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108 lines
3.3 KiB
Python
108 lines
3.3 KiB
Python
# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
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# Licensed under the BSD 3-clause license (see LICENSE.txt)
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from kernpart import kernpart
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import numpy as np
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class linear_ARD(kernpart):
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"""
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Linear ARD kernel
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:param D: the number of input dimensions
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:type D: int
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:param variances: ARD variances
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:type variances: None|np.ndarray
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"""
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def __init__(self,D,variances=None):
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self.D = D
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if variances is not None:
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assert variances.shape==(self.D,)
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else:
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variances = np.ones(self.D)
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self.Nparam = int(self.D)
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self.name = 'linear'
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self.set_param(variances)
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def get_param(self):
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return self.variances
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def set_param(self,x):
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assert x.size==(self.Nparam)
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self.variances = x
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def get_param_names(self):
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if self.D==1:
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return ['variance']
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else:
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return ['variance_%i'%i for i in range(self.variances.size)]
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def K(self,X,X2,target):
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XX = X*np.sqrt(self.variances)
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XX2 = X2*np.sqrt(self.variances)
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target += np.dot(XX, XX2.T)
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def Kdiag(self,X,target):
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np.add(target,np.sum(self.variances*np.square(X),-1),target)
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def dK_dtheta(self,partial,X,X2,target):
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product = X[:,None,:]*X2[None,:,:]
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target += (partial[:,:,None]*product).sum(0).sum(0)
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def dK_dX(self,partial,X,X2,target):
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target += (((X[:, None, :] * self.variances) + target) * partial[:,:, None]).sum(0)
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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.variances*expected),target)
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def dpsi0_dtheta(self,Z,mu,S,target):
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expected = np.square(mu) + S
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return -2.*np.sum(expected,0)
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def dpsi0_dmuS(self,Z,mu,S,target_mu,target_S):
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np.add(target_mu,2*mu*self.variances,target_mu)
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np.add(target_S,self.variances,target_S)
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def dpsi0_dZ(self,Z,mu,S,target):
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pass
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def psi1(self,Z,mu,S,target):
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"""the variance, it does nothing"""
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self.K(mu,Z,target)
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def dpsi1_dtheta(self,Z,mu,S,target):
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"""the variance, it does nothing"""
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self.dK_dtheta(mu,Z,target)
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def dpsi1_dmuS(self,Z,mu,S,target_mu,target_S):
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"""Do nothing for S, it does not affect psi1"""
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np.add(target_mu,Z/self.variances2,target_mu)
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def dpsi1_dZ(self,Z,mu,S,target):
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self.dK_dX(mu,Z,target)
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def psi2(self,Z,mu,S,target):
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"""Think N,M,M,Q """
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mu2_S = np.square(mu)+S# N,Q,
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ZZ = Z[:,None,:]*Z[None,:,:] # M,M,Q
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psi2 = ZZ*np.square(self.variances)*mu2_S
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np.add(target, psi2.sum(-1),target) # M,M
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def dpsi2_dtheta(self,Z,mu,S,target):
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mu2_S = np.square(mu)+S# N,Q,
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ZZ = Z[:,None,:]*Z[None,:,:] # M,M,Q
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target += 2.*ZZ*mu2_S*self.variances
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def dpsi2_dmuS(self,Z,mu,S,target_mu,target_S):
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"""Think N,M,M,Q """
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mu2_S = np.sum(np.square(mu)+S,0)# Q,
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ZZ = Z[:,None,:]*Z[None,:,:] # M,M,Q
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tmp = ZZ*np.square(self.variances) # M,M,Q
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np.add(target_mu, tmp*2.*mu[:,None,None,:],target_mu) #N,M,M,Q
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np.add(target_S, tmp, target_S) #N,M,M,Q
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def dpsi2_dZ(self,Z,mu,S,target):
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mu2_S = np.sum(np.square(mu)+S,0)# Q,
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target += Z[:,None,:]*np.square(self.variances)*mu2_S
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