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Made RBF-kernel compatible with diff-kernel

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This commit is contained in:
Siivola Eero 2018-09-05 15:38:03 +03:00
parent 4988aad0dd
commit 04033c1b32
2 changed files with 109 additions and 1 deletions
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90
GPy/kern/src/rbf.py
View file

@ -6,6 +6,7 @@ import numpy as np
from .stationary import Stationary
from .psi_comp import PSICOMP_RBF, PSICOMP_RBF_GPU
from ...core import Param
from paramz.caching import Cache_this
from paramz.transformations import Logexp
from .grid_kerns import GridRBF
@ -50,6 +51,27 @@ class RBF(Stationary):
def K_of_r(self, r):
return self.variance * np.exp(-0.5 * r**2)
@Cache_this(limit=3, ignore_args=())
def dK_dX(self, X, X2, dimX):
r = self._scaled_dist(X, X2)
K = self.K_of_r(r)
dist = X[:,None,dimX]-X2[None,:,dimX]
lengthscale2inv = (np.ones((X.shape[1]))/(self.lengthscale**2))[dimX]
return -1.*K*dist*lengthscale2inv
@Cache_this(limit=3, ignore_args=())
def dK_dX2(self, X, X2, dimX2):
return -self.dK_dX(X,X2, dimX2)
@Cache_this(limit=3, ignore_args=())
def dK2_dXdX2(self, X, X2, dimX, dimX2):
r = self._scaled_dist(X, X2)
K = self.K_of_r(r)
if X2 is None:
X2=X
dist = X[:,None,:]-X2[None,:,:]
lengthscale2inv = np.ones((X.shape[1]))/(self.lengthscale**2)
return -1.*K*dist[:,:,dimX]*dist[:,:,dimX2]*lengthscale2inv[dimX]*lengthscale2inv[dimX2] + (dimX==dimX2)*K*lengthscale2inv[dimX]
def dK_dr(self, r):
return -r*self.K_of_r(r)
@ -58,6 +80,74 @@ class RBF(Stationary):
def dK2_drdr_diag(self):
return -self.variance # as the diagonal of r is always filled with zeros
@Cache_this(limit=3, ignore_args=())
def dK_dvariance(self,X,X2):
return self.K(X,X2)/self.variance
@Cache_this(limit=3, ignore_args=())
def dK2_dvariancedX(self, X, X2, dim):
return self.dK_dX(X,X2, dim)/self.variance
@Cache_this(limit=3, ignore_args=())
def dK2_dvariancedX2(self, X, X2, dim):
return self.dK_dX2(X,X2, dim)/self.variance
@Cache_this(limit=3, ignore_args=())
def dK3_dvariancedXdX2(self, X, X2, dim, dimX2):
return self.dK2_dXdX2(X, X2, dim, dimX2)/self.variance
@Cache_this(limit=3, ignore_args=())
def dK2_dlengthscaledX(self, X, X2, dimX):
r = self._scaled_dist(X, X2)
K = self.K_of_r(r)
if X2 is None:
X2=X
dist = X[:,None,:]-X2[None,:,:]
lengthscaleinv = np.ones((X.shape[1]))/(self.lengthscale)
if self.ARD:
g = []
for diml in range(X.shape[1]):
g += [-1.*K*dist[:,:,dimX]*(dist[:,:,diml]**2)*(lengthscaleinv[dimX]**2)*(lengthscaleinv[diml]**3) + 2.*dist[:,:,dimX]*(lengthscaleinv[diml]**3)*K*(dimX == diml)]
else:
g = -1.*K*dist[:,:,dimX]*np.sum(dist**2, axis=2)*(lengthscaleinv[dimX]**5) + 2.*dist[:,:,dimX]*(lengthscaleinv[dimX]**3)*K
return g
@Cache_this(limit=3, ignore_args=())
def dK2_dlengthscaledX2(self, X, X2, dimX2):
tmp = self.dK2_dlengthscaledX(X, X2, dimX2)
if self.ARD:
return [-1.*g for g in tmp]
else:
return -1*tmp
@Cache_this(limit=3, ignore_args=())
def dK3_dlengthscaledXdX2(self, X, X2, dimX, dimX2):
r = self._scaled_dist(X, X2)
K = self.K_of_r(r)
if X2 is None:
X2=X
dist = X[:,None,:]-X2[None,:,:]
lengthscaleinv = np.ones((X.shape[1]))/(self.lengthscale)
lengthscale2inv = lengthscaleinv**2
if self.ARD:
g = []
for diml in range(X.shape[1]):
tmp = -1.*K*dist[:,:,dimX]*dist[:,:,dimX2]*(dist[:,:,diml]**2)*lengthscale2inv[dimX]*lengthscale2inv[dimX2]*(lengthscaleinv[diml]**3)
if dimX == dimX2:
tmp += K*lengthscale2inv[dimX]*(lengthscaleinv[diml]**3)*(dist[:,:,diml]**2)
if diml == dimX:
tmp += 2.*K*dist[:,:,dimX]*dist[:,:,dimX2]*lengthscale2inv[dimX2]*(lengthscaleinv[dimX]**3)
if diml == dimX2:
tmp += 2.*K*dist[:,:,dimX]*dist[:,:,dimX2]*lengthscale2inv[dimX]*(lengthscaleinv[dimX2]**3)
if dimX == dimX2:
tmp += -2.*K*(lengthscaleinv[dimX]**3)
g += [tmp]
else:
g = -1.*K*dist[:,:,dimX]*dist[:,:,dimX2]*np.sum(dist**2, axis=2)*(lengthscaleinv[dimX]**7) +4*K*dist[:,:,dimX]*dist[:,:,dimX2]*(lengthscaleinv[dimX]**5)
if dimX == dimX2:
g += -2.*K*(lengthscaleinv[dimX]**3) + K*(lengthscaleinv[dimX]**5)*np.sum(dist**2, axis=2)
return g
def __getstate__(self):
dc = super(RBF, self).__getstate__()

