape[1], X.shape[1]))
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# else:
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# target = np.zeros((X.shape[0], X2.shape[0], X.shape[1], X.shape[1]))
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# else: # diagonal covariance
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# if X2 is None:
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# target = np.zeros((X.shape[0], X.shape[0], X.shape[1]))
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# else:
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# target = np.zeros((X.shape[0], X2.shape[0], X.shape[1]))
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# [target.__iadd__(p.gradients_XX(dL_dK, X, X2, cov=True)) for p in self.parts]
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# return target
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def gradients_XX_diag(self, dL_dKdiag, X):
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target = np.zeros(X.shape)
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@ -132,7 +132,7 @@ class Kern(Parameterized):
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raise NotImplementedError
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def gradients_X_X2(self, dL_dK, X, X2):
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return self.gradients_X(dL_dK, X, X2), self.gradients_X(dL_dK.T, X2, X)
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def gradients_XX(self, dL_dK, X, X2):
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def gradients_XX(self, dL_dK, X, X2, cov='False'):
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"""
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.. math::
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@ -24,7 +24,7 @@ class KernCallsViaSlicerMeta(ParametersChangedMeta):
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put_clean(dct, 'update_gradients_diag', _slice_update_gradients_diag)
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put_clean(dct, 'gradients_X', _slice_gradients_X)
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put_clean(dct, 'gradients_X_X2', _slice_gradients_X)
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put_clean(dct, 'gradients_XX', _slice_gradients_XX)
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# put_clean(dct, 'gradients_XX', _slice_gradients_XX)
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put_clean(dct, 'gradients_XX_diag', _slice_gradients_X_diag)
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put_clean(dct, 'gradients_X_diag', _slice_gradients_X_diag)
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@ -112,18 +112,23 @@ def _slice_gradients_X(f):
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return ret
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return wrap
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def _slice_gradients_XX(f):
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@wraps(f)
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def wrap(self, dL_dK, X, X2=None):
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if X2 is None:
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N, M = X.shape[0], X.shape[0]
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else:
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N, M = X.shape[0], X2.shape[0]
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with _Slice_wrap(self, X, X2, ret_shape=(N, M, X.shape[1])) as s:
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#with _Slice_wrap(self, X, X2, ret_shape=None) as s:
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ret = s.handle_return_array(f(self, dL_dK, s.X, s.X2))
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return ret
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return wrap
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# def _slice_gradients_XX(f):
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# @wraps(f)
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# def wrap(self, dL_dK, X, X2=None, cov=True):
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# if X2 is None:
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# N, M = X.shape[0], X.shape[0]
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# else:
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# N, M = X.shape[0], X2.shape[0]
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# if cov==True: # full covariance
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# with _Slice_wrap(self, X, X2, ret_shape=(N, M, X.shape[1], X.shape[1])) as s:
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# #with _Slice_wrap(self, X, X2, ret_shape=None) as s:
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# ret = s.handle_return_array(f(self, dL_dK, s.X, s.X2))
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# else: # diagonal covariance
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# with _Slice_wrap(self, X, X2, ret_shape=(N, M, X.shape[1])) as s:
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# #with _Slice_wrap(self, X, X2, ret_shape=None) as s:
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# ret = s.handle_return_array(f(self, dL_dK, s.X, s.X2))
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# return ret
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# return wrap
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def _slice_gradients_X_diag(f):
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@wraps(f)
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@ -218,45 +218,60 @@ class Stationary(Kern):
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else:
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return self._gradients_X_pure(dL_dK, X, X2)
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def gradients_XX(self, dL_dK, X, X2=None):
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def gradients_XX(self, dL_dK, X, X2=None, cov=True):
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"""
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Given the derivative of the objective K(dL_dK), compute the second derivative of K wrt X and X2:
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cov = Full: returns the full covariance matrix [QxQ] of the input dimensionfor each pair or vectors
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cov = Diag: returns the diagonal of the covariance matrix [QxQ] of the input dimensionfor each pair
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or vectors (computationally more efficient if the full covariance matrix is not needed)
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..math:
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\frac{\partial^2 K}{\partial X\partial X2}
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\frac{\partial^2 K}{\partial X2 ^2} = - \frac{\partial^2 K}{\partial X\partial X2}
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..returns:
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dL2_dXdX2: NxMxQ, for X [NxQ] and X2[MxQ] (X2 is X if, X2 is None)
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Thus, we return the second derivative in X2.
