mirror of
https://github.com/SheffieldML/GPy.git
synced 2026-05-08 19:42:39 +02:00
Merge branch 'master' of github.com:SheffieldML/GPy
This commit is contained in:
James Hensman
commit
b1c2282bfc
5 changed files with 121 additions and 76 deletions
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@ -39,11 +39,13 @@ class Matern32(kernpart):
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def get_param(self):
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"""return the value of the parameters."""
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return np.hstack((self.variance,self.lengthscales))
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def set_param(self,x):
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"""set the value of the parameters."""
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assert x.size==(self.D+1)
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self.variance = x[0]
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self.lengthscales = x[1:]
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def get_param_names(self):
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"""return parameter names."""
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if self.D==1:
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@ -56,10 +58,37 @@ class Matern32(kernpart):
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if X2 is None: X2 = X
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dist = np.sqrt(np.sum(np.square((X[:,None,:]-X2[None,:,:])/self.lengthscales),-1))
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np.add(self.variance*(1+np.sqrt(3.)*dist)*np.exp(-np.sqrt(3.)*dist), target,target)
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def Kdiag(self,X,target):
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"""Compute the diagonal of the covariance matrix associated to X."""
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np.add(target,self.variance,target)
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def dK_dtheta(self,partial,X,X2,target):
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"""derivative of the covariance matrix with respect to the parameters."""
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if X2 is None: X2 = X
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dist = np.sqrt(np.sum(np.square((X[:,None,:]-X2[None,:,:])/self.lengthscales),-1))
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dvar = (1+np.sqrt(3.)*dist)*np.exp(-np.sqrt(3.)*dist)
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invdist = 1./np.where(dist!=0.,dist,np.inf)
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dist2M = np.square(X[:,None,:]-X2[None,:,:])/self.lengthscales**3
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dl = (self.variance* 3 * dist * np.exp(-np.sqrt(3.)*dist))[:,:,np.newaxis] * dist2M*invdist[:,:,np.newaxis]
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target[0] += np.sum(dvar*partial)
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target[1:] += (dl*partial[:,:,None]).sum(0).sum(0)
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def dKdiag_dtheta(self,partial,X,target):
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"""derivative of the diagonal of the covariance matrix with respect to the parameters."""
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target[0] += np.sum(partial)
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def dK_dX(self,X,X2,target):
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"""derivative of the covariance matrix with respect to X."""
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if X2 is None: X2 = X
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dist = np.sqrt(np.sum(np.square((X[:,None,:]-X2[None,:,:])/self.lengthscales),-1))[:,:,None]
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ddist_dX = (X[:,None,:]-X2[None,:,:])/self.lengthscales**2/np.where(dist!=0.,dist,np.inf)
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dK_dX += - np.transpose(3*self.variance*dist*np.exp(-np.sqrt(3)*dist)*ddist_dX,(1,0,2))
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target += np.sum(dK_dX*partial.T[:,:,None],0)
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def dKdiag_dX(self,X,target):
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pass
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def Gram_matrix(self,F,F1,F2,lower,upper):
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"""
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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.
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@ -87,25 +116,3 @@ class Matern32(kernpart):
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#return(G)
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return(self.lengthscales**3/(12.*np.sqrt(3)*self.variance) * G + 1./self.variance*np.dot(Flower,Flower.T) + self.lengthscales**2/(3.*self.variance)*np.dot(F1lower,F1lower.T))
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def dK_dtheta(self,X,X2,target):
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"""derivative of the cross-covariance matrix with respect to the parameters (shape is NxMxNparam)"""
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if X2 is None: X2 = X
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dist = np.sqrt(np.sum(np.square((X[:,None,:]-X2[None,:,:])/self.lengthscales),-1))
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dvar = (1+np.sqrt(3.)*dist)*np.exp(-np.sqrt(3.)*dist)
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invdist = 1./np.where(dist!=0.,dist,np.inf)
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dist2M = np.square(X[:,None,:]-X2[None,:,:])/self.lengthscales**3
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dl = (self.variance* 3 * dist * np.exp(-np.sqrt(3.)*dist))[:,:,np.newaxis] * dist2M*invdist[:,:,np.newaxis]
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np.add(target[:,:,0],dvar, target[:,:,0])
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np.add(target[:,:,1:],dl, target[:,:,1:])
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def dKdiag_dtheta(self,X,target):
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"""derivative of the diagonal of the covariance matrix with respect to the parameters (shape is NxNparam)"""
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np.add(target[:,0],1.,target[:,0])
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def dK_dX(self,X,X2,target):
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"""derivative of the covariance matrix with respect to X (*! shape is NxMxD !*)."""
