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SVI now implemented without natural natural gradients or batches

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This commit is contained in:
Alan Saul 2014-12-22 13:35:56 +00:00
parent b642360ede
commit a8b0d60c3e
4 changed files with 16 additions and 17 deletions
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6
GPy/core/svgp.py
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@ -33,9 +33,9 @@ class SVGP(SparseGP):
#?? self.set_data(X, Y) #?? self.set_data(X, Y)
self.m = Param('q_u_mean', np.zeros(self.num_inducing)) self.m = Param('q_u_mean', np.zeros((self.num_inducing, Y.shape[1])))
chol = choleskies.triang_to_flat(np.eye(self.num_inducing)[:,:,None]) chol = choleskies.triang_to_flat(np.tile(np.eye(self.num_inducing)[:,:,None], (1,1,Y.shape[1])))
self.chol = Param('q_u_chol', chol.flatten()) self.chol = Param('q_u_chol', chol)
self.link_parameter(self.chol) self.link_parameter(self.chol)
self.link_parameter(self.m) self.link_parameter(self.m)

8
GPy/inference/latent_function_inference/posterior.py
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@ -158,9 +158,11 @@ class Posterior(object):
#self._woodbury_inv, _ = dpotrs(self.woodbury_chol, np.eye(self.woodbury_chol.shape[0]), lower=1) #self._woodbury_inv, _ = dpotrs(self.woodbury_chol, np.eye(self.woodbury_chol.shape[0]), lower=1)
symmetrify(self._woodbury_inv) symmetrify(self._woodbury_inv)
elif self._covariance is not None: elif self._covariance is not None:
B = self._K - self._covariance B = np.atleast_3d(self._K) - np.atleast_3d(self._covariance)
tmp, _ = dpotrs(self.K_chol, B) self._woodbury_inv = np.empty_like(B)
self._woodbury_inv, _ = dpotrs(self.K_chol, tmp.T) for i in xrange(B.shape[-1]):
tmp, _ = dpotrs(self.K_chol, B[:,:,i])
self._woodbury_inv[:,:,i], _ = dpotrs(self.K_chol, tmp.T)
return self._woodbury_inv return self._woodbury_inv
@property @property

13
GPy/inference/latent_function_inference/svgp.py
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@ -37,7 +37,7 @@ class SVGP(LatentFunctionInference):
#compute the KL term #compute the KL term
Kmmim = np.dot(Kmmi, q_u_mean) Kmmim = np.dot(Kmmi, q_u_mean)
#KL = -0.5*logdetS -0.5*num_inducing + 0.5*logdetKmm + 0.5*np.sum(Kmmi*S) + 0.5*q_u_mean.dot(Kmmim) #KL = -0.5*logdetS -0.5*num_inducing + 0.5*logdetKmm + 0.5*np.sum(Kmmi*S) + 0.5*q_u_mean.dot(Kmmim)
KLs = -0.5*logdetS -0.5*self.num_inducing + 0.5*logdetKmm + 0.5*np.einsum('ij,ijk->k', Kmmi, S) + 0.5*np.sum(self.q_u_mean*Kmmim,0) KLs = -0.5*logdetS -0.5*num_inducing + 0.5*logdetKmm + 0.5*np.einsum('ij,ijk->k', Kmmi, S) + 0.5*np.sum(q_u_mean*Kmmim,0)
KL = KLs.sum() KL = KLs.sum()
dKL_dm = Kmmim dKL_dm = Kmmim
#dKL_dS = 0.5*(Kmmi - Si) #dKL_dS = 0.5*(Kmmi - Si)
@ -58,13 +58,13 @@ class SVGP(LatentFunctionInference):
#derivatives of expected likelihood #derivatives of expected likelihood
Adv = A.T[:,:,None]*dF_dv[None,:,:] # As if dF_Dv is diagonal Adv = A.T[:,:,None]*dF_dv[None,:,:] # As if dF_Dv is diagonal
Admu = A.T.dot(dF_dmu) Admu = A.T.dot(dF_dmu)
#AdvA = np.einsum('ijk,jl->ilk', Adv, A) #AdvA = np.einsum('ijk,jl->ilk', Adv, A)
#AdvA = np.dot(A.T, Adv).swapaxes(0,1) #AdvA = np.dot(A.T, Adv).swapaxes(0,1)
AdvA = np.dstack([np.dot(A.T, Adv[:,:,i].T) for i in range(self.num_classes)]) AdvA = np.dstack([np.dot(A.T, Adv[:,:,i].T) for i in range(num_outputs)])
tmp = np.einsum('ijk,jlk->il', AdvA, S).dot(Kmmi) tmp = np.einsum('ijk,jlk->il', AdvA, S).dot(Kmmi)
dF_dKmm = -Admu.dot(Kmmim.T) + AdvA.sum(-1) - tmp - tmp.T dF_dKmm = -Admu.dot(Kmmim.T) + AdvA.sum(-1) - tmp - tmp.T
dF_dKmm = 0.5*(dF_dKmm + dF_dKmm.T) # necessary? GPy bug? dF_dKmm = 0.5*(dF_dKmm + dF_dKmm.T) # necessary? GPy bug?
tmp = 2.*(np.einsum('ij,jlk->ilk', Kmmi,S) - np.eye(self.num_inducing)[:,:,None]) tmp = 2.*(np.einsum('ij,jlk->ilk', Kmmi,S) - np.eye(num_inducing)[:,:,None])
dF_dKmn = np.einsum('ijk,jlk->il', tmp, Adv) + Kmmim.dot(dF_dmu.T) dF_dKmn = np.einsum('ijk,jlk->il', tmp, Adv) + Kmmim.dot(dF_dmu.T)
dF_dm = Admu dF_dm = Admu
dF_dS = AdvA dF_dS = AdvA
@ -74,10 +74,7 @@ class SVGP(LatentFunctionInference):
log_marginal = F.sum() - KL log_marginal = F.sum() - KL
dL_dm, dL_dS, dL_dKmm, dL_dKmn = dF_dm - dKL_dm, dF_dS- dKL_dS, dF_dKmm- dKL_dKmm, dF_dKmn dL_dm, dL_dS, dL_dKmm, dL_dKmn = dF_dm - dKL_dm, dF_dS- dKL_dS, dF_dKmm- dKL_dKmm, dF_dKmn
dL_dchol = 2.*np.dot(dL_dS, L) dL_dchol = np.dstack([2.*np.dot(dL_dS[:,:,i], L[:,:,i]) for i in range(num_outputs)])
dL_dchol = choleskies.triang_to_flat(dL_dchol) dL_dchol = choleskies.triang_to_flat(dL_dchol)
return Posterior(mean=q_u_mean, cov=S, K=Kmm), log_marginal, {'dL_dKmm':dL_dKmm, 'dL_dKmn':dL_dKmn, 'dL_dKdiag': dF_dv, 'dL_dm':dL_dm, 'dL_dchol':dL_dchol, 'dL_dthetaL':dF_dthetaL} return Posterior(mean=q_u_mean, cov=S, K=Kmm), log_marginal, {'dL_dKmm':dL_dKmm, 'dL_dKmn':dL_dKmn, 'dL_dKdiag': dF_dv, 'dL_dm':dL_dm, 'dL_dchol':dL_dchol, 'dL_dthetaL':dF_dthetaL}

6
GPy/likelihoods/gaussian.py
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@ -318,9 +318,9 @@ class Gaussian(Likelihood):
def variational_expectations(self, Y, m, v, gh_points=None): def variational_expectations(self, Y, m, v, gh_points=None):
lik_var = float(self.variance) lik_var = float(self.variance)
F = -0.5*np.log(2*np.pi) -0.5*np.log(lik_var) - 0.5*(np.square(Y) + np.square(m) + v - 2*m.dot(Y))/lik_var F = -0.5*np.log(2*np.pi) -0.5*np.log(lik_var) - 0.5*(np.square(Y) + np.square(m) + v - 2*m*Y)/lik_var
dF_dmu = (Y - m)/lik_var dF_dmu = (Y - m)/lik_var
dF_dv = -0.5/lik_var dF_dv = np.ones_like(v)*(-0.5/lik_var)
dF_dlik_var = -0.5/lik_var + 0.5(np.square(Y) + np.square(m) + v - 2*m.dot(Y))/(lik_var**2) dF_dlik_var = np.sum(-0.5/lik_var + 0.5*(np.square(Y) + np.square(m) + v - 2*m*Y)/(lik_var**2))
dF_dtheta = [dF_dlik_var] dF_dtheta = [dF_dlik_var]
return F, dF_dmu, dF_dv, dF_dtheta return F, dF_dmu, dF_dv, dF_dtheta