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dL2_dXdX2: [NxMxQ] in the cov=Diag case, or [NxMxQxQ] in the cov=full case,
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for X [NxQ] and X2[MxQ] (X2 is X if, X2 is None)
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Thus, we return the second derivative in X2.
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"""
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# The off diagonals in Q are always zero, this should also be true for the Linear kernel...
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# According to multivariable chain rule, we can chain the second derivative through r:
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# d2K_dXdX2 = dK_dr*d2r_dXdX2 + d2K_drdr * dr_dX * dr_dX2:
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invdist = self._inv_dist(X, X2)
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invdist2 = invdist**2
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dL_dr = self.dK_dr_via_X(X, X2) * dL_dK
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dL_dr = self.dK_dr_via_X(X, X2) # * dL_dK we perofrm this product later
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tmp1 = dL_dr * invdist
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dL_drdr = self.dK2_drdr_via_X(X, X2) * dL_dK
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dL_drdr = self.dK2_drdr_via_X(X, X2) # * dL_dK we perofrm this product later
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tmp2 = dL_drdr * invdist2
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l2 = np.ones(X.shape[1]) * self.lengthscale**2
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l2 = np.ones(X.shape[1])*self.lengthscale**2 #np.multiply(np.ones(X.shape[1]) ,self.lengthscale**2)
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print ['l2',l2]
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if X2 is None:
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X2 = X
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tmp1 -= np.eye(X.shape[0])*self.variance
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else:
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tmp1[X==X2.T] -= self.variance
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grad = np.empty((X.shape[0], X2.shape[0], X.shape[1]), dtype=np.float64)
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#grad = np.empty(X.shape, dtype=np.float64)
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for q in range(self.input_dim):
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tmpdist2 = (X[:,[q]]-X2[:,[q]].T) ** 2
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grad[:, :, q] = ((tmp1*invdist2 - tmp2)*tmpdist2/l2[q] - tmp1)/l2[q]
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#grad[:, :, q] = ((tmp1*(((tmpdist2)*invdist2/l2[q])-1)) - (tmp2*(tmpdist2))/l2[q])/l2[q]
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#np.sum(((tmp1*(((tmpdist2)*invdist2/l2[q])-1)) - (tmp2*(tmpdist2))/l2[q])/l2[q], axis=1, out=grad[:,q])
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#np.sum( - (tmp2*(tmpdist**2)), axis=1, out=grad[:,q])
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#tmp1[X==X2.T] -= self.variance # Old version, to be removed
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# (seems to have a bug: it is subtracted to the first X1 anyway)
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tmp1[invdist2==0.] -= self.variance
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if cov==True: # full covariance
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grad = np.empty((X.shape[0], X2.shape[0], X2.shape[1], X.shape[1]), dtype=np.float64)
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for q in range(self.input_dim):
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for r in range(self.input_dim):
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tmpdist2 = (X[:,[q]]-X2[:,[q]].T)*(X[:,[r]]-X2[:,[r]].T) # Introduce temporary distance
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if r==q:
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grad[:, :, q, r] = np.multiply(dL_dK,(np.multiply((tmp1*invdist2 - tmp2),tmpdist2)/l2[r] - tmp1)/l2[q])
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else:
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grad[:, :, q, r] = np.multiply(dL_dK,(np.multiply((tmp1*invdist2 - tmp2),tmpdist2)/l2[r])/l2[q])
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else:
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# Diagonal covariance
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grad = np.empty((X.shape[0], X2.shape[0], X.shape[1]), dtype=np.float64)
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#grad = np.empty(X.shape, dtype=np.float64)
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for q in range(self.input_dim):
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tmpdist2 = (X[:,[q]]-X2[:,[q]].T) ** 2
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grad[:, :, q] = np.multiply(dL_dK,(np.multiply((tmp1*invdist2 - tmp2),tmpdist2)/l2[q] - tmp1)/l2[q])
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#grad[:, :, q] = ((tmp1*invdist2 - tmp2)*tmpdist2/l2[q] - tmp1)/l2[q]
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#grad[:, :, q] = ((tmp1*(((tmpdist2)*invdist2/l2[q])-1)) - (tmp2*(tmpdist2))/l2[q])/l2[q]
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#np.sum(((tmp1*(((tmpdist2)*invdist2/l2[q])-1)) - (tmp2*(tmpdist2))/l2[q])/l2[q], axis=1, out=grad[:,q])
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#np.sum( - (tmp2*(tmpdist**2)), axis=1, out=grad[:,q])
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return grad
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def gradients_XX_diag(self, dL_dK, X):
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