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if X2 is None: X2 = X
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dist = np.sqrt(np.sum(np.square((X[:,None,:]-X2[None,:,:])/self.lengthscales),-1))[:,:,None]
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ddist_dX = (X[:,None,:]-X2[None,:,:])/self.lengthscales**2/np.where(dist!=0.,dist,np.inf)
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target += - np.transpose(3*self.variance*dist*np.exp(-np.sqrt(3)*dist)*ddist_dX,(1,0,2))
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def dKdiag_dX(self,X,target):
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pass
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@ -33,33 +33,61 @@ class Matern52(kernpart):
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self.Nparam = self.D + 1
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self.name = 'Mat52'
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self.set_param(np.hstack((variance,lengthscales)))
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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 get_param(self):
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"""return the value of the parameters."""
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return np.hstack((self.variance,self.lengthscales))
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def set_param(self,x):
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"""set the value of the parameters."""
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assert x.size==(self.D+1)
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self.variance = x[0]
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self.lengthscales = x[1:]
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self.lengthscales2 = np.square(self.lengthscales)
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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 get_param_names(self):
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"""return parameter names."""
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if self.D==1:
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return ['variance','lengthscale']
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else:
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return ['variance']+['lengthscale_%i'%i for i in range(self.lengthscales.size)]
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def K(self,X,X2,target):
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"""Compute the covariance matrix between X and X2."""
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if X2 is None: X2 = X
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dist = np.sqrt(np.sum(np.square((X[:,None,:]-X2[None,:,:])/self.lengthscales),-1))
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np.add(self.variance*(1+np.sqrt(5.)*dist+5./3*dist**2)*np.exp(-np.sqrt(5.)*dist), target,target)
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def Kdiag(self,X,target):
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"""Compute the diagonal of the covariance matrix associated to X."""
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np.add(target,self.variance,target)
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def dK_dtheta(self,partial,X,X2,target):
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"""derivative of the covariance matrix with respect to the parameters."""
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if X2 is None: X2 = X
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dist = np.sqrt(np.sum(np.square((X[:,None,:]-X2[None,:,:])/self.lengthscales),-1))
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invdist = 1./np.where(dist!=0.,dist,np.inf)
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dist2M = np.square(X[:,None,:]-X2[None,:,:])/self.lengthscales**3
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dvar = (1+np.sqrt(5.)*dist+5./3*dist**2)*np.exp(-np.sqrt(5.)*dist)
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dl = (self.variance * 5./3 * dist * (1 + np.sqrt(5.)*dist ) * np.exp(-np.sqrt(5.)*dist))[:,:,np.newaxis] * dist2M*invdist[:,:,np.newaxis]
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target[0] += np.sum(dvar*partial)
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target[1:] += (dl*partial[:,:,None]).sum(0).sum(0)
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def dKdiag_dtheta(self,X,target):
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"""derivative of the diagonal of the covariance matrix with respect to the parameters."""
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target[0] += np.sum(partial)
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def dK_dX(self,X,X2,target):
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"""derivative of the covariance matrix with respect to X."""
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if X2 is None: X2 = X
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dist = np.sqrt(np.sum(np.square((X[:,None,:]-X2[None,:,:])/self.lengthscales),-1))[:,:,None]
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ddist_dX = (X[:,None,:]-X2[None,:,:])/self.lengthscales**2/np.where(dist!=0.,dist,np.inf)
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dK_dX += - np.transpose(self.variance*5./3*dist*(1+np.sqrt(5)*dist)*np.exp(-np.sqrt(5)*dist)*ddist_dX,(1,0,2))
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target += np.sum(dK_dX*partial.T[:,:,None],0)
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def dKdiag_dX(self,X,target):
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pass
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def Gram_matrix(self,F,F1,F2,F3,lower,upper):
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"""
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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.
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@ -91,26 +119,5 @@ class Matern52(kernpart):
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orig2 = 3./5*self.lengthscales**2 * ( np.dot(F1lower,F1lower.T) + 1./8*np.dot(Flower,F2lower.T) + 1./8*np.dot(F2lower,Flower.T))
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return(1./self.variance* (G_coef*G + orig + orig2))
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def dK_dtheta(self,X,X2,target):
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"""derivative of the cross-covariance matrix with respect to the parameters (shape is NxMxNparam)"""
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if X2 is None: X2 = X
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dist = np.sqrt(np.sum(np.square((X[:,None,:]-X2[None,:,:])/self.lengthscales),-1))
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invdist = 1./np.where(dist!=0.,dist,np.inf)
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dist2M = np.square(X[:,None,:]-X2[None,:,:])/self.lengthscales**3
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dvar = (1+np.sqrt(5.)*dist+5./3*dist**2)*np.exp(-np.sqrt(5.)*dist)
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dl = (self.variance * 5./3 * dist * (1 + np.sqrt(5.)*dist ) * np.exp(-np.sqrt(5.)*dist))[:,:,np.newaxis] * dist2M*invdist[:,:,np.newaxis]
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np.add(target[:,:,0],dvar, target[:,:,0])
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np.add(target[:,:,1:],dl, target[:,:,1:])
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def dKdiag_dtheta(self,X,target):
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"""derivative of the diagonal of the covariance matrix with respect to the parameters (shape is NxNparam)"""
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np.add(target[:,0],1.,target[:,0])
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def dK_dX(self,X,X2,target):
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"""derivative of the covariance matrix with respect to X (*! shape is NxMxD !*)."""
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if X2 is None: X2 = X
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dist = np.sqrt(np.sum(np.square((X[:,None,:]-X2[None,:,:])/self.lengthscales),-1))[:,:,None]
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ddist_dX = (X[:,None,:]-X2[None,:,:])/self.lengthscales**2/np.where(dist!=0.,dist,np.inf)
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target += - np.transpose(self.variance*5./3*dist*(1+np.sqrt(5)*dist)*np.exp(-np.sqrt(5)*dist)*ddist_dX,(1,0,2))
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def dKdiag_dX(self,X,target):
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pass
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@ -62,7 +62,7 @@ class exponential(kernpart):
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np.add(target,self.variance,target)
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def dK_dtheta(self,partial,X,X2,target):
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"""derivative of the cross-covariance matrix with respect to the parameters (shape is NxMxNparam)"""
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"""derivative of the covariance matrix with respect to the parameters."""
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if X2 is None: X2 = X
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dist = np.sqrt(np.sum(np.square((X[:,None,:]-X2[None,:,:])/self.lengthscales),-1))
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invdist = 1./np.where(dist!=0.,dist,np.inf)
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@ -73,12 +73,12 @@ class exponential(kernpart):
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target[1:] += (dl*partial[:,:,None]).sum(0).sum(0)
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def dKdiag_dtheta(self,partial,X,target):
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"""derivative of the diagonal of the covariance matrix with respect to the parameters (shape is NxNparam)"""
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"""derivative of the diagonal of the covariance matrix with respect to the parameters."""
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#NB: derivative of diagonal elements wrt lengthscale is 0
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target[0] += np.sum(partial)
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def dK_dX(self,X,X2,target):
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"""derivative of the covariance matrix with respect to X (*! shape is NxMxD !*)."""
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"""derivative of the covariance matrix with respect to X."""
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if X2 is None: X2 = X
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dist = np.sqrt(np.sum(np.square((X[:,None,:]-X2[None,:,:])/self.lengthscales),-1))[:,:,None]
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ddist_dX = (X[:,None,:]-X2[None,:,:])/self.lengthscales**2/np.where(dist!=0.,dist,np.inf)
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@ -21,6 +21,7 @@ class linear(kernpart):
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self.Nparam = 1
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self.name = 'linear'
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self.set_param(variance)
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self._Xcache, self._X2cache = np.empty(shape=(2,))
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def get_param(self):
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return self.variance
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@ -32,7 +33,8 @@ class linear(kernpart):
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return ['variance']
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def K(self,X,X2,target):
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target += self.variance * np.dot(X, X2.T)
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self._K_computations(X, X2)
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target += self.variance * self._dot_product
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def Kdiag(self,X,target):
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np.add(target,np.sum(self.variance*np.square(X),-1),target)
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@ -42,7 +44,9 @@ class linear(kernpart):
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Computes the derivatives wrt theta
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Return shape is NxMx(Ntheta)
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"""
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product = np.dot(X, X2.T)
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self._K_computations(X, X2)
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product = self._dot_product
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# product = np.dot(X, X2.T)
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target += np.sum(product*partial)
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def dK_dX(self,partial,X,X2,target):
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@ -51,6 +55,20 @@ class linear(kernpart):
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def dKdiag_dtheta(self,partial,X,target):
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target += np.sum(partial*np.square(X).sum(1))
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def _K_computations(self,X,X2):
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# (Nicolo) changed the logic here. If X2 is None, we want to cache
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# (X,X). In practice X2 should always be passed.
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if X2 is None:
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X2 = X
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if not (np.all(X==self._Xcache) and np.all(X2==self._X2cache)):
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self._Xcache = X
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self._X2cache = X2
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self._dot_product = np.dot(X,X2.T)
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else:
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# print "Cache hit!"
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pass # TODO: insert debug message here (logging framework)
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# def psi0(self,Z,mu,S,target):
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# expected = np.square(mu) + S
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# np.add(target,np.sum(self.variance*expected),target)
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@ -30,6 +30,7 @@ class rbf_ARD(kernpart):
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def get_param(self):
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return np.hstack((self.variance,self.lengthscales))
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def set_param(self,x):
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assert x.size==(self.D+1)
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self.variance = x[0]
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@ -37,61 +38,73 @@ class rbf_ARD(kernpart):
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self.lengthscales2 = np.square(self.lengthscales)
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#reset cached results
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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 get_param_names(self):
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if self.D==1:
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return ['variance','lengthscale']
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else:
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return ['variance']+['lengthscale_%i'%i for i in range(self.lengthscales.size)]
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def K(self,X,X2,target):
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self._K_computations(X,X2)
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np.add(self.variance*self._K_dvar, target,target)
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def Kdiag(self,X,target):
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np.add(target,self.variance,target)
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def dK_dtheta(self,X,X2,target):
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"""Return shape is NxMx(Ntheta)"""
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def dK_dtheta(self,partial,X,X2,target):
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self._K_computations(X,X2)
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dl = self._K_dvar[:,:,None]*self.variance*self._K_dist2/self.lengthscales
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np.add(target[:,:,0],self._K_dvar, target[:,:,0])
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np.add(target[:,:,1:],dl, target[:,:,1:])
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target[0] += np.sum(self._K_dvar*partial)
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target[1:] += (dl*partial[:,:,None]).sum(0).sum(0)
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def dKdiag_dtheta(self,X,target):
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np.add(target[:,0],1.,target[:,0])
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target[0] += np.sum(partial)
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def dK_dX(self,X,X2,target):
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self._K_computations(X,X2)
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dZ = self.variance*self._K_dvar[:,:,None]*self._K_dist/self.lengthscales2
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np.add(target,-dZ.transpose(1,0,2),target)
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dK_dX = -dZ.transpose(1,0,2)
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target += np.sum(dK_dX*partial.T[:,:,None],0)
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def dKdiag_dX(self,partial,X,target):
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pass
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def psi0(self,Z,mu,S,target):
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np.add(target, self.variance, target)
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def dpsi0_dtheta(self,Z,mu,S,target):
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target[:,0] += 1.
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target += self.variance
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def dpsi0_dtheta(self,partial,Z,mu,S,target):
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target[0] += 1.
