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https://github.com/SheffieldML/GPy.git
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[parallel vardtc] minor adjustments to work with current implementation of
psi stats
This commit is contained in:
mzwiessele
parent
c62dd85418
commit
1e006f63b5
1 changed files with 84 additions and 67 deletions
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@ -22,21 +22,21 @@ class VarDTC_minibatch(LatentFunctionInference):
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"""
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const_jitter = 1e-6
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def __init__(self, batchsize, limit=1):
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self.batchsize = batchsize
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# Cache functions
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from ...util.caching import Cacher
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self.get_trYYT = Cacher(self._get_trYYT, limit)
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self.get_YYTfactor = Cacher(self._get_YYTfactor, limit)
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self.midRes = {}
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self.batch_pos = 0 # the starting position of the current mini-batch
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def set_limit(self, limit):
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self.get_trYYT.limit = limit
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self.get_YYTfactor.limit = limit
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def _get_trYYT(self, Y):
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return param_to_array(np.sum(np.square(Y)))
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@ -51,23 +51,23 @@ class VarDTC_minibatch(LatentFunctionInference):
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return param_to_array(Y)
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else:
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return jitchol(tdot(Y))
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def inference_likelihood(self, kern, X, Z, likelihood, Y):
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"""
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The first phase of inference:
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Compute: log-likelihood, dL_dKmm
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Cached intermediate results: Kmm, KmmInv,
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"""
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num_inducing = Z.shape[0]
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num_inducing = Z.shape[0]
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num_data, output_dim = Y.shape
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if isinstance(X, VariationalPosterior):
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uncertain_inputs = True
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else:
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uncertain_inputs = False
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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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@ -77,19 +77,19 @@ class VarDTC_minibatch(LatentFunctionInference):
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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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YRY_full = 0
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for n_start in xrange(0,num_data,self.batchsize):
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n_end = min(self.batchsize+n_start, num_data)
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Y_slice = YYT_factor[n_start:n_end]
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X_slice = X[n_start:n_end]
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if uncertain_inputs:
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psi0 = kern.psi0(Z, X_slice)
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psi1 = kern.psi1(Z, X_slice)
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@ -98,7 +98,7 @@ class VarDTC_minibatch(LatentFunctionInference):
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psi0 = kern.Kdiag(X_slice)
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psi1 = kern.K(X_slice, Z)
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psi2 = None
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if het_noise:
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beta_slice = beta[n_start:n_end]
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psi0_full += (beta_slice*psi0).sum()
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@ -106,33 +106,33 @@ 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 += beta_slice*psi2
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else:
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psi2_full += psi2
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psi2_full += psi2.sum(0)
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else:
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if het_noise:
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psi2_full += beta_slice*np.outer(psi1,psi1)
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else:
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psi2_full += np.outer(psi1,psi1)
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psi2_full += np.einsum('nm,jk->mk',psi1,psi1)
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if not het_noise:
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psi0_full *= beta
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psi1Y_full *= beta
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psi2_full *= beta
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YRY_full = trYYT*beta
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#======================================================================
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# Compute Common Components
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#======================================================================
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self.psi1Y = psi1Y_full
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Kmm = kern.K(Z).copy()
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diag.add(Kmm, self.const_jitter)
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Lm = jitchol(Kmm)
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Lambda = Kmm+psi2_full
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LL = jitchol(Lambda)
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b,_ = dtrtrs(LL, psi1Y_full.T)
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@ -140,18 +140,18 @@ class VarDTC_minibatch(LatentFunctionInference):
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v,_ = dtrtrs(LL.T,b,lower=False)
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vvt = np.einsum('md,od->mo',v,v)
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LmInvPsi2LmInvT = backsub_both_sides(Lm,psi2_full,transpose='right')
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Psi2LLInvT = dtrtrs(LL,psi2_full)[0].T
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LmInvPsi2LLInvT= dtrtrs(Lm,Psi2LLInvT)[0]
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KmmInvPsi2LLInvT = dtrtrs(Lm,LmInvPsi2LLInvT,trans=True)[0]
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KmmInvPsi2P = dtrtrs(LL,KmmInvPsi2LLInvT.T, trans=True)[0].T
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dL_dpsi2R = (output_dim*KmmInvPsi2P - vvt)/2. # dL_dpsi2 with R inside psi2
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# Cache intermediate results
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self.midRes['dL_dpsi2R'] = dL_dpsi2R
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self.midRes['v'] = v
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#======================================================================
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# Compute log-likelihood
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#======================================================================
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@ -159,30 +159,33 @@ class VarDTC_minibatch(LatentFunctionInference):
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logL_R = -np.log(beta).sum()
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else:
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logL_R = -num_data*np.log(beta)
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logL = -(output_dim*(num_data*log_2_pi+logL_R+psi0_full-np.trace(LmInvPsi2LmInvT))+YRY_full-bbt)/2.-output_dim*(-np.log(np.diag(Lm)).sum()+np.log(np.diag(LL)).sum())
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logL = (
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-(output_dim*(num_data*log_2_pi+logL_R+psi0_full-np.trace(LmInvPsi2LmInvT))+YRY_full-bbt)/2.
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-output_dim*(-np.log(np.diag(Lm)).sum()+np.log(np.diag(LL)).sum())
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)
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#======================================================================
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# Compute dL_dKmm
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#======================================================================
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dL_dKmm = -(output_dim*np.einsum('md,od->mo',KmmInvPsi2LLInvT,KmmInvPsi2LLInvT) + vvt)/2.
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#======================================================================
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# Compute the Posterior distribution of inducing points p(u|Y)
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#======================================================================
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# phi_u_mean = np.dot(Kmm,v)
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# LLInvKmm,_ = dtrtrs(LL,Kmm)
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# # phi_u_var = np.einsum('ma,mb->ab',LLInvKmm,LLInvKmm)
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# phi_u_var = Kmm - np.dot(LLInvKmm.T,LLInvKmm)
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post = Posterior(woodbury_inv=KmmInvPsi2P, woodbury_vector=v, K=Kmm, mean=None, cov=None, K_chol=Lm)
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return logL, dL_dKmm, post
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def inference_minibatch(self, kern, X, Z, likelihood, Y):
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"""
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The second phase of inference: Computing the derivatives over a minibatch of Y
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The second phase of inference: Computing the derivatives over a minibatch of Y
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Compute: dL_dpsi0, dL_dpsi1, dL_dpsi2, dL_dthetaL
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return a flag showing whether it reached the end of Y (isEnd)
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"""
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@ -193,14 +196,14 @@ class VarDTC_minibatch(LatentFunctionInference):
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uncertain_inputs = True
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else:
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uncertain_inputs = False
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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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# 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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n_start = self.batch_pos
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n_end = min(self.batchsize+n_start, num_data)
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if n_end==num_data:
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@ -209,11 +212,11 @@ class VarDTC_minibatch(LatentFunctionInference):
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else:
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isEnd = False
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self.batch_pos = n_end
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num_slice = n_end-n_start
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Y_slice = YYT_factor[n_start:n_end]
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X_slice = X[n_start:n_end]
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if uncertain_inputs:
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psi0 = kern.psi0(Z, X_slice)
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psi1 = kern.psi1(Z, X_slice)
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@ -222,51 +225,51 @@ class VarDTC_minibatch(LatentFunctionInference):
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psi0 = kern.Kdiag(X_slice)
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psi1 = kern.K(X_slice, Z)
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psi2 = None
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if het_noise:
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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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#======================================================================
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# Load Intermediate Results
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#======================================================================
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dL_dpsi2R = self.midRes['dL_dpsi2R']
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v = self.midRes['v']
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#======================================================================
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# Compute dL_dpsi
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#======================================================================
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dL_dpsi0 = -0.5 * output_dim * (beta * np.ones((n_end-n_start,)))
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dL_dpsi1 = np.dot(betaY,v.T)
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if uncertain_inputs:
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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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#======================================================================
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# Compute dL_dthetaL
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#======================================================================
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if het_noise:
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if uncertain_inputs:
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psiR = np.einsum('mo,nmo->n',dL_dpsi2R,psi2)
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psiR = np.einsum('mo,nmo->',dL_dpsi2R,psi2)
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else:
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psiR = np.einsum('nm,no,mo->n',psi1,psi1,dL_dpsi2R)
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psiR = np.einsum('nm,no,mo->',psi1,psi1,dL_dpsi2R)
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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,mo->',dL_dpsi2R,psi2)
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psiR = np.einsum('mo,nmo->',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() + 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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@ -278,15 +281,15 @@ class VarDTC_minibatch(LatentFunctionInference):
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grad_dict = {'dL_dKdiag':dL_dpsi0,
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'dL_dKnm':dL_dpsi1,
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'dL_dthetaL':dL_dthetaL}
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return isEnd, (n_start,n_end), grad_dict
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def update_gradients(model):
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model._log_marginal_likelihood, dL_dKmm, model.posterior = model.inference_method.inference_likelihood(model.kern, model.X, model.Z, model.likelihood, model.Y)
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het_noise = model.likelihood.variance.size > 1
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if het_noise:
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dL_dthetaL = np.empty((model.Y.shape[0],))
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else:
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@ -295,40 +298,54 @@ def update_gradients(model):
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#gradients w.r.t. kernel
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model.kern.update_gradients_full(dL_dKmm, model.Z, None)
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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.gradients_X(dL_dKmm, model.Z)
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isEnd = False
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while not isEnd:
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isEnd, n_range, grad_dict = model.inference_method.inference_minibatch(model.kern, model.X, model.Z, model.likelihood, model.Y)
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if isinstance(model.X, VariationalPosterior):
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X_slice = model.X[n_range[0]:n_range[1]]
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dL_dpsi1 = grad_dict['dL_dpsi1']#[None, :]
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dL_dpsi2 = grad_dict['dL_dpsi2'][None, :, :]
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#gradients w.r.t. kernel
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model.kern.update_gradients_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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model.kern.update_gradients_expectations(variational_posterior=X_slice,Z=model.Z,dL_dpsi0=grad_dict['dL_dpsi0'],dL_dpsi1=dL_dpsi1,dL_dpsi2=dL_dpsi2)
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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.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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dL_dpsi0=grad_dict['dL_dpsi0'],
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dL_dpsi1=dL_dpsi1,
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dL_dpsi2=dL_dpsi2,
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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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model.set_X_gradients(X_slice, X_grad)
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X_grad = model.kern.gradients_qX_expectations(
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variational_posterior=X_slice,
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Z=model.Z,
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dL_dpsi0=grad_dict['dL_dpsi0'],
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dL_dpsi1=dL_dpsi1,
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dL_dpsi2=dL_dpsi2)
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model.X.mean[n_range[0]:n_range[1]].gradient = X_grad[0]
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model.X.variance[n_range[0]:n_range[1]].gradient = X_grad[1]
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if het_noise:
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dL_dthetaL[n_range[0]:n_range[1]] = grad_dict['dL_dthetaL']
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else:
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dL_dthetaL += grad_dict['dL_dthetaL']
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#import ipdb;ipdb.set_trace()
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model.grad_dict = grad_dict
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if isinstance(model.X, VariationalPosterior):
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# Update Log-likelihood
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model._log_marginal_likelihood -= model.variational_prior.KL_divergence(model.X)
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# update for the KL divergence
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model.variational_prior.update_gradients_KL(model.X)
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# Set the gradients w.r.t. kernel
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model.kern.gradient = kern_grad
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# Update Log-likelihood
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model._log_marginal_likelihood -= model.variational_prior.KL_divergence(model.X)
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# update for the KL divergence
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model.variational_prior.update_gradients_KL(model.X)
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# dL_dthetaL
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model.likelihood.update_gradients(dL_dthetaL)
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