mirror of
https://github.com/SheffieldML/GPy.git
synced 2026-05-11 04:52:37 +02:00
[gradients xx] getting there
This commit is contained in:
Max Zwiessele
parent
4efb92c554
commit
5d19039d90
3 changed files with 52 additions and 51 deletions
|
|
@ -449,7 +449,7 @@ class GP(Model):
|
|||
:param bool covariance: whether to include the covariance of the wishart embedding.
|
||||
:param array-like dimensions: which dimensions of the input space to use [defaults to self.get_most_significant_input_dimensions()[:2]]
|
||||
"""
|
||||
G = self.predict_wishard_embedding(Xnew, kern, mean, covariance)
|
||||
G = self.predict_wishart_embedding(Xnew, kern, mean, covariance)
|
||||
if dimensions is None:
|
||||
dimensions = self.get_most_significant_input_dimensions()[:2]
|
||||
G = G[:, dimensions][:,:,dimensions]
|
||||
|
|
|
|||
|
|
@ -70,11 +70,11 @@ class _Slice_wrap(object):
|
|||
ret[:, self.k._all_dims_active] = return_val
|
||||
elif len(self.shape) == 3: # derivative for X2!=None
|
||||
if self.diag:
|
||||
ret[:, :, self.k._all_dims_active][:, self.k._all_dims_active] = return_val
|
||||
ret.T[np.ix_(self.k._all_dims_active, self.k._all_dims_active)] = return_val.T
|
||||
else:
|
||||
ret[:, :, self.k._all_dims_active] = return_val
|
||||
elif len(self.shape) == 4: # second order derivative
|
||||
ret[:, :, self.k._all_dims_active][:, :, :, self.k._all_dims_active] = return_val
|
||||
ret.T[np.ix_(self.k._all_dims_active, self.k._all_dims_active)] = return_val.T
|
||||
return ret
|
||||
return return_val
|
||||
|
||||
|
|
|
|||
|
|
@ -223,7 +223,7 @@ class Stationary(Kern):
|
|||
Given the derivative of the objective K(dL_dK), compute the second derivative of K wrt X and X2:
|
||||
|
||||
cov = True: returns the full covariance matrix [QxQ] of the input dimensionfor each pair or vectors
|
||||
cov = False: returns the diagonal of the covariance matrix [QxQ] of the input dimensionfor each pair
|
||||
cov = False: returns the diagonal of the covariance matrix [QxQ] of the input dimensionfor each pair
|
||||
or vectors (computationally more efficient if the full covariance matrix is not needed)
|
||||
..math:
|
||||
\frac{\partial^2 K}{\partial X2 ^2} = - \frac{\partial^2 K}{\partial X\partial X2}
|
||||
|
|
@ -247,20 +247,21 @@ class Stationary(Kern):
|
|||
X2 = X
|
||||
tmp1 -= np.eye(X.shape[0])*self.variance
|
||||
else:
|
||||
#tmp1[X==X2.T] -= self.variance # Old version, to be removed
|
||||
#tmp1[X==X2.T] -= self.variance # Old version, to be removed
|
||||
# (seems to have a bug: it is subtracted to the first X1 anyway)
|
||||
tmp1[invdist2==0.] -= self.variance
|
||||
|
||||
|
||||
if cov: # full covariance
|
||||
grad = np.empty((X.shape[0], X2.shape[0], X2.shape[1], X.shape[1]), dtype=np.float64)
|
||||
for q in range(self.input_dim):
|
||||
tmpdist = (X[:,[q]]-X2[:,[q]].T)
|
||||
for r in range(self.input_dim):
|
||||
tmpdist2 = (X[:,[q]]-X2[:,[q]].T)*(X[:,[r]]-X2[:,[r]].T) # Introduce temporary distance
|
||||
tmpdist2 = tmpdist*(X[:,[r]]-X2[:,[r]].T) # Introduce temporary distance
|
||||
if r==q:
|
||||
grad[:, :, q, r] = np.multiply(dL_dK,(np.multiply((tmp1*invdist2 - tmp2),tmpdist2)/l2[r] - tmp1)/l2[q])
|
||||
else:
|
||||
grad[:, :, q, r] = np.multiply(dL_dK,(np.multiply((tmp1*invdist2 - tmp2),tmpdist2)/l2[r])/l2[q])
|
||||
else:
|
||||
else:
|
||||
# Diagonal covariance, old code
|
||||
grad = np.empty((X.shape[0], X2.shape[0], X.shape[1]), dtype=np.float64)
|
||||
#grad = np.empty(X.shape, dtype=np.float64)
|
||||
|
|
@ -336,18 +337,18 @@ class Exponential(Stationary):
|
|||
def dK_dr(self, r):
|
||||
return -self.K_of_r(r)
|
||||
|
||||
# def sde(self):
|
||||
# """
|
||||
# Return the state space representation of the covariance.
|
||||
# """
|
||||
# F = np.array([[-1/self.lengthscale]])
|
||||
# L = np.array([[1]])
|
||||
# Qc = np.array([[2*self.variance/self.lengthscale]])
|
||||
# H = np.array([[1]])
|
||||
# Pinf = np.array([[self.variance]])
|
||||
# # TODO: return the derivatives as well
|
||||
#
|
||||
# return (F, L, Qc, H, Pinf)
|
||||
# def sde(self):
|
||||
# """
|
||||
# Return the state space representation of the covariance.
|
||||
# """
|
||||
# F = np.array([[-1/self.lengthscale]])
|
||||
# L = np.array([[1]])
|
||||
# Qc = np.array([[2*self.variance/self.lengthscale]])
|
||||
# H = np.array([[1]])
|
||||
# Pinf = np.array([[self.variance]])
|
||||
# # TODO: return the derivatives as well
|
||||
#
|
||||
# return (F, L, Qc, H, Pinf)
|
||||
|
||||
|
||||
|
||||
|
|
@ -416,41 +417,41 @@ class Matern32(Stationary):
|
|||
F1lower = np.array([f(lower) for f in F1])[:, None]
|
||||
return(self.lengthscale ** 3 / (12.*np.sqrt(3) * self.variance) * G + 1. / self.variance * np.dot(Flower, Flower.T) + self.lengthscale ** 2 / (3.*self.variance) * np.dot(F1lower, F1lower.T))
|
||||
|
||||
def sde(self):
|
||||
"""
|
||||
Return the state space representation of the covariance.
|
||||
"""
|
||||
def sde(self):
|
||||
"""
|
||||
Return the state space representation of the covariance.
|
||||
"""
|
||||
variance = float(self.variance.values)
|
||||
lengthscale = float(self.lengthscale.values)
|
||||
foo = np.sqrt(3.)/lengthscale
|
||||
F = np.array([[0, 1], [-foo**2, -2*foo]])
|
||||
L = np.array([[0], [1]])
|
||||
Qc = np.array([[12.*np.sqrt(3) / lengthscale**3 * variance]])
|
||||
H = np.array([[1, 0]])
|
||||
Pinf = np.array([[variance, 0],
|
||||
[0, 3.*variance/(lengthscale**2)]])
|
||||
# Allocate space for the derivatives
|
||||
foo = np.sqrt(3.)/lengthscale
|
||||
F = np.array([[0, 1], [-foo**2, -2*foo]])
|
||||
L = np.array([[0], [1]])
|
||||
Qc = np.array([[12.*np.sqrt(3) / lengthscale**3 * variance]])
|
||||
H = np.array([[1, 0]])
|
||||
Pinf = np.array([[variance, 0],
|
||||
[0, 3.*variance/(lengthscale**2)]])
|
||||
# Allocate space for the derivatives
|
||||
dF = np.empty([F.shape[0],F.shape[1],2])
|
||||
dQc = np.empty([Qc.shape[0],Qc.shape[1],2])
|
||||
dPinf = np.empty([Pinf.shape[0],Pinf.shape[1],2])
|
||||
# The partial derivatives
|
||||
dFvariance = np.zeros([2,2])
|
||||
dFlengthscale = np.array([[0,0],
|
||||
[6./lengthscale**3,2*np.sqrt(3)/lengthscale**2]])
|
||||
dQcvariance = np.array([12.*np.sqrt(3)/lengthscale**3])
|
||||
dQclengthscale = np.array([-3*12*np.sqrt(3)/lengthscale**4*variance])
|
||||
dPinfvariance = np.array([[1,0],[0,3./lengthscale**2]])
|
||||
dPinflengthscale = np.array([[0,0],
|
||||
[0,-6*variance/lengthscale**3]])
|
||||
# Combine the derivatives
|
||||
dF[:,:,0] = dFvariance
|
||||
dF[:,:,1] = dFlengthscale
|
||||
dQc[:,:,0] = dQcvariance
|
||||
dQc[:,:,1] = dQclengthscale
|
||||
dPinf[:,:,0] = dPinfvariance
|
||||
dPinf[:,:,1] = dPinflengthscale
|
||||
dQc = np.empty([Qc.shape[0],Qc.shape[1],2])
|
||||
dPinf = np.empty([Pinf.shape[0],Pinf.shape[1],2])
|
||||
# The partial derivatives
|
||||
dFvariance = np.zeros([2,2])
|
||||
dFlengthscale = np.array([[0,0],
|
||||
[6./lengthscale**3,2*np.sqrt(3)/lengthscale**2]])
|
||||
dQcvariance = np.array([12.*np.sqrt(3)/lengthscale**3])
|
||||
dQclengthscale = np.array([-3*12*np.sqrt(3)/lengthscale**4*variance])
|
||||
dPinfvariance = np.array([[1,0],[0,3./lengthscale**2]])
|
||||
dPinflengthscale = np.array([[0,0],
|
||||
[0,-6*variance/lengthscale**3]])
|
||||
# Combine the derivatives
|
||||
dF[:,:,0] = dFvariance
|
||||
dF[:,:,1] = dFlengthscale
|
||||
dQc[:,:,0] = dQcvariance
|
||||
dQc[:,:,1] = dQclengthscale
|
||||
dPinf[:,:,0] = dPinfvariance
|
||||
dPinf[:,:,1] = dPinflengthscale
|
||||
|
||||
return (F, L, Qc, H, Pinf, dF, dQc, dPinf)
|
||||
return (F, L, Qc, H, Pinf, dF, dQc, dPinf)
|
||||
|
||||
class Matern52(Stationary):
|
||||
"""
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue