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bias kernel psi stats implemented.
This commit is contained in:
James Hensman
parent
cd22c96e00
commit
6d0a7afd4c
6 changed files with 170 additions and 113 deletions
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@ -46,3 +46,40 @@ class bias(kernpart):
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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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target += self.variance
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def psi1(self, Z, mu, S, target):
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target += self.variance
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def psi2(self, Z, mu, S, target):
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target += self.variance**2
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def dpsi0_dtheta(self, partial, Z, mu, S, target):
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target += partial.sum()
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def dpsi0_dZ(self, partial, Z, mu, S, target):
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pass
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def dpsi0_dmuS(self, partial, Z, mu, S, target_mu, target_S):
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pass
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def dpsi1_dtheta(self, partial, Z, mu, S, target):
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target += partial.sum()
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def dpsi1_dZ(self, partial, Z, mu, S, target):
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pass
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def dpsi1_dmuS(self, partial, Z, mu, S, target_mu, target_S):
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pass
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def dpsi2_dtheta(self, partial, Z, mu, S, target):
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target += 2.*self.variance*partial.sum()
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def dpsi2_dZ(self, partial, Z, mu, S, target):
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pass
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def dpsi2_dmuS(self, partial, Z, mu, S, target_mu, target_S):
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pass
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@ -201,70 +201,80 @@ class kern(parameterised):
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[p.dKdiag_dX(partial[s],X[s,i_s],target[s,i_s]) for p,i_s,s in zip(self.parts,self.input_slices,slices)]
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return target
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def psi0(self,Z,mu,S,slices_mu=None,slices_Z=None):
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def psi0(self,Z,mu,S,slices=None):
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slices = self._process_slices(slices,False)
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target = np.zeros(mu.shape[0])
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[p.psi0(Z,mu,S,target) for p in self.parts]
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[p.psi0(Z,mu[s],S[s],target[s]) for p,s in zip(self.parts,slices)]
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return target
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def dpsi0_dtheta(self,Z,mu,S):
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target = np.zeros((mu.shape[0],self.Nparam))
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[p.dpsi0_dtheta(Z,mu,S,target[s]) for p,s in zip(self.parts, self.param_slices)]
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def dpsi0_dtheta(self,partial,Z,mu,S,slices=None):
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slices = self._process_slices(slices,False)
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target = np.zeros(self.Nparam)
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[p.dpsi0_dtheta(partial[s],Z,mu[s],S[s],target[ps]) for p,ps,s in zip(self.parts, self.param_slices,slices)]
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return target
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def dpsi0_dmuS(self,Z,mu,S):
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def dpsi0_dmuS(self,partial,Z,mu,S,slices=None):
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slices = self._process_slices(slices,False)
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target_mu,target_S = np.zeros_like(mu),np.zeros_like(S)
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[p.dpsi0_dmuS(Z,mu,S,target_mu,target_S) for p in self.parts]
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[p.dpsi0_dmuS(partial,Z,mu[s],S[s],target_mu[s],target_S[s]) for p,s in zip(self.parts,slices)]
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return target_mu,target_S
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def psi1(self,Z,mu,S):
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def psi1(self,Z,mu,S,slices1=None,slices2=None):
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"""Think N,M,Q """
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slices1, slices2 = self._process_slices(slices1,slices2)
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target = np.zeros((mu.shape[0],Z.shape[0]))
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[p.psi1(Z,mu,S,target=target) for p in self.parts]
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[p.psi1(Z[s2],mu[s1],S[s1],target[s1,s2]) for p,s1,s2 in zip(self.parts,slices1,slices2)]
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return target
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def dpsi1_dtheta(self,Z,mu,S):
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def dpsi1_dtheta(self,partial,Z,mu,S,slices1=None,slices2=None):
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"""N,M,(Ntheta)"""
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target = np.zeros((mu.shape[0],Z.shape[0],self.Nparam))
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[p.dpsi1_dtheta(Z,mu,S,target[:,:,s]) for p,s in zip(self.parts, self.param_slices)]
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slices1, slices2 = self._process_slices(slices1,slices2)
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target = np.zeros((self.Nparam))
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[p.dpsi1_dtheta(partial[s2,s1],Z[s2,i_s],mu[s1,i_s],S[s1,i_s],target[ps]) for p,ps,s1,s2,i_s in zip(self.parts, self.param_slices,slices1,slices2,self.input_slices)]
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return target
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def dpsi1_dZ(self,Z,mu,S):
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def dpsi1_dZ(self,partial,Z,mu,S,slices1=None,slices2=None):
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"""N,M,Q"""
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target = np.zeros((mu.shape[0],Z.shape[0],Z.shape[1]))
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[p.dpsi1_dZ(Z,mu,S,target) for p in self.parts]
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slices1, slices2 = self._process_slices(slices1,slices2)
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target = np.zeros_like(Z)
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[p.dpsi1_dZ(partial[s2,s1],Z[s2,i_s],mu[s1,i_s],S[s1,i_s],target[s2,i_s]) for p,i_s,s1,s2 in zip(self.parts,self.input_slices,slices1,slices2)]
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return target
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def dpsi1_dmuS(self,Z,mu,S):
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def dpsi1_dmuS(self,partial,Z,mu,S,slices1=None,slices2=None):
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"""return shapes are N,M,Q"""
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target_mu, target_S = np.zeros((2,mu.shape[0],Z.shape[0],Z.shape[1]))
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[p.dpsi1_dmuS(Z,mu,S,target_mu=target_mu,target_S = target_S) for p in self.parts]
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slices1, slices2 = self._process_slices(slices1,slices2)
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target_mu, target_S = np.zeros((2,mu.shape[0],mu.shape[1]))
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[p.dpsi1_dmuS(partial[s2,s1],Z[s2,i_s],mu[s1,i_s],S[s1,i_s],target_mu[s1,i_s],target_S[s1,i_s]) for p,i_s,s1,s2 in zip(self.parts,self.input_slices,slices1,slices2)]
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return target_mu, target_S
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def psi2(self,Z,mu,S):
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def psi2(self,Z,mu,S,slices1=None,slices2=None):
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"""
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:Z: np.ndarray of inducing inputs (M x Q)
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: mu, S: np.ndarrays of means and variacnes (each N x Q)
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:returns psi2: np.ndarray (N,M,M,Q) """
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target = np.zeros((mu.shape[0],Z.shape[0],Z.shape[0]))
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[p.psi2(Z,mu,S,target=target) for p in self.parts]
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target = np.zeros((Z.shape[0],Z.shape[0]))
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slices1, slices2 = self._process_slices(slices1,slices2)
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[p.psi2(Z[s2,i_s],mu[s1,i_s],S[s1,i_s],target[s2,s2]) for p,i_s,s1,s2 in zip(self.parts,self.input_slices,slices1,slices2)]
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return target
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def dpsi2_dtheta(self,Z,mu,S):
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def dpsi2_dtheta(self,partial,Z,mu,S,slices1=None,slices2=None):
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"""Returns shape (N,M,M,Ntheta)"""
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target = np.zeros((Z.shape[0],Z.shape[0],self.Nparam))
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[p.dpsi2_dtheta(Z,mu,S,target[:,:,s]) for p,s in zip(self.parts, self.param_slices)]
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slices1, slices2 = self._process_slices(slices1,slices2)
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target = np.zeros(self.Nparam)
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[p.dpsi2_dtheta(partial[s2,s2],Z[s2,i_s],mu[s1,i_s],S[s1,i_s],target[ps]) for p,i_s,s1,s2,ps in zip(self.parts,self.input_slices,slices1,slices2,self.param_slices)]
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return target
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def dpsi2_dZ(self,Z,mu,S):
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"""N,M,M,Q"""
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target = np.zeros((mu.shape[0],Z.shape[0],Z.shape[0],Z.shape[1]))
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[p.dpsi2_dZ(Z,mu,S,target) for p in self.parts]
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def dpsi2_dZ(self,partial,Z,mu,S,slices1=None,slices2=None):
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slices1, slices2 = self._process_slices(slices1,slices2)
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target = np.zeros_like(Z)
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[p.dpsi2_dZ(partial[s2,s2],Z[s2,i_s],mu[s1,i_s],S[s1,i_s],target[s2,i_s]) for p,i_s,s1,s2 in zip(self.parts,self.input_slices,slices1,slices2)]
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return target
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def dpsi2_dmuS(self,Z,mu,S):
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def dpsi2_dmuS(self,Z,mu,S,slices1=None,slices2=None):
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"""return shapes are N,M,M,Q"""
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target_mu, target_S = np.zeros((2,mu.shape[0],Z.shape[0],Z.shape[0],Z.shape[1]))
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[p.dpsi2_dmuS(Z,mu,S,target_mu=target_mu,target_S = target_S) for p in self.parts]
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slices1, slices2 = self._process_slices(slices1,slices2)
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target_mu, target_S = np.zeros((2,mu.shape[0],mu.shape[1]))
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[p.dpsi2_dmuS(partial[s2,s2],Z[s2,i_s],mu[s1,i_s],S[s1,i_s],target_mu[s1,i_s],target_S[s1,i_s]) for p,i_s,s1,s2 in zip(self.parts,self.input_slices,slices1,slices2)]
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#TODO: there are some extra terms to compute here!
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return target_mu, target_S
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138
GPy/kern/rbf.py
138
GPy/kern/rbf.py
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@ -17,7 +17,7 @@ class rbf(kernpart):
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:param lengthscale: the lengthscale of the kernel
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:type lengthscale: float
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.. Note: for rbf with different lengthscales on each dimension, see rbf_ARD
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.. Note: for rbf with different lengthscale on each dimension, see rbf_ARD
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"""
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def __init__(self,D,variance=1.,lengthscale=1.):
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@ -81,80 +81,88 @@ class rbf(kernpart):
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self._K_exponent = -0.5*self._K_dist2
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self._K_dvar = np.exp(-0.5*self._K_dist2)
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if __name__=='__main__':
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#run some simple tests on the kernel (TODO:move these to unititest)
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#TODO: these are broken in this new structure!
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N = 10
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M = 5
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Q = 3
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def psi0(self,Z,mu,S,target):
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target += self.variance
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Z = np.random.randn(M,Q)
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mu = np.random.randn(N,Q)
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S = np.random.rand(N,Q)
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def dpsi0_dtheta(self,partial,Z,mu,S,target):
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target[0] += 1.
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var = 2.5
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lengthscales = np.ones(Q)*0.7
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def dpsi0_dmuS(self,Z,mu,S,target_mu,target_S):
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pass
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k = rbf(Q,var,lengthscales)
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def psi1(self,Z,mu,S,target):
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self._psi_computations(Z,mu,S)
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target += self._psi1
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from checkgrad import checkgrad
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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.lengthscale**3+self.lengthscale*S[:,None,:])
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d_length = self._psi1[:,:,None]*(self.lengthscale*np.square(self._psi1_dist/(self.lengthscale2+S[:,None,:])) + denom_deriv)
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target[0] += np.sum(partial*self._psi1/self.variance)
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target[1] += np.sum(d_length*partial[:,:,None])
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def k_theta_test(param,k):
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k.set_param(param)
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K = k.K(Z)
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dK_dtheta = k.dK_dtheta(Z)
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f = np.sum(K)
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df = dK_dtheta.sum(0).sum(0)
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return f,np.array(df)
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print "dk_dtheta_test"
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checkgrad(k_theta_test,np.random.randn(1+Q),args=(k,))
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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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target += np.sum(partial[:,:,None]*-self._psi1[:,:,None]*self._psi1_dist/self.lengthscale2/self._psi1_denom,0)
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def dpsi1_dmuS(self,partial,Z,mu,S,target_mu,target_S):
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self._psi_computations(Z,mu,S)
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tmp = self._psi1[:,:,None]/self.lengthscale2/self._psi1_denom
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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 psi1_mu_test(mu,k):
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mu = mu.reshape(N,Q)
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f = np.sum(k.psi1(Z,mu,S))
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df = k.dpsi1_dmuS(Z,mu,S)[0].sum(1)
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return f,df.flatten()
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print "psi1_mu_test"
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checkgrad(psi1_mu_test,np.random.randn(N*Q),args=(k,))
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def psi2(self,Z,mu,S,target):
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self._psi_computations(Z,mu,S)
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target += self._psi2.sum(0) #TODO: psi2 should be NxMxM (for het. noise)
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def psi1_S_test(S,k):
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S = S.reshape(N,Q)
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f = np.sum(k.psi1(Z,mu,S))
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df = k.dpsi1_dmuS(Z,mu,S)[1].sum(1)
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return f,df.flatten()
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print "psi1_S_test"
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checkgrad(psi1_S_test,np.random.rand(N*Q),args=(k,))
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def dpsi2_dtheta(self,partial,Z,mu,S,target):
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"""Shape N,M,M,Ntheta"""
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self._psi_computations(Z,mu,S)
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d_var = np.sum(2.*self._psi2/self.variance,0)
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d_length = self._psi2[:,:,:,None]*(0.5*self._psi2_Zdist_sq*self._psi2_denom + 2.*self._psi2_mudist_sq + 2.*S[:,None,None,:]/self.lengthscale2)/(self.lengthscale*self._psi2_denom)
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d_length = d_length.sum(0)
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target[0] += np.sum(partial*d_var)
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target[1] += np.sum(d_length*partial)
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def psi1_theta_test(theta,k):
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k.set_param(theta)
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f = np.sum(k.psi1(Z,mu,S))
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df = np.array([np.sum(grad) for grad in k.dpsi1_dtheta(Z,mu,S)])
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return f,df
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print "psi1_theta_test"
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checkgrad(psi1_theta_test,np.random.rand(1+Q),args=(k,))
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def dpsi2_dZ(self,partial,Z,mu,S,target):
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"""Returns shape N,M,M,Q"""
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self._psi_computations(Z,mu,S)
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dZ = self._psi2[:,:,:,None]/self.lengthscale2*(-0.5*self._psi2_Zdist + self._psi2_mudist/self._psi2_denom)
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target += np.sum(partial[None,:,:,None]*dZ,0).sum(1)
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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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self._psi_computations(Z,mu,S)
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tmp = self._psi2[:,:,:,None]/self.lengthscale2/self._psi2_denom
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target_mu += (partial*-tmp*2.*self._psi2_mudist).sum(1).sum(1)
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target_S += (partial*tmp*(2.*self._psi2_mudist_sq-1)).sum(1).sum(1)
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def psi2_mu_test(mu,k):
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mu = mu.reshape(N,Q)
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f = np.sum(k.psi2(Z,mu,S))
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df = k.dpsi2_dmuS(Z,mu,S)[0].sum(1).sum(1)
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return f,df.flatten()
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print "psi2_mu_test"
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checkgrad(psi2_mu_test,np.random.randn(N*Q),args=(k,))
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def _psi_computations(self,Z,mu,S):
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#here are the "statistics" for psi1 and psi2
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if not np.all(Z==self._Z):
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#Z has changed, compute Z specific stuff
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self._psi2_Zhat = 0.5*(Z[:,None,:] +Z[None,:,:]) # M,M,Q
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self._psi2_Zdist = Z[:,None,:]-Z[None,:,:] # M,M,Q
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self._psi2_Zdist_sq = np.square(self._psi2_Zdist)/self.lengthscale2 # M,M,Q
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self._Z = Z
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def psi2_S_test(S,k):
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S = S.reshape(N,Q)
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f = np.sum(k.psi2(Z,mu,S))
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df = k.dpsi2_dmuS(Z,mu,S)[1].sum(1).sum(1)
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return f,df.flatten()
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print "psi2_S_test"
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checkgrad(psi2_S_test,np.random.rand(N*Q),args=(k,))
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if not (np.all(Z==self._Z) and np.all(mu==self._mu) and np.all(S==self._S)):
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#something's changed. recompute EVERYTHING
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#TODO: make more efficient for large Q (using NDL's dot product trick)
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#psi1
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self._psi1_denom = S[:,None,:]/self.lengthscale2 + 1.
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self._psi1_dist = Z[None,:,:]-mu[:,None,:]
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self._psi1_dist_sq = np.square(self._psi1_dist)/self.lengthscale2/self._psi1_denom
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self._psi1_exponent = -0.5*np.sum(self._psi1_dist_sq+np.log(self._psi1_denom),-1)
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self._psi1 = self.variance*np.exp(self._psi1_exponent)
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#psi2
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self._psi2_denom = 2.*S[:,None,None,:]/self.lengthscale2+1. # N,M,M,Q
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self._psi2_mudist = mu[:,None,None,:]-self._psi2_Zhat #N,M,M,Q
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self._psi2_mudist_sq = np.square(self._psi2_mudist)/(self.lengthscale2*self._psi2_denom)
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self._psi2_exponent = np.sum(-self._psi2_Zdist_sq/4. -self._psi2_mudist_sq -0.5*np.log(self._psi2_denom),-1) #N,M,M
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self._psi2 = np.square(self.variance)*np.exp(self._psi2_exponent) # N,M,M
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self._Z, self._mu, self._S = Z, mu,S
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def psi2_theta_test(theta,k):
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k.set_param(theta)
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f = np.sum(k.psi2(Z,mu,S))
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df = np.array([np.sum(grad) for grad in k.dpsi2_dtheta(Z,mu,S)])
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return f,df
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print "psi2_theta_test"
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checkgrad(psi2_theta_test,np.random.rand(1+Q),args=(k,))
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|
|
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@ -54,33 +54,33 @@ class white(kernpart):
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def psi0(self,Z,mu,S,target):
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target += self.variance
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def dpsi0_dtheta(self,Z,mu,S,target):
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target += 1.
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def dpsi0_dtheta(self,partial,Z,mu,S,target):
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target += partial.sum()
|
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|
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def dpsi0_dmuS(self,Z,mu,S,target_mu,target_S):
|
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def dpsi0_dmuS(self,partial,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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pass
|
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|
||||
def dpsi1_dtheta(self,Z,mu,S,target):
|
||||
def dpsi1_dtheta(self,partial,Z,mu,S,target):
|
||||
pass
|
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|
||||
def dpsi1_dZ(self,Z,mu,S,target):
|
||||
def dpsi1_dZ(self,partial,Z,mu,S,target):
|
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pass
|
||||
|
||||
def dpsi1_dmuS(self,Z,mu,S,target_mu,target_S):
|
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def dpsi1_dmuS(self,partial,Z,mu,S,target_mu,target_S):
|
||||
pass
|
||||
|
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def psi2(self,Z,mu,S,target):
|
||||
pass
|
||||
|
||||
def dpsi2_dZ(self,Z,mu,S,target):
|
||||
def dpsi2_dZ(self,partial,Z,mu,S,target):
|
||||
pass
|
||||
|
||||
def dpsi2_dtheta(self,Z,mu,S,target):
|
||||
def dpsi2_dtheta(self,partial,Z,mu,S,target):
|
||||
pass
|
||||
|
||||
def dpsi2_dmuS(self,Z,mu,S,target_mu,target_S):
|
||||
def dpsi2_dmuS(self,partial,Z,mu,S,target_mu,target_S):
|
||||
pass
|
||||
|
||||
|
|
|
|||
|
|
@ -9,3 +9,4 @@ from warped_GP import warpedGP
|
|||
from GP_EP import GP_EP
|
||||
from generalized_FITC import generalized_FITC
|
||||
from sparse_GPLVM import sparse_GPLVM
|
||||
from uncertain_input_GP_regression import uncertain_input_GP_regression
|
||||
|
|
|
|||
|
|
@ -7,7 +7,7 @@ from ..util.linalg import mdot, jitchol, chol_inv, pdinv
|
|||
from ..util.plot import gpplot
|
||||
from .. import kern
|
||||
from ..inference.likelihoods import likelihood
|
||||
from GP_regression import GP_regression
|
||||
from sparse_GP_regression import sparse_GP_regression
|
||||
|
||||
class uncertain_input_GP_regression(sparse_GP_regression):
|
||||
"""
|
||||
|
|
@ -33,6 +33,7 @@ class uncertain_input_GP_regression(sparse_GP_regression):
|
|||
"""
|
||||
|
||||
def __init__(self,X,Y,X_uncertainty,kernel=None, beta=100., Z=None,Zslices=None,M=10,normalize_X=False,normalize_Y=False):
|
||||
self.X_uncertainty = X_uncertainty
|
||||
sparse_GP_regression.__init__(self, X, Y, kernel = kernel, beta = beta, normalize_X = normalize_X, normalize_Y = normalize_Y)
|
||||
self.trYYT = np.sum(np.square(self.Y))
|
||||
|
||||
|
|
@ -40,22 +41,22 @@ class uncertain_input_GP_regression(sparse_GP_regression):
|
|||
# kernel computations, using BGPLVM notation
|
||||
#TODO: slices for psi statistics (easy enough)
|
||||
self.Kmm = self.kern.K(self.Z)
|
||||
self.psi0 = self.kern.psi0(self.X,slices=self.Xslices).sum()
|
||||
self.psi1 = self.kern.psi1(self.Z,self.X, self.X_uncertainty)
|
||||
self.psi0 = self.kern.psi0(self.Z,self.X, self.X_uncertainty).sum()
|
||||
self.psi1 = self.kern.psi1(self.Z,self.X, self.X_uncertainty).T
|
||||
self.psi2 = self.kern.psi2(self.Z,self.X, self.X_uncertainty)
|
||||
|
||||
def dL_dtheta(self):
|
||||
#re-cast computations in psi2 back to psi1:
|
||||
dL_dtheta = self.kern.dK_dtheta(self.dL_dKmm,self.Z)
|
||||
dL_dtheta += self.kern.dpsi0_dtheta(self.dL_dpsi0, self.Z,self.X,self.X_uncertainty)
|
||||
dL_dtheta += self.kern.dpsi1_dtheta(self.dL_dpsi1,self.Z,self.X, self.X_uncertainty)
|
||||
dL_dtheta += self.kern.dpsi2_dtheta(self.dL_dpsi2,self.Z,self.X, self.X_uncertainty)
|
||||
dL_dtheta += self.kern.dpsi1_dtheta(self.dL_dpsi1.T,self.Z,self.X, self.X_uncertainty)
|
||||
dL_dtheta += self.kern.dpsi2_dtheta(self.dL_dpsi2,self.Z,self.X, self.X_uncertainty) # for multiple_beta, dL_dpsi2 will be a different shape
|
||||
return dL_dtheta
|
||||
|
||||
def dL_dZ(self):
|
||||
dL_dZ = 2.*self.kern.dK_dX(self.dL_dKmm,self.Z,)#factor of two becase of vertical and horizontal 'stripes' in dKmm_dZ
|
||||
dL_dZ += self.kern.dpsi1_dZ(dL_dpsi1,self.Z,self.X, self.X_uncertainty)
|
||||
dL_dZ += self.kern.dpsi2_dZ(dL_dpsi2,self.Z,self.X, self.X_uncertainty)
|
||||
dL_dZ += self.kern.dpsi1_dZ(self.dL_dpsi1.T,self.Z,self.X, self.X_uncertainty)
|
||||
dL_dZ += self.kern.dpsi2_dZ(self.dL_dpsi2,self.Z,self.X, self.X_uncertainty)
|
||||
return dL_dZ
|
||||
|
||||
def plot(self,*args,**kwargs):
|
||||
|
|
@ -65,5 +66,5 @@ class uncertain_input_GP_regression(sparse_GP_regression):
|
|||
"""
|
||||
sparse_GP_regression.plot(self,*args,**kwargs)
|
||||
if self.Q==1:
|
||||
pb.errorbar(self.X[:,0], pb.ylim(0) ,xerr=2*np.sqrt(self.X_uncertainty.flatten()))
|
||||
pb.errorbar(self.X[:,0], pb.ylim()[0]+np.zeros(self.N), xerr=2*np.sqrt(self.X_uncertainty.flatten()))
|
||||
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue