From 0e01877586647a650c57e125a7e66b71242fb25d Mon Sep 17 00:00:00 2001 From: James Hensman Date: Mon, 24 Feb 2014 14:55:16 +0000 Subject: [PATCH] stuf in rbf might be broken --- GPy/kern/_src/rbf.py | 182 +++++++++---------------------------------- 1 file changed, 38 insertions(+), 144 deletions(-) diff --git a/GPy/kern/_src/rbf.py b/GPy/kern/_src/rbf.py index 28115fae..356160ac 100644 --- a/GPy/kern/_src/rbf.py +++ b/GPy/kern/_src/rbf.py @@ -9,81 +9,39 @@ from ...util.linalg import tdot from ...util.misc import fast_array_equal, param_to_array from ...core.parameterization import Param from ...core.parameterization.transformations import Logexp +from stationary import Stationary -class RBF(Kern): +class RBF(Stationary): """ Radial Basis Function kernel, aka squared-exponential, exponentiated quadratic or Gaussian kernel: .. math:: - 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} + k(r) = \sigma^2 \exp \\bigg(- \\frac{1}{2} r^2 \\bigg) - where \ell_i is the lengthscale, \sigma^2 the variance and d the dimensionality of the input. - - :param input_dim: the number of input dimensions - :type input_dim: int - :param variance: the variance of the kernel - :type variance: float - :param lengthscale: the vector of lengthscale of the kernel - :type lengthscale: array or list of the appropriate size (or float if there is only one lengthscale parameter) - :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. - :type ARD: Boolean - :rtype: kernel object - - .. Note: this object implements both the ARD and 'spherical' version of the function """ - def __init__(self, input_dim, variance=1., lengthscale=None, ARD=False, name='rbf'): - super(RBF, self).__init__(input_dim, name) - self.input_dim = input_dim - self.ARD = ARD - - if not ARD: - if lengthscale is not None: - lengthscale = np.asarray(lengthscale) - assert lengthscale.size == 1, "Only one lengthscale needed for non-ARD kernel" - else: - lengthscale = np.ones(1) - else: - if lengthscale is not None: - lengthscale = np.asarray(lengthscale) - assert lengthscale.size == self.input_dim, "bad number of lengthscales" - else: - lengthscale = np.ones(self.input_dim) - - self.variance = Param('variance', variance, Logexp()) - - self.lengthscale = Param('lengthscale', lengthscale, Logexp()) - self.lengthscale.add_observer(self, self.update_lengthscale) - self.update_lengthscale(self.lengthscale) - - self.add_parameters(self.variance, self.lengthscale) - self.parameters_changed() # initializes cache - + def __init__(self, input_dim, variance=1., lengthscale=None, ARD=False, name='RBF'): + super(RBF, self).__init__(input_dim, variance, lengthscale, ARD, name) self.weave_options = {} - def update_lengthscale(self, l): - self.lengthscale2 = np.square(self.lengthscale) + def K_of_r(self, r): + return self.variance * np.exp(-0.5 * r**2) + + def dK_dr(self, r): + return -r*self.K_of_r(r) + + #---------------------------------------# + # PSI statistics # + #---------------------------------------# def parameters_changed(self): # reset cached results - self._X, self._X2 = np.empty(shape=(2, 1)) self._Z, self._mu, self._S = np.empty(shape=(3, 1)) # cached versions of Z,mu,S - def K(self, X, X2=None): - self._K_computations(X, X2) - return self.variance * self._K_dvar - - def Kdiag(self, X): - ret = np.ones(X.shape[0]) - ret[:] = self.variance - return ret def psi0(self, Z, posterior_variational): - mu = posterior_variational.mean - ret = np.empty(mu.shape[0], dtype=np.float64) - ret[:] = self.variance - return ret + return self.Kdiag(posterior_variational.mean) def psi1(self, Z, posterior_variational): mu = posterior_variational.mean @@ -97,55 +55,30 @@ class RBF(Kern): self._psi_computations(Z, mu, S) return self._psi2 - def update_gradients_full(self, dL_dK, X): - self._K_computations(X, None) - self.variance.gradient = np.sum(self._K_dvar * dL_dK) - if self.ARD: - self.lengthscale.gradient = self._dL_dlengthscales_via_K(dL_dK, X, None) - else: - self.lengthscale.gradient = (self.variance / self.lengthscale) * np.sum(self._K_dvar * self._K_dist2 * dL_dK) - - def update_gradients_sparse(self, dL_dKmm, dL_dKnm, dL_dKdiag, X, Z): - #contributions from Kdiag - self.variance.gradient = np.sum(dL_dKdiag) - - #from Knm - self._K_computations(X, Z) - self.variance.gradient += np.sum(dL_dKnm * self._K_dvar) - if self.ARD: - self.lengthscale.gradient = self._dL_dlengthscales_via_K(dL_dKnm, X, Z) - - else: - self.lengthscale.gradient = (self.variance / self.lengthscale) * np.sum(self._K_dvar * self._K_dist2 * dL_dKnm) - - #from Kmm - self._K_computations(Z, None) - self.variance.gradient += np.sum(dL_dKmm * self._K_dvar) - if self.ARD: - self.lengthscale.gradient += self._dL_dlengthscales_via_K(dL_dKmm, Z, None) - else: - self.lengthscale.gradient += (self.variance / self.lengthscale) * np.sum(self._K_dvar * self._K_dist2 * dL_dKmm) - def update_gradients_variational(self, dL_dKmm, dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, posterior_variational): + #contributions from Kmm + sself.update_gradients_full(dL_dKmm, Z) + mu = posterior_variational.mean S = posterior_variational.variance self._psi_computations(Z, mu, S) + l2 = self.lengthscale **2 #contributions from psi0: - self.variance.gradient = np.sum(dL_dpsi0) + self.variance.gradient += np.sum(dL_dpsi0) #from psi1 self.variance.gradient += np.sum(dL_dpsi1 * self._psi1 / self.variance) d_length = self._psi1[:,:,None] * ((self._psi1_dist_sq - 1.)/(self.lengthscale*self._psi1_denom) +1./self.lengthscale) dpsi1_dlength = d_length * dL_dpsi1[:, :, None] if not self.ARD: - self.lengthscale.gradient = dpsi1_dlength.sum() + self.lengthscale.gradient += dpsi1_dlength.sum() else: - self.lengthscale.gradient = dpsi1_dlength.sum(0).sum(0) + self.lengthscale.gradient += dpsi1_dlength.sum(0).sum(0) #from psi2 d_var = 2.*self._psi2 / self.variance - 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) + 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) self.variance.gradient += np.sum(dL_dpsi2 * d_var) dpsi2_dlength = d_length * dL_dpsi2[:, :, :, None] @@ -154,27 +87,20 @@ class RBF(Kern): else: self.lengthscale.gradient += dpsi2_dlength.sum(0).sum(0).sum(0) - #from Kmm - self._K_computations(Z, None) - self.variance.gradient += np.sum(dL_dKmm * self._K_dvar) - if self.ARD: - self.lengthscale.gradient += self._dL_dlengthscales_via_K(dL_dKmm, Z, None) - 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, Z, posterior_variational): mu = posterior_variational.mean S = posterior_variational.variance self._psi_computations(Z, mu, S) + l2 = self.lengthscale **2 #psi1 - denominator = (self.lengthscale2 * (self._psi1_denom)) + denominator = (l2 * (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 + term1 = self._psi2_Zdist / l2 # num_inducing, num_inducing, input_dim + term2 = self._psi2_mudist / self._psi2_denom / l2 # N, num_inducing, num_inducing, input_dim dZ = self._psi2[:, :, :, None] * (term1[None] + term2) grad += 2*(dL_dpsi2[:, :, :, None] * dZ).sum(0).sum(0) @@ -186,55 +112,22 @@ class RBF(Kern): mu = posterior_variational.mean S = posterior_variational.variance self._psi_computations(Z, mu, S) + l2 = self.lengthscale **2 #psi1 - tmp = self._psi1[:, :, None] / self.lengthscale2 / self._psi1_denom + tmp = self._psi1[:, :, None] / l2 / 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) #psi2 - tmp = self._psi2[:, :, :, None] / self.lengthscale2 / self._psi2_denom + tmp = self._psi2[:, :, :, None] / l2 / 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) - if X2 is None: - _K_dist = 2*(X[:, None, :] - X[None, :, :]) - else: - _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. - gradients_X = (-self.variance / self.lengthscale2) * np.transpose(self._K_dvar[:, :, np.newaxis] * _K_dist, (1, 0, 2)) - return np.sum(gradients_X * dL_dK.T[:, :, None], 0) - - def dKdiag_dX(self, dL_dKdiag, X): - return np.zeros(X.shape[0]) - - #---------------------------------------# - # PSI statistics # - #---------------------------------------# - #---------------------------------------# # Precomputations # #---------------------------------------# - def _K_computations(self, X, X2): - #params = self._get_params() - if not (fast_array_equal(X, self._X) and fast_array_equal(X2, self._X2)):# and fast_array_equal(self._params_save , params)): - #self._X = X.copy() - #self._params_save = params.copy() - if X2 is None: - self._X2 = None - X = X / self.lengthscale - Xsquare = np.sum(np.square(X), 1) - self._K_dist2 = -2.*tdot(X) + (Xsquare[:, None] + Xsquare[None, :]) - else: - self._X2 = X2.copy() - X = X / self.lengthscale - X2 = X2 / self.lengthscale - self._K_dist2 = -2.*np.dot(X, X2.T) + (np.sum(np.square(X), 1)[:, None] + np.sum(np.square(X2), 1)[None, :]) - self._K_dvar = np.exp(-0.5 * self._K_dist2) - def _dL_dlengthscales_via_K(self, dL_dK, X, X2): """ A helper function for update_gradients_* methods @@ -301,19 +194,20 @@ class RBF(Kern): if Z_changed or not fast_array_equal(mu, self._mu) or not fast_array_equal(S, self._S): # something's changed. recompute EVERYTHING + l2 = self.lengthscale **2 # psi1 - self._psi1_denom = S[:, None, :] / self.lengthscale2 + 1. + self._psi1_denom = S[:, None, :] / l2 + 1. self._psi1_dist = Z[None, :, :] - mu[:, None, :] - self._psi1_dist_sq = np.square(self._psi1_dist) / self.lengthscale2 / self._psi1_denom + self._psi1_dist_sq = np.square(self._psi1_dist) / l2 / self._psi1_denom self._psi1_exponent = -0.5 * np.sum(self._psi1_dist_sq + np.log(self._psi1_denom), -1) self._psi1 = self.variance * np.exp(self._psi1_exponent) # psi2 - self._psi2_denom = 2.*S[:, None, None, :] / self.lengthscale2 + 1. # N,M,M,Q + self._psi2_denom = 2.*S[:, None, None, :] / l2 + 1. # N,M,M,Q self._psi2_mudist, self._psi2_mudist_sq, self._psi2_exponent, _ = self.weave_psi2(mu, self._psi2_Zhat) # self._psi2_mudist = mu[:,None,None,:]-self._psi2_Zhat #N,M,M,Q - # self._psi2_mudist_sq = np.square(self._psi2_mudist)/(self.lengthscale2*self._psi2_denom) + # self._psi2_mudist_sq = np.square(self._psi2_mudist)/(l2*self._psi2_denom) # 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 self._psi2 = np.square(self.variance) * np.exp(self._psi2_exponent) # N,M,M,Q @@ -332,11 +226,11 @@ class RBF(Kern): psi2_Zdist_sq = self._psi2_Zdist_sq _psi2_denom = self._psi2_denom.squeeze().reshape(N, self.input_dim) half_log_psi2_denom = 0.5 * np.log(self._psi2_denom).squeeze().reshape(N, self.input_dim) - variance_sq = float(np.square(self.variance)) + variance_sq = np.float64(np.square(self.variance)) if self.ARD: - lengthscale2 = self.lengthscale2 + lengthscale2 = self.lengthscale **2 else: - lengthscale2 = np.ones(input_dim) * self.lengthscale2 + lengthscale2 = np.ones(input_dim) * self.lengthscale2**2 code = """ double tmp;