mirror of
https://github.com/SheffieldML/GPy.git
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Merge branch 'devel' of github.com:SheffieldML/GPy into devel
This commit is contained in:
Max Zwiessele
commit
dfdb1c24e6
12 changed files with 247 additions and 126 deletions
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@ -66,7 +66,7 @@ class SparseGP(GP):
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#gradients wrt Z
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self.Z.gradient = self.kern.gradients_X(dL_dKmm, self.Z)
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self.Z.gradient += self.kern.gradients_Z_expectations(
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self.grad_dict['dL_dpsi1'], self.grad_dict['dL_dpsi2'], Z=self.Z, variational_posterior=self.X)
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self.grad_dict['dL_dpsi0'], self.grad_dict['dL_dpsi1'], self.grad_dict['dL_dpsi2'], Z=self.Z, variational_posterior=self.X)
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else:
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#gradients wrt kernel
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self.kern.update_gradients_diag(self.grad_dict['dL_dKdiag'], self.X)
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@ -71,12 +71,13 @@ class VarDTC_minibatch(LatentFunctionInference):
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#see whether we've got a different noise variance for each datum
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beta = 1./np.fmax(likelihood.variance, 1e-6)
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het_noise = beta.size > 1
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if het_noise:
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self.batchsize = 1
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# VVT_factor is a matrix such that tdot(VVT_factor) = VVT...this is for efficiency!
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#self.YYTfactor = beta*self.get_YYTfactor(Y)
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YYT_factor = Y
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trYYT = self.get_trYYT(Y)
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psi2_full = np.zeros((num_inducing,num_inducing))
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psi1Y_full = np.zeros((output_dim,num_inducing)) # DxM
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psi0_full = 0
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@ -105,19 +106,18 @@ class VarDTC_minibatch(LatentFunctionInference):
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YRY_full += (beta_slice*np.square(Y_slice).sum(axis=-1)).sum()
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else:
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psi0_full += psi0.sum()
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psi1Y_full += np.dot(Y_slice.T,psi1) # DxM
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psi1Y_full += np.dot(Y_slice.T,psi1) # DxM
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if uncertain_inputs:
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if het_noise:
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psi2_full += np.einsum('n,nmo->mo',beta_slice,psi2)
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psi2_full += beta_slice*psi2
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else:
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psi2_full += psi2.sum(axis=0)
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psi2_full += psi2
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else:
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if het_noise:
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psi2_full += np.einsum('n,nm,no->mo',beta_slice,psi1,psi1)
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psi2_full += beta_slice*np.outer(psi1,psi1)
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else:
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psi2_full += tdot(psi1.T)
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psi2_full += np.outer(psi1,psi1)
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if not het_noise:
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psi0_full *= beta
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@ -224,7 +224,7 @@ class VarDTC_minibatch(LatentFunctionInference):
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psi2 = None
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if het_noise:
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beta = beta[n_start:n_end]
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beta = beta[n_start] # assuming batchsize==1
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betaY = beta*Y_slice
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betapsi1 = np.einsum('n,nm->nm',beta,psi1)
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@ -245,7 +245,7 @@ class VarDTC_minibatch(LatentFunctionInference):
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dL_dpsi1 = np.dot(betaY,v.T)
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if uncertain_inputs:
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dL_dpsi2 = np.einsum('n,mo->nmo',beta * np.ones((n_end-n_start,)),dL_dpsi2R)
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dL_dpsi2 = beta* dL_dpsi2R
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else:
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dL_dpsi1 += np.dot(betapsi1,dL_dpsi2R)*2.
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dL_dpsi2 = None
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@ -263,11 +263,11 @@ class VarDTC_minibatch(LatentFunctionInference):
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dL_dthetaL = ((np.square(betaY)).sum(axis=-1) + np.square(beta)*(output_dim*psi0)-output_dim*beta)/2. - np.square(beta)*psiR- (betaY*np.dot(betapsi1,v)).sum(axis=-1)
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else:
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if uncertain_inputs:
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psiR = np.einsum('mo,nmo->',dL_dpsi2R,psi2)
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psiR = np.einsum('mo,mo->',dL_dpsi2R,psi2)
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else:
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psiR = np.einsum('nm,no,mo->',psi1,psi1,dL_dpsi2R)
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dL_dthetaL = ((np.square(betaY)).sum() + np.square(beta)*output_dim*(psi0.sum())-num_slice*output_dim*beta)/2. - np.square(beta)*psiR- (betaY*np.dot(betapsi1,v)).sum()
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dL_dthetaL = ((np.square(betaY)).sum() + beta*beta*output_dim*(psi0.sum())-num_slice*output_dim*beta)/2. - beta*beta*psiR- (betaY*np.dot(betapsi1,v)).sum()
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if uncertain_inputs:
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grad_dict = {'dL_dpsi0':dL_dpsi0,
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@ -297,7 +297,7 @@ def update_gradients(model):
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kern_grad = model.kern.gradient.copy()
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#gradients w.r.t. Z
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model.Z.gradient[:,model.kern.active_dims] = model.kern.gradients_X(dL_dKmm, model.Z)
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model.Z.gradient = model.kern.gradients_X(dL_dKmm, model.Z)
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isEnd = False
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while not isEnd:
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@ -310,8 +310,8 @@ def update_gradients(model):
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kern_grad += model.kern.gradient
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#gradients w.r.t. Z
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model.Z.gradient[:,model.kern.active_dims] += model.kern.gradients_Z_expectations(
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grad_dict['dL_dpsi1'], grad_dict['dL_dpsi2'], Z=model.Z, variational_posterior=X_slice)
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model.Z.gradient += model.kern.gradients_Z_expectations(
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dL_dpsi0=grad_dict['dL_dpsi0'], dL_dpsi1=grad_dict['dL_dpsi1'], dL_dpsi2=grad_dict['dL_dpsi2'], Z=model.Z, variational_posterior=X_slice)
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#gradients w.r.t. posterior parameters of X
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X_grad = model.kern.gradients_qX_expectations(variational_posterior=X_slice, Z=model.Z, dL_dpsi0=grad_dict['dL_dpsi0'], dL_dpsi1=grad_dict['dL_dpsi1'], dL_dpsi2=grad_dict['dL_dpsi2'])
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@ -119,7 +119,7 @@ class Add(CombinationKernel):
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eff_dL_dpsi1 += dL_dpsi2.sum(1) * p2.psi1(Z, variational_posterior) * 2.
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p1.update_gradients_expectations(dL_dpsi0, eff_dL_dpsi1, dL_dpsi2, Z, variational_posterior)
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def gradients_Z_expectations(self, dL_dpsi1, dL_dpsi2, Z, variational_posterior):
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def gradients_Z_expectations(self, dL_psi0, dL_dpsi1, dL_dpsi2, Z, variational_posterior):
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from static import White, Bias
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target = np.zeros(Z.shape)
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for p1 in self.parts:
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@ -170,4 +170,4 @@ class Add(CombinationKernel):
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return self
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def input_sensitivity(self):
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return reduce(np.add, [k.input_sensitivity() for k in self.parts])
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return reduce(np.add, [k.input_sensitivity() for k in self.parts])
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@ -103,7 +103,7 @@ class Kern(Parameterized):
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"""
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raise NotImplementedError
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def gradients_Z_expectations(self, dL_dpsi1, dL_dpsi2, Z, variational_posterior):
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def gradients_Z_expectations(self, dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, variational_posterior):
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"""
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Returns the derivative of the objective wrt Z, using the chain rule
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through the expectation variables.
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@ -124,9 +124,9 @@ def _slice_update_gradients_expectations(f):
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def _slice_gradients_Z_expectations(f):
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@wraps(f)
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def wrap(self, dL_dpsi1, dL_dpsi2, Z, variational_posterior):
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def wrap(self, dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, variational_posterior):
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with _Slice_wrap(self, Z, variational_posterior) as s:
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ret = s.handle_return_array(f(self, dL_dpsi1, dL_dpsi2, s.X, s.X2))
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ret = s.handle_return_array(f(self, dL_dpsi0, dL_dpsi1, dL_dpsi2, s.X, s.X2))
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return ret
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return wrap
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@ -169,7 +169,7 @@ class Linear(Kern):
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else:
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self.variances.gradient += 2.*np.sum(dL_dpsi2 * self.psi2(Z, variational_posterior))/self.variances
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def gradients_Z_expectations(self, dL_dpsi1, dL_dpsi2, Z, variational_posterior):
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def gradients_Z_expectations(self, dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, variational_posterior):
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if isinstance(variational_posterior, variational.SpikeAndSlabPosterior):
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gamma = variational_posterior.binary_prob
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mu = variational_posterior.mean
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@ -9,12 +9,23 @@ import numpy as np
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from GPy.util.caching import Cache_this
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@Cache_this(limit=1)
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def _Z_distances(Z):
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Zhat = 0.5 * (Z[:, None, :] + Z[None, :, :]) # M,M,Q
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Zdist = 0.5 * (Z[:, None, :] - Z[None, :, :]) # M,M,Q
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return Zhat, Zdist
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def psicomputations(variance, lengthscale, Z, mu, S, gamma):
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"""
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Z - MxQ
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mu - NxQ
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S - NxQ
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gamma - NxQ
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"""
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# here are the "statistics" for psi0, psi1 and psi2
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# Produced intermediate results:
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# _psi1 NxM
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psi0 = np.empty(mu.shape[0])
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psi0[:] = variance
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psi1 = _psi1computations(variance, lengthscale, Z, mu, S, gamma)
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psi2 = _psi2computations(variance, lengthscale, Z, mu, S, gamma)
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return psi0, psi1, psi2
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@Cache_this(limit=1)
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def _psi1computations(variance, lengthscale, Z, mu, S, gamma):
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"""
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Z - MxQ
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@ -22,15 +33,10 @@ def _psi1computations(variance, lengthscale, Z, mu, S, gamma):
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S - NxQ
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gamma - NxQ
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"""
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# here are the "statistics" for psi1 and psi2
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# here are the "statistics" for psi1
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# Produced intermediate results:
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# _psi1 NxM
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# _dpsi1_dvariance NxM
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# _dpsi1_dlengthscale NxMxQ
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# _dpsi1_dZ NxMxQ
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# _dpsi1_dgamma NxMxQ
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# _dpsi1_dmu NxMxQ
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# _dpsi1_dS NxMxQ
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lengthscale2 = np.square(lengthscale)
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@ -40,25 +46,15 @@ def _psi1computations(variance, lengthscale, Z, mu, S, gamma):
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_psi1_dist = Z[None, :, :] - mu[:, None, :] # NxMxQ
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_psi1_dist_sq = np.square(_psi1_dist) / (lengthscale2 * _psi1_denom) # NxMxQ
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_psi1_common = gamma[:,None,:] / (lengthscale2*_psi1_denom*_psi1_denom_sqrt) #Nx1xQ
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_psi1_exponent1 = np.log(gamma[:,None,:]) -0.5 * (_psi1_dist_sq + np.log(_psi1_denom)) # NxMxQ
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_psi1_exponent2 = np.log(1.-gamma[:,None,:]) -0.5 * (np.square(Z[None,:,:])/lengthscale2) # NxMxQ
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_psi1_exponent1 = np.log(gamma[:,None,:]) - (_psi1_dist_sq + np.log(_psi1_denom))/2. # NxMxQ
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_psi1_exponent2 = np.log(1.-gamma[:,None,:]) - (np.square(Z[None,:,:])/lengthscale2)/2. # NxMxQ
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_psi1_exponent_max = np.maximum(_psi1_exponent1,_psi1_exponent2)
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_psi1_exponent = _psi1_exponent_max+np.log(np.exp(_psi1_exponent1-_psi1_exponent_max) + np.exp(_psi1_exponent2-_psi1_exponent_max)) #NxMxQ
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_psi1_exp_sum = _psi1_exponent.sum(axis=-1) #NxM
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_psi1_exp_dist_sq = np.exp(-0.5*_psi1_dist_sq) # NxMxQ
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_psi1_exp_Z = np.exp(-0.5*np.square(Z[None,:,:])/lengthscale2) # 1xMxQ
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_psi1_q = variance * np.exp(_psi1_exp_sum[:,:,None] - _psi1_exponent) # NxMxQ
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_psi1 = variance * np.exp(_psi1_exp_sum) # NxM
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_dpsi1_dvariance = _psi1 / variance # NxM
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_dpsi1_dgamma = _psi1_q * (_psi1_exp_dist_sq/_psi1_denom_sqrt-_psi1_exp_Z) # NxMxQ
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_dpsi1_dmu = _psi1_q * (_psi1_exp_dist_sq * _psi1_dist * _psi1_common) # NxMxQ
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_dpsi1_dS = _psi1_q * (_psi1_exp_dist_sq * _psi1_common * 0.5 * (_psi1_dist_sq - 1.)) # NxMxQ
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_dpsi1_dZ = _psi1_q * (- _psi1_common * _psi1_dist * _psi1_exp_dist_sq - (1-gamma[:,None,:])/lengthscale2*Z[None,:,:]*_psi1_exp_Z) # NxMxQ
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_dpsi1_dlengthscale = 2.*lengthscale*_psi1_q * (0.5*_psi1_common*(S[:,None,:]/lengthscale2+_psi1_dist_sq)*_psi1_exp_dist_sq + 0.5*(1-gamma[:,None,:])*np.square(Z[None,:,:]/lengthscale2)*_psi1_exp_Z) # NxMxQ
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return _psi1, _dpsi1_dvariance, _dpsi1_dgamma, _dpsi1_dmu, _dpsi1_dS, _dpsi1_dZ, _dpsi1_dlengthscale
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return _psi1
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@Cache_this(limit=1)
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def _psi2computations(variance, lengthscale, Z, mu, S, gamma):
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"""
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Z - MxQ
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@ -66,19 +62,14 @@ def _psi2computations(variance, lengthscale, Z, mu, S, gamma):
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S - NxQ
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gamma - NxQ
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"""
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# here are the "statistics" for psi1 and psi2
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# here are the "statistics" for psi2
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# Produced intermediate results:
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# _psi2 NxMxM
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# _psi2_dvariance NxMxM
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# _psi2_dlengthscale NxMxMxQ
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# _psi2_dZ NxMxMxQ
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# _psi2_dgamma NxMxMxQ
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# _psi2_dmu NxMxMxQ
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# _psi2_dS NxMxMxQ
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# _psi2 MxM
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lengthscale2 = np.square(lengthscale)
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_psi2_Zhat, _psi2_Zdist = _Z_distances(Z)
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_psi2_Zhat = 0.5 * (Z[:, None, :] + Z[None, :, :]) # M,M,Q
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_psi2_Zdist = 0.5 * (Z[:, None, :] - Z[None, :, :]) # M,M,Q
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_psi2_Zdist_sq = np.square(_psi2_Zdist / lengthscale) # M,M,Q
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_psi2_Z_sq_sum = (np.square(Z[:,None,:])+np.square(Z[None,:,:]))/lengthscale2 # MxMxQ
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@ -93,15 +84,130 @@ def _psi2computations(variance, lengthscale, Z, mu, S, gamma):
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_psi2_exponent_max = np.maximum(_psi2_exponent1, _psi2_exponent2)
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_psi2_exponent = _psi2_exponent_max+np.log(np.exp(_psi2_exponent1-_psi2_exponent_max) + np.exp(_psi2_exponent2-_psi2_exponent_max))
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_psi2_exp_sum = _psi2_exponent.sum(axis=-1) #NxM
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_psi2_q = np.square(variance) * np.exp(_psi2_exp_sum[:,:,:,None]-_psi2_exponent) # NxMxMxQ
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_psi2 = variance*variance * (np.exp(_psi2_exp_sum).sum(axis=0)) # MxM
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return _psi2
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def psiDerivativecomputations(dL_dpsi0, dL_dpsi1, dL_dpsi2, variance, lengthscale, Z, variational_posterior):
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ARD = (len(lengthscale)!=1)
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dvar_psi1, dl_psi1, dZ_psi1, dmu_psi1, dS_psi1, dgamma_psi1 = _psi1compDer(dL_dpsi1, variance, lengthscale, Z, variational_posterior.mean, variational_posterior.variance, variational_posterior.binary_prob)
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dvar_psi2, dl_psi2, dZ_psi2, dmu_psi2, dS_psi2, dgamma_psi2 = _psi2compDer(dL_dpsi2, variance, lengthscale, Z, variational_posterior.mean, variational_posterior.variance, variational_posterior.binary_prob)
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dL_dvar = np.sum(dL_dpsi0) + dvar_psi1 + dvar_psi2
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dL_dlengscale = dl_psi1 + dl_psi2
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if not ARD:
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dL_dlengscale = dL_dlengscale.sum()
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dL_dgamma = dgamma_psi1 + dgamma_psi2
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dL_dmu = dmu_psi1 + dmu_psi2
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dL_dS = dS_psi1 + dS_psi2
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dL_dZ = dZ_psi1 + dZ_psi2
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return dL_dvar, dL_dlengscale, dL_dZ, dL_dmu, dL_dS, dL_dgamma
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def _psi1compDer(dL_dpsi1, variance, lengthscale, Z, mu, S, gamma):
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"""
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dL_dpsi1 - NxM
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Z - MxQ
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mu - NxQ
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S - NxQ
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gamma - NxQ
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"""
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# here are the "statistics" for psi1
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# Produced intermediate results: dL_dparams w.r.t. psi1
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# _dL_dvariance 1
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# _dL_dlengthscale Q
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# _dL_dZ MxQ
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# _dL_dgamma NxQ
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# _dL_dmu NxQ
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# _dL_dS NxQ
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lengthscale2 = np.square(lengthscale)
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# psi1
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_psi1_denom = S / lengthscale2 + 1. # NxQ
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_psi1_denom_sqrt = np.sqrt(_psi1_denom) #NxQ
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_psi1_dist = Z[None, :, :] - mu[:, None, :] # NxMxQ
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_psi1_dist_sq = np.square(_psi1_dist) / (lengthscale2 * _psi1_denom[:,None,:]) # NxMxQ
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_psi1_common = gamma / (lengthscale2*_psi1_denom*_psi1_denom_sqrt) #NxQ
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_psi1_exponent1 = np.log(gamma[:,None,:]) -0.5 * (_psi1_dist_sq + np.log(_psi1_denom[:, None,:])) # NxMxQ
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_psi1_exponent2 = np.log(1.-gamma[:,None,:]) -0.5 * (np.square(Z[None,:,:])/lengthscale2) # NxMxQ
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_psi1_exponent_max = np.maximum(_psi1_exponent1,_psi1_exponent2)
|
||||
_psi1_exponent = _psi1_exponent_max+np.log(np.exp(_psi1_exponent1-_psi1_exponent_max) + np.exp(_psi1_exponent2-_psi1_exponent_max)) #NxMxQ
|
||||
_psi1_exp_sum = _psi1_exponent.sum(axis=-1) #NxM
|
||||
_psi1_exp_dist_sq = np.exp(-0.5*_psi1_dist_sq) # NxMxQ
|
||||
_psi1_exp_Z = np.exp(-0.5*np.square(Z[None,:,:])/lengthscale2) # 1xMxQ
|
||||
_psi1_q = variance * np.exp(_psi1_exp_sum[:,:,None] - _psi1_exponent) # NxMxQ
|
||||
_psi1 = variance * np.exp(_psi1_exp_sum) # NxM
|
||||
_dL_dvariance = np.einsum('nm,nm->',dL_dpsi1, _psi1)/variance # 1
|
||||
_dL_dgamma = np.einsum('nm,nmq,nmq->nq',dL_dpsi1, _psi1_q, (_psi1_exp_dist_sq/_psi1_denom_sqrt[:,None,:]-_psi1_exp_Z)) # NxQ
|
||||
_dL_dmu = np.einsum('nm, nmq, nmq, nmq, nq->nq',dL_dpsi1,_psi1_q,_psi1_exp_dist_sq,_psi1_dist,_psi1_common) # NxQ
|
||||
_dL_dS = np.einsum('nm,nmq,nmq,nq,nmq->nq',dL_dpsi1,_psi1_q,_psi1_exp_dist_sq,_psi1_common,(_psi1_dist_sq-1.))/2. # NxQ
|
||||
_dL_dZ = np.einsum('nm,nmq,nmq->mq',dL_dpsi1,_psi1_q, (- _psi1_common[:,None,:] * _psi1_dist * _psi1_exp_dist_sq - (1-gamma[:,None,:])/lengthscale2*Z[None,:,:]*_psi1_exp_Z))
|
||||
_dL_dlengthscale = lengthscale* np.einsum('nm,nmq,nmq->q',dL_dpsi1,_psi1_q,(_psi1_common[:,None,:]*(S[:,None,:]/lengthscale2+_psi1_dist_sq)*_psi1_exp_dist_sq + (1-gamma[:,None,:])*np.square(Z[None,:,:]/lengthscale2)*_psi1_exp_Z))
|
||||
|
||||
# _dpsi1_dmu = _psi1_q * (_psi1_exp_dist_sq * _psi1_dist * _psi1_common) # NxMxQ
|
||||
# _dpsi1_dS = _psi1_q * (_psi1_exp_dist_sq * _psi1_common * 0.5 * (_psi1_dist_sq - 1.)) # NxMxQ
|
||||
# _dpsi1_dZ = _psi1_q * (- _psi1_common * _psi1_dist * _psi1_exp_dist_sq - (1-gamma[:,None,:])/lengthscale2*Z[None,:,:]*_psi1_exp_Z) # NxMxQ
|
||||
# _dpsi1_dlengthscale = 2.*lengthscale*_psi1_q * (0.5*_psi1_common*(S[:,None,:]/lengthscale2+_psi1_dist_sq)*_psi1_exp_dist_sq + 0.5*(1-gamma[:,None,:])*np.square(Z[None,:,:]/lengthscale2)*_psi1_exp_Z) # NxMxQ
|
||||
|
||||
return _dL_dvariance, _dL_dlengthscale, _dL_dZ, _dL_dmu, _dL_dS, _dL_dgamma
|
||||
|
||||
def _psi2compDer(dL_dpsi2, variance, lengthscale, Z, mu, S, gamma):
|
||||
"""
|
||||
Z - MxQ
|
||||
mu - NxQ
|
||||
S - NxQ
|
||||
gamma - NxQ
|
||||
dL_dpsi2 - MxM
|
||||
"""
|
||||
# here are the "statistics" for psi2
|
||||
# Produced the derivatives w.r.t. psi2:
|
||||
# _dL_dvariance 1
|
||||
# _dL_dlengthscale Q
|
||||
# _dL_dZ MxQ
|
||||
# _dL_dgamma NxQ
|
||||
# _dL_dmu NxQ
|
||||
# _dL_dS NxQ
|
||||
|
||||
lengthscale2 = np.square(lengthscale)
|
||||
|
||||
_psi2_Zhat = 0.5 * (Z[:, None, :] + Z[None, :, :]) # M,M,Q
|
||||
_psi2_Zdist = 0.5 * (Z[:, None, :] - Z[None, :, :]) # M,M,Q
|
||||
_psi2_Zdist_sq = np.square(_psi2_Zdist / lengthscale) # M,M,Q
|
||||
_psi2_Z_sq_sum = (np.square(Z[:,None,:])+np.square(Z[None,:,:]))/lengthscale2 # MxMxQ
|
||||
|
||||
# psi2
|
||||
_psi2_denom = 2.*S / lengthscale2 + 1. # NxQ
|
||||
_psi2_denom_sqrt = np.sqrt(_psi2_denom)
|
||||
_psi2_mudist = mu[:,None,None,:]-_psi2_Zhat #N,M,M,Q
|
||||
_psi2_mudist_sq = np.square(_psi2_mudist)/(lengthscale2*_psi2_denom[:,None,None,:])
|
||||
_psi2_common = gamma/(lengthscale2 * _psi2_denom * _psi2_denom_sqrt) # NxQ
|
||||
_psi2_exponent1 = -_psi2_Zdist_sq -_psi2_mudist_sq -0.5*np.log(_psi2_denom[:,None,None,:])+np.log(gamma[:,None,None,:]) #N,M,M,Q
|
||||
_psi2_exponent2 = np.log(1.-gamma[:,None,None,:]) - 0.5*(_psi2_Z_sq_sum) # NxMxMxQ
|
||||
_psi2_exponent_max = np.maximum(_psi2_exponent1, _psi2_exponent2)
|
||||
_psi2_exponent = _psi2_exponent_max+np.log(np.exp(_psi2_exponent1-_psi2_exponent_max) + np.exp(_psi2_exponent2-_psi2_exponent_max))
|
||||
_psi2_exp_sum = _psi2_exponent.sum(axis=-1) #NxM
|
||||
_psi2_q = variance*variance * np.exp(_psi2_exp_sum[:,:,:,None]-_psi2_exponent) # NxMxMxQ
|
||||
_psi2_exp_dist_sq = np.exp(-_psi2_Zdist_sq -_psi2_mudist_sq) # NxMxMxQ
|
||||
_psi2_exp_Z = np.exp(-0.5*_psi2_Z_sq_sum) # MxMxQ
|
||||
_psi2 = np.square(variance) * np.exp(_psi2_exp_sum) # N,M,M
|
||||
_dpsi2_dvariance = 2. * _psi2/variance # NxMxM
|
||||
_dpsi2_dgamma = _psi2_q * (_psi2_exp_dist_sq/_psi2_denom_sqrt - _psi2_exp_Z) # NxMxMxQ
|
||||
_dpsi2_dmu = _psi2_q * (-2.*_psi2_common*_psi2_mudist * _psi2_exp_dist_sq) # NxMxMxQ
|
||||
_dpsi2_dS = _psi2_q * (_psi2_common * (2.*_psi2_mudist_sq - 1.) * _psi2_exp_dist_sq) # NxMxMxQ
|
||||
_dpsi2_dZ = 2.*_psi2_q * (_psi2_common*(-_psi2_Zdist*_psi2_denom+_psi2_mudist)*_psi2_exp_dist_sq - (1-gamma[:,None,None,:])*Z[:,None,:]/lengthscale2*_psi2_exp_Z) # NxMxMxQ
|
||||
_dpsi2_dlengthscale = 2.*lengthscale* _psi2_q * (_psi2_common*(S[:,None,None,:]/lengthscale2+_psi2_Zdist_sq*_psi2_denom+_psi2_mudist_sq)*_psi2_exp_dist_sq+(1-gamma[:,None,None,:])*_psi2_Z_sq_sum*0.5/lengthscale2*_psi2_exp_Z) # NxMxMxQ
|
||||
_psi2 = variance*variance * (np.exp(_psi2_exp_sum).sum(axis=0)) # MxM
|
||||
_dL_dvariance = np.einsum('mo,mo->',dL_dpsi2,_psi2)*2./variance
|
||||
_dL_dgamma = np.einsum('mo,nmoq,nmoq->nq',dL_dpsi2,_psi2_q,(_psi2_exp_dist_sq/_psi2_denom_sqrt[:,None,None,:] - _psi2_exp_Z))
|
||||
_dL_dmu = -2.*np.einsum('mo,nmoq,nq,nmoq,nmoq->nq',dL_dpsi2,_psi2_q,_psi2_common,_psi2_mudist,_psi2_exp_dist_sq)
|
||||
_dL_dS = np.einsum('mo,nmoq,nq,nmoq,nmoq->nq',dL_dpsi2,_psi2_q, _psi2_common, (2.*_psi2_mudist_sq-1.), _psi2_exp_dist_sq)
|
||||
_dL_dZ = 2.*np.einsum('mo,nmoq,nmoq->mq',dL_dpsi2,_psi2_q,(_psi2_common[:,None,None,:]*(-_psi2_Zdist*_psi2_denom[:,None,None,:]+_psi2_mudist)*_psi2_exp_dist_sq - (1-gamma[:,None,None,:])*Z[:,None,:]/lengthscale2*_psi2_exp_Z))
|
||||
# print _psi2_common[:,None,None,:]*(S[:,None,None,:]/lengthscale2+_psi2_Zdist_sq*_psi2_denom[:,None,None,:]+_psi2_mudist_sq)*_psi2_exp_dist_sq #+(1-gamma[:,None,None,:])*_psi2_Z_sq_sum*0.5/lengthscale2*_psi2_exp_Z)
|
||||
_dL_dlengthscale = 2.*lengthscale* np.einsum('mo,nmoq,nmoq->q',dL_dpsi2,_psi2_q,(_psi2_common[:,None,None,:]*(S[:,None,None,:]/lengthscale2+_psi2_Zdist_sq*_psi2_denom[:,None,None,:]+_psi2_mudist_sq)*_psi2_exp_dist_sq+(1-gamma[:,None,None,:])*_psi2_Z_sq_sum*0.5/lengthscale2*_psi2_exp_Z))
|
||||
|
||||
|
||||
# _dpsi2_dvariance = 2. * _psi2/variance # NxMxM
|
||||
# _dpsi2_dgamma = _psi2_q * (_psi2_exp_dist_sq/_psi2_denom_sqrt - _psi2_exp_Z) # NxMxMxQ
|
||||
# _dpsi2_dmu = _psi2_q * (-2.*_psi2_common*_psi2_mudist * _psi2_exp_dist_sq) # NxMxMxQ
|
||||
# _dpsi2_dS = _psi2_q * (_psi2_common * (2.*_psi2_mudist_sq - 1.) * _psi2_exp_dist_sq) # NxMxMxQ
|
||||
# _dpsi2_dZ = 2.*_psi2_q * (_psi2_common*(-_psi2_Zdist*_psi2_denom+_psi2_mudist)*_psi2_exp_dist_sq - (1-gamma[:,None,None,:])*Z[:,None,:]/lengthscale2*_psi2_exp_Z) # NxMxMxQ
|
||||
# _dpsi2_dlengthscale = 2.*lengthscale* _psi2_q * (_psi2_common*(S[:,None,None,:]/lengthscale2+_psi2_Zdist_sq*_psi2_denom+_psi2_mudist_sq)*_psi2_exp_dist_sq+(1-gamma[:,None,None,:])*_psi2_Z_sq_sum*0.5/lengthscale2*_psi2_exp_Z) # NxMxMxQ
|
||||
|
||||
return _psi2, _dpsi2_dvariance, _dpsi2_dgamma, _dpsi2_dmu, _dpsi2_dS, _dpsi2_dZ, _dpsi2_dlengthscale
|
||||
return _dL_dvariance, _dL_dlengthscale, _dL_dZ, _dL_dmu, _dL_dS, _dL_dgamma
|
||||
|
|
|
|||
|
|
@ -42,9 +42,11 @@ class RBF(Stationary):
|
|||
#---------------------------------------#
|
||||
|
||||
def psi0(self, Z, variational_posterior):
|
||||
if self.useGPU:
|
||||
if isinstance(variational_posterior, variational.SpikeAndSlabPosterior):
|
||||
if isinstance(variational_posterior, variational.SpikeAndSlabPosterior):
|
||||
if self.useGPU:
|
||||
return self.psicomp.psicomputations(self.variance, self.lengthscale, Z, variational_posterior.mean, variational_posterior.variance, variational_posterior.binary_prob)[0]
|
||||
else:
|
||||
return ssrbf_psi_comp.psicomputations(self.variance, self.lengthscale, Z, variational_posterior.mean, variational_posterior.variance, variational_posterior.binary_prob)[0]
|
||||
else:
|
||||
return self.Kdiag(variational_posterior.mean)
|
||||
|
||||
|
|
@ -53,7 +55,7 @@ class RBF(Stationary):
|
|||
if self.useGPU:
|
||||
return self.psicomp.psicomputations(self.variance, self.lengthscale, Z, variational_posterior.mean, variational_posterior.variance, variational_posterior.binary_prob)[1]
|
||||
else:
|
||||
psi1, _, _, _, _, _, _ = ssrbf_psi_comp._psi1computations(self.variance, self.lengthscale, Z, variational_posterior.mean, variational_posterior.variance, variational_posterior.binary_prob)
|
||||
return ssrbf_psi_comp.psicomputations(self.variance, self.lengthscale, Z, variational_posterior.mean, variational_posterior.variance, variational_posterior.binary_prob)[1]
|
||||
else:
|
||||
_, _, _, psi1 = self._psi1computations(Z, variational_posterior)
|
||||
return psi1
|
||||
|
|
@ -63,7 +65,7 @@ class RBF(Stationary):
|
|||
if self.useGPU:
|
||||
return self.psicomp.psicomputations(self.variance, self.lengthscale, Z, variational_posterior.mean, variational_posterior.variance, variational_posterior.binary_prob)[2]
|
||||
else:
|
||||
psi2, _, _, _, _, _, _ = ssrbf_psi_comp._psi2computations(self.variance, self.lengthscale, Z, variational_posterior.mean, variational_posterior.variance, variational_posterior.binary_prob)
|
||||
return ssrbf_psi_comp.psicomputations(self.variance, self.lengthscale, Z, variational_posterior.mean, variational_posterior.variance, variational_posterior.binary_prob)[2]
|
||||
else:
|
||||
_, _, _, _, psi2 = self._psi2computations(Z, variational_posterior)
|
||||
return psi2
|
||||
|
|
@ -74,26 +76,30 @@ class RBF(Stationary):
|
|||
if self.useGPU:
|
||||
self.psicomp.update_gradients_expectations(dL_dpsi0, dL_dpsi1, dL_dpsi2, self.variance, self.lengthscale, Z, variational_posterior)
|
||||
else:
|
||||
# dL_dvar, dL_dlengscale, dL_dZ, dL_dgamma, dL_dmu, dL_dS = ssrbf_psi_comp.psiDerivativecomputations(dL_dpsi0, dL_dpsi1, dL_dpsi2, self.variance, self.lengthscale, Z, variational_posterior)
|
||||
dL_dvar, dL_dlengscale, _, _, _, _ = ssrbf_psi_comp.psiDerivativecomputations(dL_dpsi0, dL_dpsi1, dL_dpsi2, self.variance, self.lengthscale, Z, variational_posterior)
|
||||
self.variance.gradient = dL_dvar
|
||||
self.lengthscale.gradient = dL_dlengscale
|
||||
|
||||
_, _dpsi1_dvariance, _, _, _, _, _dpsi1_dlengthscale = ssrbf_psi_comp._psi1computations(self.variance, self.lengthscale, Z, variational_posterior.mean, variational_posterior.variance, variational_posterior.binary_prob)
|
||||
_, _dpsi2_dvariance, _, _, _, _, _dpsi2_dlengthscale = ssrbf_psi_comp._psi2computations(self.variance, self.lengthscale, Z, variational_posterior.mean, variational_posterior.variance, variational_posterior.binary_prob)
|
||||
|
||||
#contributions from psi0:
|
||||
self.variance.gradient = np.sum(dL_dpsi0)
|
||||
|
||||
#from psi1
|
||||
self.variance.gradient += np.sum(dL_dpsi1 * _dpsi1_dvariance)
|
||||
if self.ARD:
|
||||
self.lengthscale.gradient = (dL_dpsi1[:,:,None]*_dpsi1_dlengthscale).reshape(-1,self.input_dim).sum(axis=0)
|
||||
else:
|
||||
self.lengthscale.gradient = (dL_dpsi1[:,:,None]*_dpsi1_dlengthscale).sum()
|
||||
|
||||
#from psi2
|
||||
self.variance.gradient += (dL_dpsi2 * _dpsi2_dvariance).sum()
|
||||
if self.ARD:
|
||||
self.lengthscale.gradient += (dL_dpsi2[:,:,:,None] * _dpsi2_dlengthscale).reshape(-1,self.input_dim).sum(axis=0)
|
||||
else:
|
||||
self.lengthscale.gradient += (dL_dpsi2[:,:,:,None] * _dpsi2_dlengthscale).sum()
|
||||
# _, _dpsi1_dvariance, _, _, _, _, _dpsi1_dlengthscale = ssrbf_psi_comp._psi1computations(self.variance, self.lengthscale, Z, variational_posterior.mean, variational_posterior.variance, variational_posterior.binary_prob)
|
||||
# _, _dpsi2_dvariance, _, _, _, _, _dpsi2_dlengthscale = ssrbf_psi_comp._psi2computations(self.variance, self.lengthscale, Z, variational_posterior.mean, variational_posterior.variance, variational_posterior.binary_prob)
|
||||
#
|
||||
# #contributions from psi0:
|
||||
# self.variance.gradient = np.sum(dL_dpsi0)
|
||||
#
|
||||
# #from psi1
|
||||
# self.variance.gradient += np.sum(dL_dpsi1 * _dpsi1_dvariance)
|
||||
# if self.ARD:
|
||||
# self.lengthscale.gradient = (dL_dpsi1[:,:,None]*_dpsi1_dlengthscale).reshape(-1,self.input_dim).sum(axis=0)
|
||||
# else:
|
||||
# self.lengthscale.gradient = (dL_dpsi1[:,:,None]*_dpsi1_dlengthscale).sum()
|
||||
#
|
||||
# #from psi2
|
||||
# self.variance.gradient += (dL_dpsi2 * _dpsi2_dvariance).sum()
|
||||
# if self.ARD:
|
||||
# self.lengthscale.gradient += (dL_dpsi2[:,:,:,None] * _dpsi2_dlengthscale).reshape(-1,self.input_dim).sum(axis=0)
|
||||
# else:
|
||||
# self.lengthscale.gradient += (dL_dpsi2[:,:,:,None] * _dpsi2_dlengthscale).sum()
|
||||
|
||||
elif isinstance(variational_posterior, variational.NormalPosterior):
|
||||
l2 = self.lengthscale**2
|
||||
|
|
@ -126,22 +132,25 @@ class RBF(Stationary):
|
|||
else:
|
||||
raise ValueError, "unknown distriubtion received for psi-statistics"
|
||||
|
||||
def gradients_Z_expectations(self, dL_dpsi1, dL_dpsi2, Z, variational_posterior):
|
||||
def gradients_Z_expectations(self, dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, variational_posterior):
|
||||
# Spike-and-Slab GPLVM
|
||||
if isinstance(variational_posterior, variational.SpikeAndSlabPosterior):
|
||||
if self.useGPU:
|
||||
return self.psicomp.gradients_Z_expectations(dL_dpsi1, dL_dpsi2, self.variance, self.lengthscale, Z, variational_posterior)
|
||||
else:
|
||||
_, _, _, _, _, _dpsi1_dZ, _ = ssrbf_psi_comp._psi1computations(self.variance, self.lengthscale, Z, variational_posterior.mean, variational_posterior.variance, variational_posterior.binary_prob)
|
||||
_, _, _, _, _, _dpsi2_dZ, _ = ssrbf_psi_comp._psi2computations(self.variance, self.lengthscale, Z, variational_posterior.mean, variational_posterior.variance, variational_posterior.binary_prob)
|
||||
|
||||
#psi1
|
||||
grad = (dL_dpsi1[:, :, None] * _dpsi1_dZ).sum(axis=0)
|
||||
|
||||
#psi2
|
||||
grad += (dL_dpsi2[:, :, :, None] * _dpsi2_dZ).sum(axis=0).sum(axis=1)
|
||||
|
||||
return grad
|
||||
_, _, dL_dZ, _, _, _ = ssrbf_psi_comp.psiDerivativecomputations(dL_dpsi0, dL_dpsi1, dL_dpsi2, self.variance, self.lengthscale, Z, variational_posterior)
|
||||
return dL_dZ
|
||||
|
||||
# _, _, _, _, _, _dpsi1_dZ, _ = ssrbf_psi_comp._psi1computations(self.variance, self.lengthscale, Z, variational_posterior.mean, variational_posterior.variance, variational_posterior.binary_prob)
|
||||
# _, _, _, _, _, _dpsi2_dZ, _ = ssrbf_psi_comp._psi2computations(self.variance, self.lengthscale, Z, variational_posterior.mean, variational_posterior.variance, variational_posterior.binary_prob)
|
||||
#
|
||||
# #psi1
|
||||
# grad = (dL_dpsi1[:, :, None] * _dpsi1_dZ).sum(axis=0)
|
||||
#
|
||||
# #psi2
|
||||
# grad += (dL_dpsi2[:, :, :, None] * _dpsi2_dZ).sum(axis=0).sum(axis=1)
|
||||
#
|
||||
# return grad
|
||||
|
||||
elif isinstance(variational_posterior, variational.NormalPosterior):
|
||||
l2 = self.lengthscale **2
|
||||
|
|
@ -167,26 +176,29 @@ class RBF(Stationary):
|
|||
if isinstance(variational_posterior, variational.SpikeAndSlabPosterior):
|
||||
if self.useGPU:
|
||||
return self.psicomp.gradients_qX_expectations(dL_dpsi1, dL_dpsi2, self.variance, self.lengthscale, Z, variational_posterior)
|
||||
else:
|
||||
ndata = variational_posterior.mean.shape[0]
|
||||
|
||||
_, _, _dpsi1_dgamma, _dpsi1_dmu, _dpsi1_dS, _, _ = ssrbf_psi_comp._psi1computations(self.variance, self.lengthscale, Z, variational_posterior.mean, variational_posterior.variance, variational_posterior.binary_prob)
|
||||
_, _, _dpsi2_dgamma, _dpsi2_dmu, _dpsi2_dS, _, _ = ssrbf_psi_comp._psi2computations(self.variance, self.lengthscale, Z, variational_posterior.mean, variational_posterior.variance, variational_posterior.binary_prob)
|
||||
|
||||
#psi1
|
||||
grad_mu = (dL_dpsi1[:, :, None] * _dpsi1_dmu).sum(axis=1)
|
||||
grad_S = (dL_dpsi1[:, :, None] * _dpsi1_dS).sum(axis=1)
|
||||
grad_gamma = (dL_dpsi1[:,:,None] * _dpsi1_dgamma).sum(axis=1)
|
||||
|
||||
#psi2
|
||||
grad_mu += (dL_dpsi2[:, :, :, None] * _dpsi2_dmu).reshape(ndata,-1,self.input_dim).sum(axis=1)
|
||||
grad_S += (dL_dpsi2[:, :, :, None] * _dpsi2_dS).reshape(ndata,-1,self.input_dim).sum(axis=1)
|
||||
grad_gamma += (dL_dpsi2[:,:,:, None] * _dpsi2_dgamma).reshape(ndata,-1,self.input_dim).sum(axis=1)
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if self.group_spike_prob:
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grad_gamma[:] = grad_gamma.mean(axis=0)
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return grad_mu, grad_S, grad_gamma
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else:
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_, _, _, dL_dmu, dL_dS, dL_dgamma = ssrbf_psi_comp.psiDerivativecomputations(dL_dpsi0, dL_dpsi1, dL_dpsi2, self.variance, self.lengthscale, Z, variational_posterior)
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return dL_dmu, dL_dS, dL_dgamma
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# ndata = variational_posterior.mean.shape[0]
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#
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# _, _, _dpsi1_dgamma, _dpsi1_dmu, _dpsi1_dS, _, _ = ssrbf_psi_comp._psi1computations(self.variance, self.lengthscale, Z, variational_posterior.mean, variational_posterior.variance, variational_posterior.binary_prob)
|
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# _, _, _dpsi2_dgamma, _dpsi2_dmu, _dpsi2_dS, _, _ = ssrbf_psi_comp._psi2computations(self.variance, self.lengthscale, Z, variational_posterior.mean, variational_posterior.variance, variational_posterior.binary_prob)
|
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#
|
||||
# #psi1
|
||||
# grad_mu = (dL_dpsi1[:, :, None] * _dpsi1_dmu).sum(axis=1)
|
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# grad_S = (dL_dpsi1[:, :, None] * _dpsi1_dS).sum(axis=1)
|
||||
# grad_gamma = (dL_dpsi1[:,:,None] * _dpsi1_dgamma).sum(axis=1)
|
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#
|
||||
# #psi2
|
||||
# grad_mu += (dL_dpsi2[:, :, :, None] * _dpsi2_dmu).reshape(ndata,-1,self.input_dim).sum(axis=1)
|
||||
# grad_S += (dL_dpsi2[:, :, :, None] * _dpsi2_dS).reshape(ndata,-1,self.input_dim).sum(axis=1)
|
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# grad_gamma += (dL_dpsi2[:,:,:, None] * _dpsi2_dgamma).reshape(ndata,-1,self.input_dim).sum(axis=1)
|
||||
#
|
||||
# if self.group_spike_prob:
|
||||
# grad_gamma[:] = grad_gamma.mean(axis=0)
|
||||
#
|
||||
# return grad_mu, grad_S, grad_gamma
|
||||
|
||||
elif isinstance(variational_posterior, variational.NormalPosterior):
|
||||
|
||||
|
|
|
|||
|
|
@ -25,7 +25,7 @@ class Static(Kern):
|
|||
def gradients_X_diag(self, dL_dKdiag, X):
|
||||
return np.zeros(X.shape)
|
||||
|
||||
def gradients_Z_expectations(self, dL_dpsi1, dL_dpsi2, Z, variational_posterior):
|
||||
def gradients_Z_expectations(self, dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, variational_posterior):
|
||||
return np.zeros(Z.shape)
|
||||
|
||||
def gradients_qX_expectations(self, dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, variational_posterior):
|
||||
|
|
|
|||
|
|
@ -11,7 +11,7 @@ from ..likelihoods import Gaussian
|
|||
from ..inference.optimization import SCG
|
||||
from ..util import linalg
|
||||
from ..core.parameterization.variational import SpikeAndSlabPrior, SpikeAndSlabPosterior
|
||||
from ..inference.latent_function_inference.var_dtc_parallel import update_gradients
|
||||
from ..inference.latent_function_inference.var_dtc_parallel import update_gradients, VarDTC_minibatch
|
||||
from ..inference.latent_function_inference.var_dtc_gpu import VarDTC_GPU
|
||||
|
||||
|
||||
|
|
@ -41,7 +41,7 @@ class SSGPLVM(SparseGP):
|
|||
if X_variance is None: # The variance of the variational approximation (S)
|
||||
X_variance = np.random.uniform(0,.1,X.shape)
|
||||
|
||||
gamma = np.empty_like(X) # The posterior probabilities of the binary variable in the variational approximation
|
||||
gamma = np.empty_like(X, order='F') # The posterior probabilities of the binary variable in the variational approximation
|
||||
gamma[:] = 0.5 + 0.01 * np.random.randn(X.shape[0], input_dim)
|
||||
|
||||
if group_spike:
|
||||
|
|
@ -60,12 +60,15 @@ class SSGPLVM(SparseGP):
|
|||
pi = np.empty((input_dim))
|
||||
pi[:] = 0.5
|
||||
self.variational_prior = SpikeAndSlabPrior(pi=pi) # the prior probability of the latent binary variable b
|
||||
|
||||
X = np.asfortranarray(X)
|
||||
X_variance = np.asfortranarray(X_variance)
|
||||
gamma = np.asfortranarray(gamma)
|
||||
X = SpikeAndSlabPosterior(X, X_variance, gamma)
|
||||
|
||||
if group_spike:
|
||||
kernel.group_spike_prob = True
|
||||
self.variational_prior.group_spike_prob = True
|
||||
|
||||
|
||||
SparseGP.__init__(self, X, Y, Z, kernel, likelihood, inference_method, name, **kwargs)
|
||||
self.add_parameter(self.X, index=0)
|
||||
|
|
@ -76,7 +79,7 @@ class SSGPLVM(SparseGP):
|
|||
X.mean.gradient, X.variance.gradient, X.binary_prob.gradient = X_grad
|
||||
|
||||
def parameters_changed(self):
|
||||
if isinstance(self.inference_method, VarDTC_GPU):
|
||||
if isinstance(self.inference_method, VarDTC_GPU) or isinstance(self.inference_method, VarDTC_minibatch):
|
||||
update_gradients(self)
|
||||
return
|
||||
|
||||
|
|
|
|||
|
|
@ -8,7 +8,7 @@ import numpy as np
|
|||
from GPy.util.pca import pca
|
||||
|
||||
def initialize_latent(init, input_dim, Y):
|
||||
Xr = np.random.randn(Y.shape[0], input_dim)
|
||||
Xr = np.asfortranarray(np.random.randn(Y.shape[0], input_dim))
|
||||
if init == 'PCA':
|
||||
p = pca(Y)
|
||||
PC = p.project(Y, min(input_dim, Y.shape[1]))
|
||||
|
|
@ -20,4 +20,4 @@ def initialize_latent(init, input_dim, Y):
|
|||
Xr -= Xr.mean(0)
|
||||
Xr /= Xr.var(0)
|
||||
|
||||
return Xr, var/var.max()
|
||||
return Xr, var/var.max()
|
||||
|
|
|
|||
|
|
@ -123,7 +123,7 @@ def dtrtrs(A, B, lower=1, trans=0, unitdiag=0):
|
|||
:returns:
|
||||
|
||||
"""
|
||||
A = force_F_ordered(A)
|
||||
A = np.asfortranarray(A)
|
||||
#Note: B does not seem to need to be F ordered!
|
||||
return lapack.dtrtrs(A, B, lower=lower, trans=trans, unitdiag=unitdiag)
|
||||
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue