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Merge branch 'params' of github.com:SheffieldML/GPy into params

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James Hensman 2014-02-21 17:32:48 +00:00
commit 205fe3cbd0
5 changed files with 100 additions and 111 deletions
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1
GPy/core/sparse_gp.py
View file

@ -58,6 +58,7 @@ class SparseGP(GP):
def parameters_changed(self):
self.posterior, self._log_marginal_likelihood, self.grad_dict = self.inference_method.inference(self.kern, self.X, self.X_variance, self.Z, self.likelihood, self.Y)
self.likelihood.update_gradients(self.grad_dict.pop('partial_for_likelihood'))
if self.has_uncertain_inputs():
self.kern.update_gradients_variational(mu=self.X, S=self.X_variance, Z=self.Z, **self.grad_dict)
self.Z.gradient = self.kern.gradients_Z_variational(mu=self.X, S=self.X_variance, Z=self.Z, **self.grad_dict)

194
GPy/inference/latent_function_inference/var_dtc.py
View file

@ -60,18 +60,88 @@ class VarDTC(object):
trYYT = self.get_trYYT(Y)
# do the inference:
dL_dKmm, dL_dpsi0, dL_dpsi1, dL_dpsi2, Cpsi1Vf, \
psi1, Lm, LB, log_marginal, Kmm, partial_for_likelihood = _do_inference_on(
kern, X, X_variance, Z, likelihood,
uncertain_inputs, output_dim,
beta, VVT_factor, trYYT)
het_noise = beta.size < 1
num_inducing = Z.shape[0]
num_data = X.shape[0]
# kernel computations, using BGPLVM notation
Kmm = kern.K(Z)
psi0, psi1, psi2 = _compute_psi(kern, X, X_variance, Z, uncertain_inputs)
Lm = jitchol(Kmm)
# The rather complex computations of A
if uncertain_inputs:
if het_noise:
psi2_beta = psi2 * (beta.flatten().reshape(num_data, 1, 1)).sum(0)
else:
psi2_beta = psi2.sum(0) * beta
#if 0:
# evals, evecs = linalg.eigh(psi2_beta)
# clipped_evals = np.clip(evals, 0., 1e6) # TODO: make clipping configurable
# if not np.array_equal(evals, clipped_evals):
# pass # print evals
# tmp = evecs * np.sqrt(clipped_evals)
# tmp = tmp.T
# no backsubstitution because of bound explosion on tr(A) if not...
LmInv = dtrtri(Lm)
A = LmInv.dot(psi2_beta.dot(LmInv.T))
else:
if het_noise:
tmp = psi1 * (np.sqrt(beta.reshape(num_data, 1)))
else:
tmp = psi1 * (np.sqrt(beta))
tmp, _ = dtrtrs(Lm, tmp.T, lower=1)
A = tdot(tmp) #print A.sum()
likelihood.update_gradients(partial_for_likelihood)
# factor B
B = np.eye(num_inducing) + A
LB = jitchol(B)
psi1Vf = np.dot(psi1.T, VVT_factor)
# back substutue C into psi1Vf
tmp, _ = dtrtrs(Lm, psi1Vf, lower=1, trans=0)
_LBi_Lmi_psi1Vf, _ = dtrtrs(LB, tmp, lower=1, trans=0)
tmp, _ = dtrtrs(LB, _LBi_Lmi_psi1Vf, lower=1, trans=1)
Cpsi1Vf, _ = dtrtrs(Lm, tmp, lower=1, trans=1)
# data fit and derivative of L w.r.t. Kmm
delit = tdot(_LBi_Lmi_psi1Vf)
data_fit = np.trace(delit)
DBi_plus_BiPBi = backsub_both_sides(LB, output_dim * np.eye(num_inducing) + delit)
delit = -0.5 * DBi_plus_BiPBi
delit += -0.5 * B * output_dim
delit += output_dim * np.eye(num_inducing)
# Compute dL_dKmm
dL_dKmm = backsub_both_sides(Lm, delit)
# derivatives of L w.r.t. psi
dL_dpsi0, dL_dpsi1, dL_dpsi2 = _compute_dL_dpsi(num_inducing, num_data, output_dim, beta, Lm,
VVT_factor, Cpsi1Vf, DBi_plus_BiPBi,
psi1, het_noise, uncertain_inputs)
# log marginal likelihood
log_marginal = _compute_log_marginal_likelihood(likelihood, num_data, output_dim, beta, het_noise,
psi0, A, LB, trYYT, data_fit)
#put the gradients in the right places
partial_for_likelihood = _compute_partial_for_likelihood(likelihood,
het_noise, uncertain_inputs, LB,
_LBi_Lmi_psi1Vf, DBi_plus_BiPBi, Lm, A,
psi0, psi1, beta,
data_fit, num_data, output_dim, trYYT)
#likelihood.update_gradients(partial_for_likelihood)
if uncertain_inputs:
grad_dict = {'dL_dKmm': dL_dKmm, 'dL_dpsi0':dL_dpsi0, 'dL_dpsi1':dL_dpsi1, 'dL_dpsi2':dL_dpsi2}
grad_dict = {'dL_dKmm': dL_dKmm,
'dL_dpsi0':dL_dpsi0,
'dL_dpsi1':dL_dpsi1,
'dL_dpsi2':dL_dpsi2,
'partial_for_likelihood':partial_for_likelihood}
else:
grad_dict = {'dL_dKmm': dL_dKmm, 'dL_dKdiag':dL_dpsi0, 'dL_dKnm':dL_dpsi1}
grad_dict = {'dL_dKmm': dL_dKmm,
'dL_dKdiag':dL_dpsi0,
'dL_dKnm':dL_dpsi1,
'partial_for_likelihood':partial_for_likelihood}
#get sufficient things for posterior prediction
#TODO: do we really want to do this in the loop?
@ -184,9 +254,10 @@ class VarDTCMissingData(object):
LB = jitchol(B)
psi1Vf = psi1.T.dot(VVT_factor)
_LBi_Lmi_psi1Vf, Cpsi1Vf = _compute_psi1Vf(Lm, LB, psi1Vf)
#LB_all[ind, :,:] = LB
tmp, _ = dtrtrs(Lm, psi1Vf, lower=1, trans=0)
_LBi_Lmi_psi1Vf, _ = dtrtrs(LB, tmp, lower=1, trans=0)
tmp, _ = dtrtrs(LB, _LBi_Lmi_psi1Vf, lower=1, trans=1)
Cpsi1Vf, _ = dtrtrs(Lm, tmp, lower=1, trans=1)
# data fit and derivative of L w.r.t. Kmm
delit = tdot(_LBi_Lmi_psi1Vf)
@ -233,16 +304,19 @@ class VarDTCMissingData(object):
from ...util import diag
diag.add(Bi, 1)
woodbury_inv_all[:, :, ind] = backsub_both_sides(Lm, Bi)[:,:,None]
# gradients:
likelihood.update_gradients(partial_for_likelihood)
# gradients:
if uncertain_inputs:
grad_dict = {'dL_dKmm': dL_dKmm, 'dL_dpsi0':dL_dpsi0_all, 'dL_dpsi1':dL_dpsi1_all, 'dL_dpsi2':dL_dpsi2_all}
kern.update_gradients_variational(mu=X, S=X_variance, Z=Z, **grad_dict)
grad_dict = {'dL_dKmm': dL_dKmm,
'dL_dpsi0':dL_dpsi0,
'dL_dpsi1':dL_dpsi1,
'dL_dpsi2':dL_dpsi2,
'partial_for_likelihood':partial_for_likelihood}
else:
grad_dict = {'dL_dKmm': dL_dKmm, 'dL_dKdiag':dL_dpsi0_all, 'dL_dKnm':dL_dpsi1_all}
kern.update_gradients_sparse(X=X, Z=Z, **grad_dict)
grad_dict = {'dL_dKmm': dL_dKmm,
'dL_dKdiag':dL_dpsi0,
'dL_dKnm':dL_dpsi1,
'partial_for_likelihood':partial_for_likelihood}
#get sufficient things for posterior prediction
#TODO: do we really want to do this in the loop?
@ -266,33 +340,6 @@ class VarDTCMissingData(object):
return post, log_marginal, grad_dict
def _compute_A(num_data, uncertain_inputs, beta, het_noise, psi1, psi2, Lm):
# The rather complex computations of A
if uncertain_inputs:
if het_noise:
psi2_beta = psi2 * (beta.flatten().reshape(num_data, 1, 1)).sum(0)
else:
psi2_beta = psi2.sum(0) * beta
#if 0:
# evals, evecs = linalg.eigh(psi2_beta)
# clipped_evals = np.clip(evals, 0., 1e6) # TODO: make clipping configurable
# if not np.array_equal(evals, clipped_evals):
# pass # print evals
# tmp = evecs * np.sqrt(clipped_evals)
# tmp = tmp.T
# no backsubstitution because of bound explosion on tr(A) if not...
LmInv = dtrtri(Lm)
A = LmInv.dot(psi2_beta.dot(LmInv.T))
else:
if het_noise:
tmp = psi1 * (np.sqrt(beta.reshape(num_data, 1)))
else:
tmp = psi1 * (np.sqrt(beta))
tmp, _ = dtrtrs(Lm, tmp.T, lower=1)
A = tdot(tmp) #print A.sum()
return A
def _compute_psi(kern, X, X_variance, Z, uncertain_inputs):
if uncertain_inputs:
psi0 = kern.psi0(Z, X, X_variance)
@ -304,22 +351,6 @@ def _compute_psi(kern, X, X_variance, Z, uncertain_inputs):
psi2 = None
return psi0, psi1, psi2
def _compute_Kmm(kern, X, X_variance, Z, uncertain_inputs):
Kmm = kern.K(Z)
psi0, psi1, psi2 = _compute_psi(kern, X, X_variance, Z, uncertain_inputs)
return Kmm, psi0, psi1, psi2
def _compute_dL_dKmm(num_inducing, output_dim, Lm, B, LB, _LBi_Lmi_psi1Vf):
# Compute dL_dKmm
delit = tdot(_LBi_Lmi_psi1Vf)
data_fit = np.trace(delit)
DBi_plus_BiPBi = backsub_both_sides(LB, output_dim * np.eye(num_inducing) + delit)
delit = -0.5 * DBi_plus_BiPBi
delit += -0.5 * B * output_dim
delit += output_dim * np.eye(num_inducing)
dL_dKmm = backsub_both_sides(Lm, delit)
return DBi_plus_BiPBi, data_fit, dL_dKmm
def _compute_dL_dpsi(num_inducing, num_data, output_dim, beta, Lm, VVT_factor, Cpsi1Vf, DBi_plus_BiPBi, psi1, het_noise, uncertain_inputs):
dL_dpsi0 = -0.5 * output_dim * (beta * np.ones([num_data, 1])).flatten()
dL_dpsi1 = np.dot(VVT_factor, Cpsi1Vf.T)
@ -343,15 +374,6 @@ def _compute_dL_dpsi(num_inducing, num_data, output_dim, beta, Lm, VVT_factor, C
return dL_dpsi0, dL_dpsi1, dL_dpsi2
def _compute_psi1Vf(Lm, LB, psi1Vf):
# back substutue C into psi1Vf
tmp, _ = dtrtrs(Lm, psi1Vf, lower=1, trans=0)
_LBi_Lmi_psi1Vf, _ = dtrtrs(LB, tmp, lower=1, trans=0)
tmp, _ = dtrtrs(LB, _LBi_Lmi_psi1Vf, lower=1, trans=1)
Cpsi1Vf, _ = dtrtrs(Lm, tmp, lower=1, trans=1)
return _LBi_Lmi_psi1Vf, Cpsi1Vf
def _compute_partial_for_likelihood(likelihood, het_noise, uncertain_inputs, LB, _LBi_Lmi_psi1Vf, DBi_plus_BiPBi, Lm, A, psi0, psi1, beta, data_fit, num_data, output_dim, trYYT):
# the partial derivative vector for the likelihood
if likelihood.size == 0:
@ -393,35 +415,3 @@ def _compute_log_marginal_likelihood(likelihood, num_data, output_dim, beta, het
lik_4 = 0.5 * data_fit
log_marginal = lik_1 + lik_2 + lik_3 + lik_4
return log_marginal
def _do_inference_on(kern, X, X_variance, Z, likelihood, uncertain_inputs, output_dim, beta, VVT_factor, trYYT):
het_noise = beta.size < 1
num_inducing = Z.shape[0]
num_data = X.shape[0]
# kernel computations, using BGPLVM notation
Kmm, psi0, psi1, psi2 = _compute_Kmm(kern, X, X_variance, Z, uncertain_inputs)
#factor Kmm # TODO: cache?
Lm = jitchol(Kmm)
A = _compute_A(num_data, uncertain_inputs, beta, het_noise, psi1, psi2, Lm)
# factor B
B = np.eye(num_inducing) + A
LB = jitchol(B)
psi1Vf = np.dot(psi1.T, VVT_factor)
_LBi_Lmi_psi1Vf, Cpsi1Vf = _compute_psi1Vf(Lm, LB, psi1Vf)
# data fit and derivative of L w.r.t. Kmm
DBi_plus_BiPBi, data_fit, dL_dKmm = _compute_dL_dKmm(num_inducing, output_dim,
Lm, B, LB, _LBi_Lmi_psi1Vf)
# derivatives of L w.r.t. psi
dL_dpsi0, dL_dpsi1, dL_dpsi2 = _compute_dL_dpsi(num_inducing, num_data, output_dim, beta, Lm,
VVT_factor, Cpsi1Vf, DBi_plus_BiPBi,
psi1, het_noise, uncertain_inputs)
# log marginal likelihood
log_marginal = _compute_log_marginal_likelihood(likelihood, num_data, output_dim, beta, het_noise,
psi0, A, LB, trYYT, data_fit)
#put the gradients in the right places
partial_for_likelihood = _compute_partial_for_likelihood(likelihood,
het_noise, uncertain_inputs, LB,
_LBi_Lmi_psi1Vf, DBi_plus_BiPBi, Lm, A,
psi0, psi1, beta,
data_fit, num_data, output_dim, trYYT)
return dL_dKmm, dL_dpsi0, dL_dpsi1, dL_dpsi2, Cpsi1Vf, psi1, Lm, LB, log_marginal, Kmm, partial_for_likelihood

10
GPy/kern/_src/linear.py
View file

@ -130,9 +130,8 @@ class Linear(Kern):
if self.ARD: grad += tmp.sum(0).sum(0).sum(0)
else: grad += tmp.sum()
#from Kmm
self.update_gradients_full(dL_dpsi1, mu, Z)
grad += self.variances.gradient
self._set_gradient(grad)
self.update_gradients_full(dL_dKmm, Z, None)
self.variances.gradient += grad
def gradients_Z_variational(self, dL_dKmm, dL_dpsi0, dL_dpsi1, dL_dpsi2, mu, S, Z):
# Kmm
@ -211,7 +210,6 @@ class Linear(Kern):
def _weave_dpsi2_dZ(self, dL_dpsi2, Z, mu, S, target):
AZA = self.variances*self._ZAinner(mu, S, Z)
code="""
int n,m,mm,q;
@ -220,7 +218,7 @@ class Linear(Kern):
for(q=0;q<input_dim;q++){
for(mm=0;mm<num_inducing;mm++){
for(n=0;n<N;n++){
target(m,q) += dL_dpsi2(n,m,mm)*AZA(n,mm,q);
target(m,q) += 2*dL_dpsi2(n,m,mm)*AZA(n,mm,q);
}
}
}
@ -235,7 +233,7 @@ class Linear(Kern):
'extra_link_args' : ['-lgomp']}
N,num_inducing,input_dim = mu.shape[0],Z.shape[0],mu.shape[1]
mu, AZA, target, dL_dpsi2 = param_to_array(mu, AZA, target, dL_dpsi2)
mu = param_to_array(mu)
weave.inline(code, support_code=support_code, libraries=['gomp'],
arg_names=['N','num_inducing','input_dim','AZA','target','dL_dpsi2'],
type_converters=weave.converters.blitz,**weave_options)

4
GPy/kern/_src/rbf.py
View file

@ -54,7 +54,7 @@ class RBF(Kern):
self.variance = Param('variance', variance, Logexp())
self.lengthscale = Param('lengthscale', lengthscale, Logexp())
self.lengthscale.add_observer(self.update_lengthscale)
self.lengthscale.add_observer(self, self.update_lengthscale)
self.update_lengthscale(self.lengthscale)
self.add_parameters(self.variance, self.lengthscale)
@ -167,7 +167,7 @@ class RBF(Kern):
term1 = self._psi2_Zdist / self.lengthscale2 # num_inducing, num_inducing, input_dim
term2 = self._psi2_mudist / self._psi2_denom / self.lengthscale2 # N, num_inducing, num_inducing, input_dim
dZ = self._psi2[:, :, :, None] * (term1[None] + term2)
grad += (dL_dpsi2[:, :, :, None] * dZ).sum(0).sum(0)
grad += 2*(dL_dpsi2[:, :, :, None] * dZ).sum(0).sum(0)
grad += self.gradients_X(dL_dKmm, Z, None)

2
GPy/plotting/matplot_dep/models_plots.py
View file

@ -92,7 +92,7 @@ def plot_fit(model, plot_limits=None, which_data_rows='all',
ax.plot(Xnew, yi[:,None], Tango.colorsHex['darkBlue'], linewidth=0.25)
#ax.plot(Xnew, yi[:,None], marker='x', linestyle='--',color=Tango.colorsHex['darkBlue']) #TODO apply this line for discrete outputs.
#add error bars for uncertain (if input uncertainty is being modelled)
if hasattr(model,"has_uncertain_inputs") and model.has_uncertain_inputs():
ax.errorbar(model.X[which_data_rows, free_dims], model.Y[which_data_rows, which_data_ycols],