mirror of
https://github.com/SheffieldML/GPy.git
synced 2026-06-05 14:55:15 +02:00
added new gradient functinoality to rbf
This commit is contained in:
James Hensman
parent
2c4d7cca76
commit
eb52600537
1 changed files with 119 additions and 99 deletions
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@ -36,7 +36,7 @@ class RBF(Kernpart):
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super(RBF, self).__init__(input_dim, name)
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super(RBF, self).__init__(input_dim, name)
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self.input_dim = input_dim
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self.input_dim = input_dim
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self.ARD = ARD
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self.ARD = ARD
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if not ARD:
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if not ARD:
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if lengthscale is not None:
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if lengthscale is not None:
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lengthscale = np.asarray(lengthscale)
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lengthscale = np.asarray(lengthscale)
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@ -55,7 +55,7 @@ class RBF(Kernpart):
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self.lengthscale.add_observer(self, self.update_lengthscale)
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self.lengthscale.add_observer(self, self.update_lengthscale)
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self.add_parameters(self.variance, self.lengthscale)
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self.add_parameters(self.variance, self.lengthscale)
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self.parameters_changed() # initializes cache
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self.parameters_changed() # initializes cache
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#self.update_inv_lengthscale(self.lengthscale)
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#self.update_inv_lengthscale(self.lengthscale)
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#self.parameters_changed()
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#self.parameters_changed()
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# initialize cache
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# initialize cache
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@ -67,99 +67,90 @@ class RBF(Kernpart):
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# 'extra_compile_args': ['-fopenmp -O3'], # -march=native'],
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# 'extra_compile_args': ['-fopenmp -O3'], # -march=native'],
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# 'extra_link_args' : ['-lgomp']}
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# 'extra_link_args' : ['-lgomp']}
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self.weave_options = {}
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self.weave_options = {}
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def on_input_change(self, X):
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def on_input_change(self, X):
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#self._K_computations(X, None)
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#self._K_computations(X, None)
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pass
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pass
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def update_lengthscale(self, l):
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def update_lengthscale(self, l):
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self.lengthscale2 = np.square(self.lengthscale)
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self.lengthscale2 = np.square(self.lengthscale)
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def parameters_changed(self):
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def parameters_changed(self):
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# reset cached results
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# reset cached results
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#self._X, self._X2, self._params_save = np.empty(shape=(3, 1))
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#self._Z, self._mu, self._S = np.empty(shape=(3, 1)) # cached versions of Z,mu,S
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self._X, self._X2 = np.empty(shape=(2, 1))
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self._X, self._X2 = np.empty(shape=(2, 1))
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self._Z, self._mu, self._S = np.empty(shape=(3, 1)) # cached versions of Z,mu,S
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self._Z, self._mu, self._S = np.empty(shape=(3, 1)) # cached versions of Z,mu,S
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pass
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# def _get_params(self):
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# return np.hstack((self.variance, self.lengthscale))
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# #
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# def _set_params(self, x):
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# assert x.size == (self.num_params)
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# #self.variance = x[0]
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# #self.lengthscale = x[1:]
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#
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# #self.lengthscale2 = np.square(self.lengthscale)
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#
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# # reset cached results
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# #self._X, self._X2, self._params_save = np.empty(shape=(3, 1))
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# #self._Z, self._mu, self._S = np.empty(shape=(3, 1)) # cached versions of Z,mu,S
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#
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# def _get_param_names(self):
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# if self.num_params == 2:
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# return ['variance', 'lengthscale']
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# else:
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# return ['variance'] + ['lengthscale_%i' % i for i in range(self.lengthscale.size)]
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def K(self, X, X2, target):
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def K(self, X, X2, target):
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#if self._X is None or X.base is not self._X.base or X2 is not None:
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self._K_computations(X, X2)
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self._K_computations(X, X2)
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target += self.variance * self._K_dvar
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target += self.variance * self._K_dvar
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def Kdiag(self, X, target):
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def Kdiag(self, X, target):
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np.add(target, self.variance, target)
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np.add(target, self.variance, target)
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def dK_dtheta(self, dL_dK, X, X2, target):
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def update_gradients_full(self, dL_dK, X):
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#if self._X is None or X.base is not self._X.base or X2 is not None:
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self._K_computations(X, X2)
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self._K_computations(X, X2)
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target[0] += np.sum(self._K_dvar * dL_dK)
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self.variance.gradient = np.sum(self._K_dvar * dL_dK)
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if self.ARD:
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if self.ARD:
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dvardLdK = self._K_dvar * dL_dK
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self.lengthscale.gradient = self._dL_dlengthscales_via_K(dL_dK, X, None)
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var_len3 = self.variance / np.power(self.lengthscale, 3)
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if X2 is None:
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# save computation for the symmetrical case
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dvardLdK = dvardLdK + dvardLdK.T
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code = """
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int q,i,j;
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double tmp;
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for(q=0; q<input_dim; q++){
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tmp = 0;
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for(i=0; i<num_data; i++){
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for(j=0; j<i; j++){
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tmp += (X(i,q)-X(j,q))*(X(i,q)-X(j,q))*dvardLdK(i,j);
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}
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}
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target(q+1) += var_len3(q)*tmp;
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}
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"""
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num_data, num_inducing, input_dim = X.shape[0], X.shape[0], self.input_dim
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X = param_to_array(X)
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weave.inline(code, arg_names=['num_data', 'num_inducing', 'input_dim', 'X', 'target', 'dvardLdK', 'var_len3'], type_converters=weave.converters.blitz, **self.weave_options)
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else:
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code = """
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int q,i,j;
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double tmp;
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for(q=0; q<input_dim; q++){
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tmp = 0;
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for(i=0; i<num_data; i++){
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for(j=0; j<num_inducing; j++){
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tmp += (X(i,q)-X2(j,q))*(X(i,q)-X2(j,q))*dvardLdK(i,j);
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}
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}
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target(q+1) += var_len3(q)*tmp;
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}
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"""
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num_data, num_inducing, input_dim = X.shape[0], X2.shape[0], self.input_dim
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# [np.add(target[1+q:2+q],var_len3[q]*np.sum(dvardLdK*np.square(X[:,q][:,None]-X2[:,q][None,:])),target[1+q:2+q]) for q in range(self.input_dim)]
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X, X2 = param_to_array(X, X2)
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weave.inline(code, arg_names=['num_data', 'num_inducing', 'input_dim', 'X', 'X2', 'target', 'dvardLdK', 'var_len3'], type_converters=weave.converters.blitz, **self.weave_options)
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else:
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else:
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target[1] += (self.variance / self.lengthscale) * np.sum(self._K_dvar * self._K_dist2 * dL_dK)
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self.lengthscale.gradient = (self.variance / self.lengthscale) * np.sum(self._K_dvar * self._K_dist2 * dL_dK)
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def update_gradients_sparse(self, dL_dKmm, dL_dKnm, dL_dKdiag, X, Z):
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#contributions from Kdiag
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self.variance.gradient = np.sum(dL_dKdiag)
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#from Knm
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self._K_computations(X, Z)
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self.variance.gradient += np.sum(dL_dKnm * self._K_dvar)
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if self.ARD:
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self.lengthscales.gradient = self._dL_dlengthscales_via_K(dL_dKnm, X, Z)
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else:
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self.lengthscale.gradient = (self.variance / self.lengthscale) * np.sum(self._K_dvar * self._K_dist2 * dL_dK)
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#from Kmm
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self._K_computations(Z, None)
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self.variance.gradient += np.sum(dL_dKmm * self._K_dvar)
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if self.ARD:
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self.lengthscales.gradient += self._dL_dlengthscales_via_K(dL_dKmm, Z, None)
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else:
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self.lengthscale.gradient += (self.variance / self.lengthscale) * np.sum(self._K_dvar * self._K_dist2 * dL_dK)
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def update_gradients_variational(self, dL_dKmm, dL_dpsi0, dL_dpsi1, dL_dpsi2, mu, S, Z):
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self._psi_computations(Z, mu, S)
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#contributions from psi0:
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self.variance.gradient = np.sum(dL_dpsi0)
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#from psi1
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self.variance.gradient += np.sum(dL_dpsi1 * self._psi1 / self.variance)
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d_length = self._psi1[:,:,None] * ((self._psi1_dist_sq - 1.)/(self.lengthscale*self._psi1_denom) +1./self.lengthscale)
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dpsi1_dlength = d_length * dL_dpsi1[:, :, None]
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if not self.ARD:
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self.lengthscale.gradeint = dpsi1_dlength.sum()
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else:
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self.lengthscale.gradient = dpsi1_dlength.sum(0).sum(0)
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#from psi2
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d_var = 2.*self._psi2 / self.variance
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d_length = 2.*self._psi2[:, :, :, None] * (self._psi2_Zdist_sq * self._psi2_denom + self._psi2_mudist_sq + S[:, None, None, :] / self.lengthscale2) / (self.lengthscale * self._psi2_denom)
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self.variance.gradient += np.sum(dL_dpsi2 * d_var)
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dpsi2_dlength = d_length * dL_dpsi2[:, :, :, None]
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if not self.ARD:
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self.lengthscale.gradient += dpsi2_dlength.sum()
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else:
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self.lengthscale.gradient += dpsi2_dlength.sum(0).sum(0).sum(0)
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#from Kmm
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self._K_computations(Z, None)
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self.variance.gradient += np.sum(dL_dKmm * self._K_dvar)
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if self.ARD:
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self.lengthscales.gradient += self._dL_dlengthscales_via_K(dL_dKmm, Z, None)
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else:
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self.lengthscale.gradient += (self.variance / self.lengthscale) * np.sum(self._K_dvar * self._K_dist2 * dL_dK)
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def dKdiag_dtheta(self, dL_dKdiag, X, target):
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# NB: derivative of diagonal elements wrt lengthscale is 0
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target[0] += np.sum(dL_dKdiag)
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def dK_dX(self, dL_dK, X, X2, target):
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def dK_dX(self, dL_dK, X, X2, target):
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#if self._X is None or X.base is not self._X.base or X2 is not None:
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#if self._X is None or X.base is not self._X.base or X2 is not None:
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@ -182,8 +173,6 @@ class RBF(Kernpart):
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def psi0(self, Z, mu, S, target):
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def psi0(self, Z, mu, S, target):
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target += self.variance
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target += self.variance
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def dpsi0_dtheta(self, dL_dpsi0, Z, mu, S, target):
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target[0] += np.sum(dL_dpsi0)
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def dpsi0_dmuS(self, dL_dpsi0, Z, mu, S, target_mu, target_S):
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def dpsi0_dmuS(self, dL_dpsi0, Z, mu, S, target_mu, target_S):
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pass
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pass
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@ -192,16 +181,6 @@ class RBF(Kernpart):
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self._psi_computations(Z, mu, S)
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self._psi_computations(Z, mu, S)
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target += self._psi1
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target += self._psi1
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def dpsi1_dtheta(self, dL_dpsi1, Z, mu, S, target):
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self._psi_computations(Z, mu, S)
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target[0] += np.sum(dL_dpsi1 * self._psi1 / self.variance)
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d_length = self._psi1[:,:,None] * ((self._psi1_dist_sq - 1.)/(self.lengthscale*self._psi1_denom) +1./self.lengthscale)
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dpsi1_dlength = d_length * dL_dpsi1[:, :, None]
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if not self.ARD:
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target[1] += dpsi1_dlength.sum()
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else:
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target[1:] += dpsi1_dlength.sum(0).sum(0)
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def dpsi1_dZ(self, dL_dpsi1, Z, mu, S, target):
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def dpsi1_dZ(self, dL_dpsi1, Z, mu, S, target):
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self._psi_computations(Z, mu, S)
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self._psi_computations(Z, mu, S)
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denominator = (self.lengthscale2 * (self._psi1_denom))
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denominator = (self.lengthscale2 * (self._psi1_denom))
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@ -218,19 +197,6 @@ class RBF(Kernpart):
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self._psi_computations(Z, mu, S)
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self._psi_computations(Z, mu, S)
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target += self._psi2
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target += self._psi2
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def dpsi2_dtheta(self, dL_dpsi2, Z, mu, S, target):
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"""Shape N,num_inducing,num_inducing,Ntheta"""
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self._psi_computations(Z, mu, S)
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d_var = 2.*self._psi2 / self.variance
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d_length = 2.*self._psi2[:, :, :, None] * (self._psi2_Zdist_sq * self._psi2_denom + self._psi2_mudist_sq + S[:, None, None, :] / self.lengthscale2) / (self.lengthscale * self._psi2_denom)
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target[0] += np.sum(dL_dpsi2 * d_var)
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dpsi2_dlength = d_length * dL_dpsi2[:, :, :, None]
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if not self.ARD:
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target[1] += dpsi2_dlength.sum()
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else:
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target[1:] += dpsi2_dlength.sum(0).sum(0).sum(0)
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def dpsi2_dZ(self, dL_dpsi2, Z, mu, S, target):
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def dpsi2_dZ(self, dL_dpsi2, Z, mu, S, target):
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self._psi_computations(Z, mu, S)
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self._psi_computations(Z, mu, S)
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term1 = self._psi2_Zdist / self.lengthscale2 # num_inducing, num_inducing, input_dim
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term1 = self._psi2_Zdist / self.lengthscale2 # num_inducing, num_inducing, input_dim
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@ -266,6 +232,60 @@ class RBF(Kernpart):
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self._K_dist2 = -2.*np.dot(X, X2.T) + (np.sum(np.square(X), 1)[:, None] + np.sum(np.square(X2), 1)[None, :])
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self._K_dist2 = -2.*np.dot(X, X2.T) + (np.sum(np.square(X), 1)[:, None] + np.sum(np.square(X2), 1)[None, :])
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self._K_dvar = np.exp(-0.5 * self._K_dist2)
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self._K_dvar = np.exp(-0.5 * self._K_dist2)
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def _dL_dlengthscales_via_K(self, dL_dK, X, X2):
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"""
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A helper function for update_gradients_* methods
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Computes the derivative of the objective L wrt the lengthscales via
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dL_dl = sum_{i,j}(dL_dK_{ij} dK_dl)
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assumes self._K_computations has just been called.
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This is only valid if self.ARD=True
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"""
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target = np.zeros(self.input_dim)
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dvardLdK = self._K_dvar * dL_dK
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var_len3 = self.variance / np.power(self.lengthscale, 3)
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if X2 is None:
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# save computation for the symmetrical case
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dvardLdK = dvardLdK + dvardLdK.T
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code = """
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int q,i,j;
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double tmp;
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for(q=0; q<input_dim; q++){
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tmp = 0;
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for(i=0; i<num_data; i++){
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for(j=0; j<i; j++){
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tmp += (X(i,q)-X(j,q))*(X(i,q)-X(j,q))*dvardLdK(i,j);
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}
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}
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target(q) += var_len3(q)*tmp;
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}
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"""
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num_data, num_inducing, input_dim = X.shape[0], X.shape[0], self.input_dim
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X = param_to_array(X)
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weave.inline(code, arg_names=['num_data', 'num_inducing', 'input_dim', 'X', 'target', 'dvardLdK', 'var_len3'], type_converters=weave.converters.blitz, **self.weave_options)
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else:
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code = """
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int q,i,j;
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double tmp;
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for(q=0; q<input_dim; q++){
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tmp = 0;
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for(i=0; i<num_data; i++){
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for(j=0; j<num_inducing; j++){
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tmp += (X(i,q)-X2(j,q))*(X(i,q)-X2(j,q))*dvardLdK(i,j);
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}
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}
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target(q) += var_len3(q)*tmp;
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|
}
|
||||||
|
"""
|
||||||
|
num_data, num_inducing, input_dim = X.shape[0], X2.shape[0], self.input_dim
|
||||||
|
X, X2 = param_to_array(X, X2)
|
||||||
|
weave.inline(code, arg_names=['num_data', 'num_inducing', 'input_dim', 'X', 'X2', 'target', 'dvardLdK', 'var_len3'], type_converters=weave.converters.blitz, **self.weave_options)
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
def _psi_computations(self, Z, mu, S):
|
def _psi_computations(self, Z, mu, S):
|
||||||
# here are the "statistics" for psi1 and psi2
|
# here are the "statistics" for psi1 and psi2
|
||||||
Z_changed = not fast_array_equal(Z, self._Z)
|
Z_changed = not fast_array_equal(Z, self._Z)
|
||||||
|
|
|
||||||
Loading…
Add table
Add a link
Reference in a new issue