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stuf in rbf might be broken
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James Hensman
parent
f4e270ae53
commit
0e01877586
1 changed files with 38 additions and 144 deletions
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@ -9,81 +9,39 @@ 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 stationary import Stationary
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class RBF(Kern):
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class RBF(Stationary):
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"""
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Radial Basis Function kernel, aka squared-exponential, exponentiated quadratic or Gaussian kernel:
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.. math::
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k(r) = \sigma^2 \exp \\bigg(- \\frac{1}{2} r^2 \\bigg) \ \ \ \ \ \\text{ where } r^2 = \sum_{i=1}^d \\frac{ (x_i-x^\prime_i)^2}{\ell_i^2}
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k(r) = \sigma^2 \exp \\bigg(- \\frac{1}{2} r^2 \\bigg)
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where \ell_i is the lengthscale, \sigma^2 the variance and d the dimensionality of the input.
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:param input_dim: the number of input dimensions
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:type input_dim: int
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:param variance: the variance of the kernel
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:type variance: float
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:param lengthscale: the vector of lengthscale of the kernel
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:type lengthscale: array or list of the appropriate size (or float if there is only one lengthscale parameter)
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:param ARD: Auto Relevance Determination. If equal to "False", the kernel is isotropic (ie. one single lengthscale parameter \ell), otherwise there is one lengthscale parameter per dimension.
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:type ARD: Boolean
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:rtype: kernel object
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.. Note: this object implements both the ARD and 'spherical' version of the function
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"""
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def __init__(self, input_dim, variance=1., lengthscale=None, ARD=False, name='rbf'):
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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.ARD = ARD
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if not ARD:
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if lengthscale is not None:
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lengthscale = np.asarray(lengthscale)
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assert lengthscale.size == 1, "Only one lengthscale needed for non-ARD kernel"
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else:
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lengthscale = np.ones(1)
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else:
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if lengthscale is not None:
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lengthscale = np.asarray(lengthscale)
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assert lengthscale.size == self.input_dim, "bad number of lengthscales"
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else:
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lengthscale = np.ones(self.input_dim)
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self.variance = Param('variance', variance, Logexp())
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self.lengthscale = Param('lengthscale', lengthscale, Logexp())
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self.lengthscale.add_observer(self, self.update_lengthscale)
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self.update_lengthscale(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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def __init__(self, input_dim, variance=1., lengthscale=None, ARD=False, name='RBF'):
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super(RBF, self).__init__(input_dim, variance, lengthscale, ARD, name)
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self.weave_options = {}
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def update_lengthscale(self, l):
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self.lengthscale2 = np.square(self.lengthscale)
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def K_of_r(self, r):
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return self.variance * np.exp(-0.5 * r**2)
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def dK_dr(self, r):
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return -r*self.K_of_r(r)
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#---------------------------------------#
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# PSI statistics #
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#---------------------------------------#
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def parameters_changed(self):
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# reset cached results
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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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def K(self, X, X2=None):
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self._K_computations(X, X2)
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return self.variance * self._K_dvar
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def Kdiag(self, X):
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ret = np.ones(X.shape[0])
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ret[:] = self.variance
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return ret
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def psi0(self, Z, posterior_variational):
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mu = posterior_variational.mean
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ret = np.empty(mu.shape[0], dtype=np.float64)
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ret[:] = self.variance
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return ret
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return self.Kdiag(posterior_variational.mean)
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def psi1(self, Z, posterior_variational):
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mu = posterior_variational.mean
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@ -97,55 +55,30 @@ class RBF(Kern):
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self._psi_computations(Z, mu, S)
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return self._psi2
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def update_gradients_full(self, dL_dK, X):
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self._K_computations(X, None)
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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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self.lengthscale.gradient = self._dL_dlengthscales_via_K(dL_dK, X, 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_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.lengthscale.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_dKnm)
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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.lengthscale.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_dKmm)
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def update_gradients_variational(self, dL_dKmm, dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, posterior_variational):
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#contributions from Kmm
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sself.update_gradients_full(dL_dKmm, Z)
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mu = posterior_variational.mean
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S = posterior_variational.variance
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self._psi_computations(Z, mu, S)
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l2 = self.lengthscale **2
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#contributions from psi0:
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self.variance.gradient = np.sum(dL_dpsi0)
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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.gradient = dpsi1_dlength.sum()
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self.lengthscale.gradient += 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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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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d_length = 2.*self._psi2[:, :, :, None] * (self._psi2_Zdist_sq * self._psi2_denom + self._psi2_mudist_sq + S[:, None, None, :] / l2) / (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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@ -154,27 +87,20 @@ class RBF(Kern):
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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.lengthscale.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_dKmm)
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def gradients_Z_variational(self, dL_dKmm, dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, posterior_variational):
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mu = posterior_variational.mean
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S = posterior_variational.variance
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self._psi_computations(Z, mu, S)
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l2 = self.lengthscale **2
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#psi1
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denominator = (self.lengthscale2 * (self._psi1_denom))
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denominator = (l2 * (self._psi1_denom))
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dpsi1_dZ = -self._psi1[:, :, None] * ((self._psi1_dist / denominator))
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grad = np.sum(dL_dpsi1[:, :, None] * dpsi1_dZ, 0)
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#psi2
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term1 = self._psi2_Zdist / self.lengthscale2 # num_inducing, num_inducing, input_dim
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term2 = self._psi2_mudist / self._psi2_denom / self.lengthscale2 # N, num_inducing, num_inducing, input_dim
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term1 = self._psi2_Zdist / l2 # num_inducing, num_inducing, input_dim
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term2 = self._psi2_mudist / self._psi2_denom / l2 # N, num_inducing, num_inducing, input_dim
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dZ = self._psi2[:, :, :, None] * (term1[None] + term2)
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grad += 2*(dL_dpsi2[:, :, :, None] * dZ).sum(0).sum(0)
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@ -186,55 +112,22 @@ class RBF(Kern):
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mu = posterior_variational.mean
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S = posterior_variational.variance
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self._psi_computations(Z, mu, S)
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l2 = self.lengthscale **2
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#psi1
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tmp = self._psi1[:, :, None] / self.lengthscale2 / self._psi1_denom
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tmp = self._psi1[:, :, None] / l2 / self._psi1_denom
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grad_mu = np.sum(dL_dpsi1[:, :, None] * tmp * self._psi1_dist, 1)
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grad_S = np.sum(dL_dpsi1[:, :, None] * 0.5 * tmp * (self._psi1_dist_sq - 1), 1)
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#psi2
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tmp = self._psi2[:, :, :, None] / self.lengthscale2 / self._psi2_denom
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tmp = self._psi2[:, :, :, None] / l2 / self._psi2_denom
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grad_mu += -2.*(dL_dpsi2[:, :, :, None] * tmp * self._psi2_mudist).sum(1).sum(1)
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grad_S += (dL_dpsi2[:, :, :, None] * tmp * (2.*self._psi2_mudist_sq - 1)).sum(1).sum(1)
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return grad_mu, grad_S
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def gradients_X(self, dL_dK, X, X2=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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self._K_computations(X, X2)
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if X2 is None:
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_K_dist = 2*(X[:, None, :] - X[None, :, :])
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else:
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_K_dist = X[:, None, :] - X2[None, :, :] # don't cache this in _K_computations because it is high memory. If this function is being called, chances are we're not in the high memory arena.
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gradients_X = (-self.variance / self.lengthscale2) * np.transpose(self._K_dvar[:, :, np.newaxis] * _K_dist, (1, 0, 2))
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return np.sum(gradients_X * dL_dK.T[:, :, None], 0)
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def dKdiag_dX(self, dL_dKdiag, X):
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return np.zeros(X.shape[0])
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#---------------------------------------#
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# PSI statistics #
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#---------------------------------------#
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#---------------------------------------#
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# Precomputations #
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#---------------------------------------#
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def _K_computations(self, X, X2):
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#params = self._get_params()
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if not (fast_array_equal(X, self._X) and fast_array_equal(X2, self._X2)):# and fast_array_equal(self._params_save , params)):
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#self._X = X.copy()
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#self._params_save = params.copy()
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if X2 is None:
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self._X2 = None
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X = X / self.lengthscale
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Xsquare = np.sum(np.square(X), 1)
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self._K_dist2 = -2.*tdot(X) + (Xsquare[:, None] + Xsquare[None, :])
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else:
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self._X2 = X2.copy()
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X = X / self.lengthscale
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X2 = X2 / self.lengthscale
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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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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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@ -301,19 +194,20 @@ class RBF(Kern):
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if Z_changed or not fast_array_equal(mu, self._mu) or not fast_array_equal(S, self._S):
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# something's changed. recompute EVERYTHING
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l2 = self.lengthscale **2
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# psi1
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self._psi1_denom = S[:, None, :] / self.lengthscale2 + 1.
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self._psi1_denom = S[:, None, :] / l2 + 1.
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self._psi1_dist = Z[None, :, :] - mu[:, None, :]
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self._psi1_dist_sq = np.square(self._psi1_dist) / self.lengthscale2 / self._psi1_denom
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self._psi1_dist_sq = np.square(self._psi1_dist) / l2 / self._psi1_denom
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self._psi1_exponent = -0.5 * np.sum(self._psi1_dist_sq + np.log(self._psi1_denom), -1)
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self._psi1 = self.variance * np.exp(self._psi1_exponent)
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# psi2
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self._psi2_denom = 2.*S[:, None, None, :] / self.lengthscale2 + 1. # N,M,M,Q
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self._psi2_denom = 2.*S[:, None, None, :] / l2 + 1. # N,M,M,Q
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self._psi2_mudist, self._psi2_mudist_sq, self._psi2_exponent, _ = self.weave_psi2(mu, self._psi2_Zhat)
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# self._psi2_mudist = mu[:,None,None,:]-self._psi2_Zhat #N,M,M,Q
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# self._psi2_mudist_sq = np.square(self._psi2_mudist)/(self.lengthscale2*self._psi2_denom)
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# self._psi2_mudist_sq = np.square(self._psi2_mudist)/(l2*self._psi2_denom)
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# self._psi2_exponent = np.sum(-self._psi2_Zdist_sq -self._psi2_mudist_sq -0.5*np.log(self._psi2_denom),-1) #N,M,M,Q
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self._psi2 = np.square(self.variance) * np.exp(self._psi2_exponent) # N,M,M,Q
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@ -332,11 +226,11 @@ class RBF(Kern):
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psi2_Zdist_sq = self._psi2_Zdist_sq
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_psi2_denom = self._psi2_denom.squeeze().reshape(N, self.input_dim)
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half_log_psi2_denom = 0.5 * np.log(self._psi2_denom).squeeze().reshape(N, self.input_dim)
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variance_sq = float(np.square(self.variance))
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variance_sq = np.float64(np.square(self.variance))
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if self.ARD:
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lengthscale2 = self.lengthscale2
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lengthscale2 = self.lengthscale **2
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else:
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lengthscale2 = np.ones(input_dim) * self.lengthscale2
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lengthscale2 = np.ones(input_dim) * self.lengthscale2**2
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code = """
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double tmp;
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