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def dpsi0_dmuS(self,Z,mu,S,target_mu,target_S):
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pass
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def psi1(self,Z,mu,S,target):
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"""Think N,M,Q """
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self._psi_computations(Z,mu,S)
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np.add(target, self._psi1,target)
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def dpsi1_dtheta(self,Z,mu,S,target):
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"""N,Q,(Ntheta)"""
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def dpsi1_dtheta(self,partial,Z,mu,S,target):
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self._psi_computations(Z,mu,S)
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denom_deriv = S[:,None,:]/(self.lengthscales**3+self.lengthscales*S[:,None,:])
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d_length = self._psi1[:,:,None]*(self.lengthscales*np.square(self._psi1_dist/(self.lengthscales2+S[:,None,:])) + denom_deriv)
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target[:,:,0] += self._psi1/self.variance
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target[:,:,1:] += d_length
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def dpsi1_dZ(self,Z,mu,S,target):
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target[0] += np.sum(partial*self._psi1/self.variance)
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target[1:] += (d_length*partial[:,:,None]).sum(0).sum(0)
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def dpsi1_dZ(self,partial,Z,mu,S,target):
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self._psi_computations(Z,mu,S)
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np.add(target,-self._psi1[:,:,None]*self._psi1_dist/self.lengthscales2/self._psi1_denom,target)
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target += np.sum(partial[:,:,None]*-self._psi1[:,:,None]*self._psi1_dist/self.lengthscales2/self._psi1_denom,0)
|
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|
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def dpsi1_dmuS(self,Z,mu,S,target_mu,target_S):
|
||||
def dpsi1_dmuS(self,partial,Z,mu,S,target_mu,target_S):
|
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"""return shapes are N,M,Q"""
|
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self._psi_computations(Z,mu,S)
|
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tmp = self._psi1[:,:,None]/self.lengthscales2/self._psi1_denom
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np.add(target_mu,tmp*self._psi1_dist,target_mu)
|
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np.add(target_S, 0.5*tmp*(self._psi1_dist_sq-1), target_S)
|
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target_mu += np.sum(partial*tmp*self._psi1_dist,1)
|
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target_S += np.sum(partial*0.5*tmp*(self._psi1_dist_sq-1),1)
|
||||
|
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def psi2(self,Z,mu,S,target):
|
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"""shape N,M,M"""
|
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self._psi_computations(Z,mu,S)
|
||||
np.add(target, self._psi2,target)
|
||||
target += self._psi2.sum(0) #TODO: psi2 should be NxMxM (for het. noise)
|
||||
|
||||
def dpsi2_dtheta(self,Z,mu,S,target):
|
||||
"""Shape N,M,M,Ntheta"""
|
||||
|
|
@ -99,21 +112,21 @@ class rbf_ARD(kernpart):
|
|||
d_var = np.sum(2.*self._psi2/self.variance,0)
|
||||
d_length = self._psi2[:,:,:,None]*(0.5*self._psi2_Zdist_sq*self._psi2_denom + 2.*self._psi2_mudist_sq + 2.*S[:,None,None,:]/self.lengthscales2)/(self.lengthscales*self._psi2_denom)
|
||||
d_length = d_length.sum(0)
|
||||
target[:,:,0] += d_var
|
||||
target[:,:,1:] += d_length
|
||||
target[0] += np.sum(partial*d_var)
|
||||
target[1:] += (d_length*partial[:,:,None]).sum(0).sum(0)
|
||||
|
||||
def dpsi2_dZ(self,Z,mu,S,target):
|
||||
"""Returns shape N,M,M,Q"""
|
||||
self._psi_computations(Z,mu,S)
|
||||
dZ = self._psi2[:,:,:,None]/self.lengthscales2*(-0.5*self._psi2_Zdist + self._psi2_mudist/self._psi2_denom)
|
||||
target += dZ
|
||||
target += np.sum(partial[None,:,:,None]*dZ,0).sum(1)
|
||||
|
||||
def dpsi2_dmuS(self,Z,mu,S,target_mu,target_S):
|
||||
"""Think N,M,M,Q """
|
||||
self._psi_computations(Z,mu,S)
|
||||
tmp = self._psi2[:,:,:,None]/self.lengthscales2/self._psi2_denom
|
||||
np.add(target_mu, -tmp*(2.*self._psi2_mudist),target_mu) #N,M,M,Q
|
||||
np.add(target_S, tmp*(2.*self._psi2_mudist_sq-1), target_S) #N,M,M,Q
|
||||
target_mu += (partial*-tmp*2.*self._psi2_mudist).sum(1).sum(1)
|
||||
target_S += (partial*tmp*(2.*self._psi2_mudist_sq-1)).sum(1).sum(1)
|
||||
|
||||
def _K_computations(self,X,X2):
|
||||
if not (np.all(X==self._X) and np.all(X2==self._X2)):
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue