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derivatives of the exponential kernel in the right format

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Nicolas 2012-11-30 17:39:04 +00:00
parent 46754db658
commit d71ad99db9
1 changed files with 31 additions and 23 deletions
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54
GPy/kern/exponential.py
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@ -37,26 +37,57 @@ class exponential(kernpart):
def get_param(self):
"""return the value of the parameters."""
return np.hstack((self.variance,self.lengthscales))
def set_param(self,x):
"""set the value of the parameters."""
assert x.size==(self.D+1)
self.variance = x[0]
self.lengthscales = x[1:]
def get_param_names(self):
"""return parameter names."""
if self.D==1:
return ['variance','lengthscale']
else:
return ['variance']+['lengthscale_%i'%i for i in range(self.lengthscales.size)]
def K(self,X,X2,target):
"""Compute the covariance matrix between X and X2."""
if X2 is None: X2 = X
dist = np.sqrt(np.sum(np.square((X[:,None,:]-X2[None,:,:])/self.lengthscales),-1))
np.add(self.variance*np.exp(-dist), target,target)
def Kdiag(self,X,target):
"""Compute the diagonal of the covariance matrix associated to X."""
np.add(target,self.variance,target)
def dK_dtheta(self,partial,X,X2,target):
"""derivative of the cross-covariance matrix with respect to the parameters (shape is NxMxNparam)"""
if X2 is None: X2 = X
dist = np.sqrt(np.sum(np.square((X[:,None,:]-X2[None,:,:])/self.lengthscales),-1))
invdist = 1./np.where(dist!=0.,dist,np.inf)
dist2M = np.square(X[:,None,:]-X2[None,:,:])/self.lengthscales**3
dvar = np.exp(-dist)
dl = self.variance*dvar[:,:,None]*dist2M*invdist[:,:,None]
target[0] += np.sum(dvar*partial)
target[1:] += (dl*partial[:,:,None]).sum(0).sum(0)
def dKdiag_dtheta(self,partial,X,target):
"""derivative of the diagonal of the covariance matrix with respect to the parameters (shape is NxNparam)"""
#NB: derivative of diagonal elements wrt lengthscale is 0
target[0] += np.sum(partial)
def dK_dX(self,X,X2,target):
"""derivative of the covariance matrix with respect to X (*! shape is NxMxD !*)."""
if X2 is None: X2 = X
dist = np.sqrt(np.sum(np.square((X[:,None,:]-X2[None,:,:])/self.lengthscales),-1))[:,:,None]
ddist_dX = (X[:,None,:]-X2[None,:,:])/self.lengthscales**2/np.where(dist!=0.,dist,np.inf)
dK_dX = - np.transpose(self.variance*np.exp(-dist)*ddist_dX,(1,0,2))
target += np.sum(dK_dX*partial.T[:,:,None],0)
def dKdiag_dX(self,X,target):
pass
def Gram_matrix(self,F,F1,lower,upper):
"""
Return the Gram matrix of the vector of functions F with respect to the RKHS norm. The use of this function is limited to D=1.
@ -79,29 +110,6 @@ class exponential(kernpart):
Flower = np.array([f(lower) for f in F])[:,None]
return(self.lengthscales/2./self.variance * G + 1./self.variance * np.dot(Flower,Flower.T))
def dK_dtheta(self,X,X2,target):
"""derivative of the cross-covariance matrix with respect to the parameters (shape is NxMxNparam)"""
if X2 is None: X2 = X
dist = np.sqrt(np.sum(np.square((X[:,None,:]-X2[None,:,:])/self.lengthscales),-1))
invdist = 1./np.where(dist!=0.,dist,np.inf)
dist2M = np.square(X[:,None,:]-X2[None,:,:])/self.lengthscales**3
dvar = np.exp(-dist)
dl = self.variance*dvar[:,:,None]*dist2M*invdist[:,:,np.newaxis]
np.add(target[:,:,0],dvar, target[:,:,0])
np.add(target[:,:,1:],dl, target[:,:,1:])
def dKdiag_dtheta(self,X,target):
"""derivative of the diagonal of the covariance matrix with respect to the parameters (shape is NxNparam)"""
np.add(target[:,0],1.,target[:,0])
def dK_dX(self,X,X2,target):
"""derivative of the covariance matrix with respect to X (*! shape is NxMxD !*)."""
if X2 is None: X2 = X
dist = np.sqrt(np.sum(np.square((X[:,None,:]-X2[None,:,:])/self.lengthscales),-1))[:,:,None]
ddist_dX = (X[:,None,:]-X2[None,:,:])/self.lengthscales**2/np.where(dist!=0.,dist,np.inf)
target += - np.transpose(self.variance*np.exp(-dist)*ddist_dX,(1,0,2))
def dKdiag_dX(self,X,target):
pass