20
GPy/kern/src/stationary.py
View file

@ -212,7 +212,6 @@ class Stationary(Kern):
r = self._scaled_dist(X, X2)
self.lengthscale.gradient = -np.sum(dL_dr*r)/self.lengthscale
def update_gradients_direct(self, dL_dVar, dL_dLen):
"""
Specially intended for the Grid regression case.
@ -222,6 +221,10 @@ class Stationary(Kern):
"""
self.variance.gradient = dL_dVar
self.lengthscale.gradient = dL_dLen
def append_gradients_direct(self, dL_dVar, dL_dLen):
self.variance.gradient += dL_dVar
self.lengthscale.gradient += dL_dLen
def _inv_dist(self, X, X2=None):
"""
@ -307,6 +310,21 @@ class Stationary(Kern):
l4 = np.ones(X.shape[1])*self.lengthscale**2
return dL_dK_diag * (np.eye(X.shape[1]) * -self.dK2_drdr_diag()/(l4))[None, :,:]# np.zeros(X.shape+(X.shape[1],))
#return np.ones(X.shape) * d2L_dK * self.variance/self.lengthscale**2 # np.zeros(X.shape)
def dgradients_dX(self, X, X2, dimX):
g1 = self.dK2_dvariancedX(X, X2, dimX)
g2 = self.dK2_dlengthscaledX(X, X2, dimX)
return [g1, g2]
def dgradients_dX2(self, X, X2, dimX2):
g1 = self.dK2_dvariancedX2(X, X2, dimX2)
g2 = self.dK2_dlengthscaledX2(X, X2, dimX2)
return [g1, g2]
def dgradients2_dXdX2(self, X, X2, dimX, dimX2):
g1 = self.dK3_dvariancedXdX2(X, X2, dimX, dimX2)
g2 = self.dK3_dlengthscaledXdX2(X, X2, dimX, dimX2)
return [g1, g2]
def _gradients_X_pure(self, dL_dK, X, X2=None):
invdist = self._inv_dist(X, X2)