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sometidying of the psi statistic cross terms
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James Hensman
parent
f881e65761
commit
393662b05d
2 changed files with 29 additions and 51 deletions
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@ -371,16 +371,17 @@ class kern(parameterised):
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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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:param Z: np.ndarray of inducing inputs (M x Q)
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:param mu, S: np.ndarrays of means and variances (each N x Q)
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:returns psi2: np.ndarray (N,M,M)
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"""
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target = np.zeros((mu.shape[0],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[s1,s2,s2]) for p,i_s,s1,s2 in zip(self.parts,self.input_slices,slices1,slices2)]
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#compute the "cross" terms
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for p1, p2 in itertools.combinations(self.parts,2):
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#white doesn;t compine with anything
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#white doesn;t combine with anything
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if p1.name=='white' or p2.name=='white':
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pass
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#rbf X bias
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@ -396,28 +397,9 @@ class kern(parameterised):
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else:
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raise NotImplementedError, "psi2 cannot be computed for this kernel"
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# "crossterms". Here we are recomputing psi1 for white (we don't need to), but it's
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# not really expensive, since it's just a matrix of zeroes.
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# psi1_matrices = [np.zeros((mu.shape[0], Z.shape[0])) for p in self.parts]
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# [p.psi1(Z[s2],mu[s1],S[s1],psi1_target[s1,s2]) for p,s1,s2,psi1_target in zip(self.parts,slices1,slices2, psi1_matrices)]
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crossterms = 0.0
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# for 3 kernels this returns something like
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# [(0,1), (0,2), (1,2)]
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# in theory, we should also account for (1,0), (2,0) and so on, but
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# the transpose deals exactly with that
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# for a,b in itertools.combinations(psi1_matrices, 2):
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# tmp = np.multiply(a,b)
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# crossterms += tmp[:,None,:] + tmp[:, :,None]
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return target + crossterms
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return target
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def dpsi2_dtheta(self,partial,partial1,Z,mu,S,slices1=None,slices2=None):
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"""Returns shape (N,M,M,Ntheta)"""
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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[s1,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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@ -429,7 +411,7 @@ class kern(parameterised):
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ipsl1, ipsl2 = self.input_slices[i1], self.input_slices[i2]
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ps1, ps2 = self.param_slices[i1], self.param_slices[i2]
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#white doesn;t compine with anything
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#white doesn;t combine with anything
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if p1.name=='white' or p2.name=='white':
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pass
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#rbf X bias
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@ -447,26 +429,6 @@ class kern(parameterised):
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else:
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raise NotImplementedError, "psi2 cannot be computed for this kernel"
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# # "crossterms"
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# # 1. get all the psi1 statistics
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# psi1_matrices = [np.zeros((mu.shape[0], Z.shape[0])) for p in self.parts]
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# [p.psi1(Z[s2],mu[s1],S[s1],psi1_target[s1,s2]) for p,s1,s2,psi1_target in zip(self.parts,slices1,slices2, psi1_matrices)]
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# partial1 = np.ones_like(partial1)
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# # 2. get all the dpsi1/dtheta gradients
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# psi1_gradients = [np.zeros(self.Nparam) for p in self.parts]
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# [p.dpsi1_dtheta(partial1[s2,s1],Z[s2,i_s],mu[s1,i_s],S[s1,i_s],psi1g_target[ps]) for p,ps,s1,s2,i_s,psi1g_target in zip(self.parts, self.param_slices,slices1,slices2,self.input_slices,psi1_gradients)]
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# # 3. multiply them somehow
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# for a,b in itertools.combinations(range(len(psi1_matrices)), 2):
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# tmp = (psi1_gradients[a][None, None] * psi1_matrices[b][:,:, None])
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# # target += (tmp[None] + tmp[:,None]).sum(0).sum(0).sum(0)
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# # gne = (psi1_gradients[a].sum()*psi1_matrices[b].sum())
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# # target += gne
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# #target += (gne[None] + gne[:, None]).sum(0)
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# target += (partial.sum(0)[:,:,None] * (tmp[:, None] + tmp[:,:,None]).sum(0)).sum(0).sum(0)
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return self._transform_gradients(target)
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def dpsi2_dZ(self,partial,Z,mu,S,slices1=None,slices2=None):
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@ -475,16 +437,15 @@ class kern(parameterised):
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[p.dpsi2_dZ(partial[s1,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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#compute the "cross" terms
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#TODO: slices (need to iterate around the input slices also...)
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for p1, p2 in itertools.combinations(self.parts,2):
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#white doesn;t compine with anything
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#white doesn;t combine with anything
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if p1.name=='white' or p2.name=='white':
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pass
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#rbf X bias
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elif p1.name=='bias' and p2.name=='rbf':
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target += p2.dpsi1_dX(partial.sum(1)*p1.variance,Z,mu,S)
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target += p2.dpsi1_dX(partial.sum(1)*p1.variance,Z,mu,S,target)
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elif p2.name=='bias' and p1.name=='rbf':
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target += p1.dpsi1_dZ(partial.sum(2)*p2.variance,Z,mu,S)
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target += p1.dpsi1_dZ(partial.sum(2)*p2.variance,Z,mu,S,target)
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#rbf X linear
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elif p1.name=='linear' and p2.name=='rbf':
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raise NotImplementedError #TODO
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@ -502,7 +463,24 @@ class kern(parameterised):
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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[s1,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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#compute the "cross" terms
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for p1, p2 in itertools.combinations(self.parts,2):
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#white doesn;t combine with anything
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if p1.name=='white' or p2.name=='white':
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pass
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#rbf X bias
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elif p1.name=='bias' and p2.name=='rbf':
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target += p2.dpsi1_dmuS(partial.sum(1)*p1.variance,Z,mu,S,target_mu,target_S)
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elif p2.name=='bias' and p1.name=='rbf':
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target += p1.dpsi1_dmuS(partial.sum(2)*p2.variance,Z,mu,S,target_mu,target_S)
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#rbf X linear
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elif p1.name=='linear' and p2.name=='rbf':
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raise NotImplementedError #TODO
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elif p2.name=='linear' and p1.name=='rbf':
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raise NotImplementedError #TODO
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else:
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raise NotImplementedError, "psi2 cannot be computed for this kernel"
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return target_mu, target_S
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def plot(self, x = None, plot_limits=None,which_functions='all',resolution=None,*args,**kwargs):
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