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[inference] changed gaussian variance to precision (which it really is)

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Max Zwiessele 2015-09-11 16:59:55 +01:00
parent 8132084de6
commit 69f6cfa6f7
5 changed files with 45 additions and 45 deletions
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38
GPy/inference/latent_function_inference/dtc.py
View file

@ -28,8 +28,8 @@ class DTC(LatentFunctionInference):
num_data, output_dim = Y.shape
#make sure the noise is not hetero
gaussian_variance = 1./likelihood.gaussian_variance(Y_metadata)
if gaussian_variance.size > 1:
precision = 1./likelihood.gaussian_variance(Y_metadata)
if precision.size > 1:
raise NotImplementedError("no hetero noise with this implementation of DTC")
Kmm = kern.K(Z)
@ -42,7 +42,7 @@ class DTC(LatentFunctionInference):
Kmmi, L, Li, _ = pdinv(Kmm)
# Compute A
LiUTbeta = np.dot(Li, U.T)*np.sqrt(gaussian_variance)
LiUTbeta = np.dot(Li, U.T)*np.sqrt(precision)
A = tdot(LiUTbeta) + np.eye(num_inducing)
# factor A
@ -50,7 +50,7 @@ class DTC(LatentFunctionInference):
# back substutue to get b, P, v
tmp, _ = dtrtrs(L, Uy, lower=1)
b, _ = dtrtrs(LA, tmp*gaussian_variance, lower=1)
b, _ = dtrtrs(LA, tmp*precision, lower=1)
tmp, _ = dtrtrs(LA, b, lower=1, trans=1)
v, _ = dtrtrs(L, tmp, lower=1, trans=1)
tmp, _ = dtrtrs(LA, Li, lower=1, trans=0)
@ -59,8 +59,8 @@ class DTC(LatentFunctionInference):
#compute log marginal
log_marginal = -0.5*num_data*output_dim*np.log(2*np.pi) + \
-np.sum(np.log(np.diag(LA)))*output_dim + \
0.5*num_data*output_dim*np.log(gaussian_variance) + \
-0.5*gaussian_variance*np.sum(np.square(Y)) + \
0.5*num_data*output_dim*np.log(precision) + \
-0.5*precision*np.sum(np.square(Y)) + \
0.5*np.sum(np.square(b))
# Compute dL_dKmm
@ -70,11 +70,11 @@ class DTC(LatentFunctionInference):
# Compute dL_dU
vY = np.dot(v.reshape(-1,1),Y.T)
dL_dU = vY - np.dot(vvT_P, U.T)
dL_dU *= gaussian_variance
dL_dU *= precision
#compute dL_dR
Uv = np.dot(U, v)
dL_dR = 0.5*(np.sum(U*np.dot(U,P), 1) - 1./gaussian_variance + np.sum(np.square(Y), 1) - 2.*np.sum(Uv*Y, 1) + np.sum(np.square(Uv), 1))*gaussian_variance**2
dL_dR = 0.5*(np.sum(U*np.dot(U,P), 1) - 1./precision + np.sum(np.square(Y), 1) - 2.*np.sum(Uv*Y, 1) + np.sum(np.square(Uv), 1))*precision**2
dL_dthetaL = likelihood.exact_inference_gradients(dL_dR)
@ -97,8 +97,8 @@ class vDTC(object):
num_data, output_dim = Y.shape
#make sure the noise is not hetero
gaussian_variance = 1./likelihood.gaussian_variance(Y_metadata)
if gaussian_variance.size > 1:
precision = 1./likelihood.gaussian_variance(Y_metadata)
if precision.size > 1:
raise NotImplementedError("no hetero noise with this implementation of DTC")
Kmm = kern.K(Z)
@ -111,9 +111,9 @@ class vDTC(object):
Kmmi, L, Li, _ = pdinv(Kmm)
# Compute A
LiUTbeta = np.dot(Li, U.T)*np.sqrt(gaussian_variance)
LiUTbeta = np.dot(Li, U.T)*np.sqrt(precision)
A_ = tdot(LiUTbeta)
trace_term = -0.5*(np.sum(Knn)*gaussian_variance - np.trace(A_))
trace_term = -0.5*(np.sum(Knn)*precision - np.trace(A_))
A = A_ + np.eye(num_inducing)
# factor A
@ -121,7 +121,7 @@ class vDTC(object):
# back substutue to get b, P, v
tmp, _ = dtrtrs(L, Uy, lower=1)
b, _ = dtrtrs(LA, tmp*gaussian_variance, lower=1)
b, _ = dtrtrs(LA, tmp*precision, lower=1)
tmp, _ = dtrtrs(LA, b, lower=1, trans=1)
v, _ = dtrtrs(L, tmp, lower=1, trans=1)
tmp, _ = dtrtrs(LA, Li, lower=1, trans=0)
@ -131,8 +131,8 @@ class vDTC(object):
#compute log marginal
log_marginal = -0.5*num_data*output_dim*np.log(2*np.pi) + \
-np.sum(np.log(np.diag(LA)))*output_dim + \
0.5*num_data*output_dim*np.log(gaussian_variance) + \
-0.5*gaussian_variance*np.sum(np.square(Y)) + \
0.5*num_data*output_dim*np.log(precision) + \
-0.5*precision*np.sum(np.square(Y)) + \
0.5*np.sum(np.square(b)) + \
trace_term
@ -145,15 +145,15 @@ class vDTC(object):
vY = np.dot(v.reshape(-1,1),Y.T)
#dL_dU = vY - np.dot(vvT_P, U.T)
dL_dU = vY - np.dot(vvT_P - Kmmi, U.T)
dL_dU *= gaussian_variance
dL_dU *= precision
#compute dL_dR
Uv = np.dot(U, v)
dL_dR = 0.5*(np.sum(U*np.dot(U,P), 1) - 1./gaussian_variance + np.sum(np.square(Y), 1) - 2.*np.sum(Uv*Y, 1) + np.sum(np.square(Uv), 1) )*gaussian_variance**2
dL_dR -=gaussian_variance*trace_term/num_data
dL_dR = 0.5*(np.sum(U*np.dot(U,P), 1) - 1./precision + np.sum(np.square(Y), 1) - 2.*np.sum(Uv*Y, 1) + np.sum(np.square(Uv), 1) )*precision**2
dL_dR -=precision*trace_term/num_data
dL_dthetaL = likelihood.exact_inference_gradients(dL_dR)
grad_dict = {'dL_dKmm': dL_dK, 'dL_dKdiag':np.zeros_like(Knn) + -0.5*gaussian_variance, 'dL_dKnm':dL_dU.T, 'dL_dthetaL':dL_dthetaL}
grad_dict = {'dL_dKmm': dL_dK, 'dL_dKdiag':np.zeros_like(Knn) + -0.5*precision, 'dL_dKnm':dL_dU.T, 'dL_dthetaL':dL_dthetaL}
#construct a posterior object
post = Posterior(woodbury_inv=Kmmi-P, woodbury_vector=v, K=Kmm, mean=None, cov=None, K_chol=L)

8
GPy/inference/latent_function_inference/exact_gaussian_inference.py
View file

@ -22,7 +22,7 @@ class ExactGaussianInference(LatentFunctionInference):
def __init__(self):
pass#self._YYTfactor_cache = caching.cache()
def inference(self, kern, X, likelihood, Y, mean_function=None, Y_metadata=None, K=None, gaussian_variance=None):
def inference(self, kern, X, likelihood, Y, mean_function=None, Y_metadata=None, K=None, precision=None):
"""
Returns a Posterior class containing essential quantities of the posterior
"""
@ -32,8 +32,8 @@ class ExactGaussianInference(LatentFunctionInference):
else:
m = mean_function.f(X)
if gaussian_variance is None:
gaussian_variance = likelihood.gaussian_variance(Y_metadata)
if precision is None:
precision = likelihood.gaussian_variance(Y_metadata)
YYT_factor = Y-m
@ -41,7 +41,7 @@ class ExactGaussianInference(LatentFunctionInference):
K = kern.K(X)
Ky = K.copy()
diag.add(Ky, gaussian_variance+1e-8)
diag.add(Ky, precision+1e-8)
Wi, LW, LWi, W_logdet = pdinv(Ky)

4
GPy/inference/latent_function_inference/expectation_propagation.py
View file

@ -35,7 +35,7 @@ class EP(ExactGaussianInference):
# TODO: update approximation in the end as well? Maybe even with a switch?
pass
def inference(self, kern, X, likelihood, Y, mean_function=None, Y_metadata=None, gaussian_variance=None, K=None):
def inference(self, kern, X, likelihood, Y, mean_function=None, Y_metadata=None, precision=None, K=None):
num_data, output_dim = Y.shape
assert output_dim ==1, "ep in 1D only (for now!)"
@ -49,7 +49,7 @@ class EP(ExactGaussianInference):
#if we've already run EP, just use the existing approximation stored in self._ep_approximation
mu, Sigma, mu_tilde, tau_tilde, Z_hat = self._ep_approximation
return super(EP, self).inference(kern, X, likelihood, mu_tilde[:,None], mean_function=mean_function, Y_metadata=Y_metadata, gaussian_variance=1./tau_tilde, K=K)
return super(EP, self).inference(kern, X, likelihood, mu_tilde[:,None], mean_function=mean_function, Y_metadata=Y_metadata, precision=1./tau_tilde, K=K)
def expectation_propagation(self, K, Y, likelihood, Y_metadata):

2
GPy/inference/latent_function_inference/expectation_propagation_dtc.py
View file

@ -46,7 +46,7 @@ class EPDTC(VarDTC):
return super(EPDTC, self).inference(kern, X, Z, likelihood, mu_tilde,
mean_function=mean_function,
Y_metadata=Y_metadata,
gaussian_variance=tau_tilde,
precision=tau_tilde,
Lm=Lm, dL_dKmm=dL_dKmm,
psi0=psi0, psi1=psi1, psi2=psi2)

38
GPy/inference/latent_function_inference/var_dtc.py
View file

@ -64,7 +64,7 @@ class VarDTC(LatentFunctionInference):
def get_VVTfactor(self, Y, prec):
return Y * prec # TODO chache this, and make it effective
def inference(self, kern, X, Z, likelihood, Y, Y_metadata=None, mean_function=None, gaussian_variance=None, Lm=None, dL_dKmm=None, psi0=None, psi1=None, psi2=None):
def inference(self, kern, X, Z, likelihood, Y, Y_metadata=None, mean_function=None, precision=None, Lm=None, dL_dKmm=None, psi0=None, psi1=None, psi2=None):
assert mean_function is None, "inference with a mean function not implemented"
num_data, output_dim = Y.shape
@ -72,16 +72,16 @@ class VarDTC(LatentFunctionInference):
uncertain_inputs = isinstance(X, VariationalPosterior)
if gaussian_variance is None:
if precision is None:
#assume Gaussian likelihood
gaussian_variance = 1./np.fmax(likelihood.gaussian_variance(Y_metadata), self.const_jitter)
precision = 1./np.fmax(likelihood.gaussian_variance(Y_metadata), self.const_jitter)
if gaussian_variance.ndim == 1:
gaussian_variance = gaussian_variance[:, None]
het_noise = gaussian_variance.size > 1
if precision.ndim == 1:
precision = precision[:, None]
het_noise = precision.size > 1
VVT_factor = gaussian_variance*Y
#VVT_factor = gaussian_variance*Y
VVT_factor = precision*Y
#VVT_factor = precision*Y
trYYT = self.get_trYYT(Y)
# kernel computations, using BGPLVM notation
@ -98,16 +98,16 @@ class VarDTC(LatentFunctionInference):
psi1 = kern.psi1(Z, X)
if het_noise:
if psi2 is None:
psi2_beta = (kern.psi2n(Z, X) * gaussian_variance[:, :, None]).sum(0)
psi2_beta = (kern.psi2n(Z, X) * precision[:, :, None]).sum(0)
else:
psi2_beta = (psi2 * gaussian_variance[:, :, None]).sum(0)
psi2_beta = (psi2 * precision[:, :, None]).sum(0)
else:
if psi2 is None:
psi2_beta = kern.psi2(Z,X) * gaussian_variance
psi2_beta = kern.psi2(Z,X) * precision
elif psi2.ndim == 3:
psi2_beta = psi2.sum(0) * gaussian_variance
psi2_beta = psi2.sum(0) * precision
else:
psi2_beta = psi2 * gaussian_variance
psi2_beta = psi2 * precision
LmInv = dtrtri(Lm)
A = LmInv.dot(psi2_beta.dot(LmInv.T))
else:
@ -116,9 +116,9 @@ class VarDTC(LatentFunctionInference):
if psi1 is None:
psi1 = kern.K(X, Z)
if het_noise:
tmp = psi1 * (np.sqrt(gaussian_variance))
tmp = psi1 * (np.sqrt(precision))
else:
tmp = psi1 * (np.sqrt(gaussian_variance))
tmp = psi1 * (np.sqrt(precision))
tmp, _ = dtrtrs(Lm, tmp.T, lower=1)
A = tdot(tmp) #print A.sum()
@ -144,19 +144,19 @@ class VarDTC(LatentFunctionInference):
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, gaussian_variance, Lm,
dL_dpsi0, dL_dpsi1, dL_dpsi2 = _compute_dL_dpsi(num_inducing, num_data, output_dim, precision, 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, gaussian_variance, het_noise,
log_marginal = _compute_log_marginal_likelihood(likelihood, num_data, output_dim, precision, het_noise,
psi0, A, LB, trYYT, data_fit, Y)
#noise derivatives
dL_dR = _compute_dL_dR(likelihood,
het_noise, uncertain_inputs, LB,
_LBi_Lmi_psi1Vf, DBi_plus_BiPBi, Lm, A,
psi0, psi1, gaussian_variance,
psi0, psi1, precision,
data_fit, num_data, output_dim, trYYT, Y, VVT_factor)
dL_dthetaL = likelihood.exact_inference_gradients(dL_dR,Y_metadata)
@ -181,7 +181,7 @@ class VarDTC(LatentFunctionInference):
else:
print('foobar')
import ipdb; ipdb.set_trace()
psi1V = np.dot(Y.T*gaussian_variance, psi1).T
psi1V = np.dot(Y.T*precision, psi1).T
tmp, _ = dtrtrs(Lm, psi1V, lower=1, trans=0)
tmp, _ = dpotrs(LB, tmp, lower=1)
woodbury_vector, _ = dtrtrs(Lm, tmp, lower=1, trans=1)