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

This commit is contained in:
Ricardo 2014-07-11 10:43:02 +01:00
commit 369cc0ba2b
25 changed files with 737 additions and 277 deletions

View file

@ -9,6 +9,8 @@ import numpy as np
from ...util.misc import param_to_array
from . import LatentFunctionInference
log_2_pi = np.log(2*np.pi)
import logging, itertools
logger = logging.getLogger('vardtc')
class VarDTC(LatentFunctionInference):
"""
@ -36,11 +38,11 @@ class VarDTC(LatentFunctionInference):
return param_to_array(np.sum(np.square(Y)))
def __getstate__(self):
# has to be overridden, as Cacher objects cannot be pickled.
# has to be overridden, as Cacher objects cannot be pickled.
return self.limit
def __setstate__(self, state):
# has to be overridden, as Cacher objects cannot be pickled.
# has to be overridden, as Cacher objects cannot be pickled.
self.limit = state
from ...util.caching import Cacher
self.get_trYYT = Cacher(self._get_trYYT, self.limit)
@ -196,18 +198,19 @@ class VarDTCMissingData(LatentFunctionInference):
def __init__(self, limit=1, inan=None):
from ...util.caching import Cacher
self._Y = Cacher(self._subarray_computations, limit)
self._inan = inan
if inan is not None: self._inan = ~inan
else: self._inan = None
pass
def set_limit(self, limit):
self._Y.limit = limit
def __getstate__(self):
# has to be overridden, as Cacher objects cannot be pickled.
# has to be overridden, as Cacher objects cannot be pickled.
return self._Y.limit, self._inan
def __setstate__(self, state):
# has to be overridden, as Cacher objects cannot be pickled.
# has to be overridden, as Cacher objects cannot be pickled.
from ...util.caching import Cacher
self.limit = state[0]
self._inan = state[1]
@ -217,21 +220,35 @@ class VarDTCMissingData(LatentFunctionInference):
if self._inan is None:
inan = np.isnan(Y)
has_none = inan.any()
self._inan = ~inan
else:
inan = self._inan
has_none = True
if has_none:
from ...util.subarray_and_sorting import common_subarrays
self._subarray_indices = []
for v,ind in common_subarrays(inan, 1).iteritems():
if not np.all(v):
v = ~np.array(v, dtype=bool)
ind = np.array(ind, dtype=int)
if ind.size == Y.shape[1]:
ind = slice(None)
self._subarray_indices.append([v,ind])
Ys = [Y[v, :][:, ind] for v, ind in self._subarray_indices]
traces = [(y**2).sum() for y in Ys]
#print "caching missing data slices, this can take several minutes depending on the number of unique dimensions of the data..."
#csa = common_subarrays(inan, 1)
size = Y.shape[1]
#logger.info('preparing subarrays {:3.3%}'.format((i+1.)/size))
Ys = []
next_ten = [0.]
count = itertools.count()
for v, y in itertools.izip(inan.T, Y.T[:,:,None]):
i = count.next()
if ((i+1.)/size) >= next_ten[0]:
logger.info('preparing subarrays {:>6.1%}'.format((i+1.)/size))
next_ten[0] += .1
Ys.append(y[v,:])
next_ten = [0.]
count = itertools.count()
def trace(y):
i = count.next()
if ((i+1.)/size) >= next_ten[0]:
logger.info('preparing traces {:>6.1%}'.format((i+1.)/size))
next_ten[0] += .1
y = y[inan[:,i],i:i+1]
return np.einsum('ij,ij->', y,y)
traces = [trace(Y) for _ in xrange(size)]
return Ys, traces
else:
self._subarray_indices = [[slice(None),slice(None)]]
@ -253,7 +270,6 @@ class VarDTCMissingData(LatentFunctionInference):
beta_all = 1./np.fmax(likelihood.gaussian_variance(Y_metadata), 1e-6)
het_noise = beta_all.size != 1
import itertools
num_inducing = Z.shape[0]
dL_dpsi0_all = np.zeros(Y.shape[0])
@ -273,22 +289,24 @@ class VarDTCMissingData(LatentFunctionInference):
Lm = jitchol(Kmm)
if uncertain_inputs: LmInv = dtrtri(Lm)
VVT_factor_all = np.empty(Y.shape)
full_VVT_factor = VVT_factor_all.shape[1] == Y.shape[1]
if not full_VVT_factor:
psi1V = np.dot(Y.T*beta_all, psi1_all).T
#VVT_factor_all = np.empty(Y.shape)
#full_VVT_factor = VVT_factor_all.shape[1] == Y.shape[1]
#if not full_VVT_factor:
# psi1V = np.dot(Y.T*beta_all, psi1_all).T
for y, trYYT, [v, ind] in itertools.izip(Ys, traces, self._subarray_indices):
if het_noise: beta = beta_all[ind]
#logger.info('computing dimension-wise likelihood and derivatives')
#size = len(Ys)
size = Y.shape[1]
next_ten = 0
for i, [y, v, trYYT] in enumerate(itertools.izip(Ys, self._inan.T, traces)):
if ((i+1.)/size) >= next_ten:
logger.info('inference {:> 6.1%}'.format((i+1.)/size))
next_ten += .1
if het_noise: beta = beta_all[i]
else: beta = beta_all
VVT_factor = (beta*y)
try:
VVT_factor_all[v, ind].flat = VVT_factor.flat
except ValueError:
mult = np.ravel_multi_index((v.nonzero()[0][:,None],ind[None,:]), VVT_factor_all.shape)
VVT_factor_all.flat[mult] = VVT_factor
output_dim = y.shape[1]
VVT_factor = (y*beta)
output_dim = 1#len(ind)
psi0 = psi0_all[v]
psi1 = psi1_all[v, :]
@ -347,19 +365,20 @@ class VarDTCMissingData(LatentFunctionInference):
psi0, psi1, beta,
data_fit, num_data, output_dim, trYYT, Y)
if full_VVT_factor: woodbury_vector[:, ind] = Cpsi1Vf
else:
print 'foobar'
tmp, _ = dtrtrs(Lm, psi1V, lower=1, trans=0)
tmp, _ = dpotrs(LB, tmp, lower=1)
woodbury_vector[:, ind] = dtrtrs(Lm, tmp, lower=1, trans=1)[0]
#if full_VVT_factor:
woodbury_vector[:, i:i+1] = Cpsi1Vf
#else:
# print 'foobar'
# tmp, _ = dtrtrs(Lm, psi1V, lower=1, trans=0)
# tmp, _ = dpotrs(LB, tmp, lower=1)
# woodbury_vector[:, ind] = dtrtrs(Lm, tmp, lower=1, trans=1)[0]
#import ipdb;ipdb.set_trace()
Bi, _ = dpotri(LB, lower=1)
symmetrify(Bi)
Bi = -dpotri(LB, lower=1)[0]
diag.add(Bi, 1)
woodbury_inv_all[:, :, ind] = backsub_both_sides(Lm, Bi)[:,:,None]
woodbury_inv_all[:, :, i:i+1] = backsub_both_sides(Lm, Bi)[:,:,None]
dL_dthetaL = likelihood.exact_inference_gradients(dL_dR)
@ -376,23 +395,6 @@ class VarDTCMissingData(LatentFunctionInference):
'dL_dKnm':dL_dpsi1_all,
'dL_dthetaL':dL_dthetaL}
#get sufficient things for posterior prediction
#TODO: do we really want to do this in the loop?
#if not full_VVT_factor:
# print 'foobar'
# psi1V = np.dot(Y.T*beta_all, psi1_all).T
# tmp, _ = dtrtrs(Lm, psi1V, lower=1, trans=0)
# tmp, _ = dpotrs(LB_all, tmp, lower=1)
# woodbury_vector, _ = dtrtrs(Lm, tmp, lower=1, trans=1)
#import ipdb;ipdb.set_trace()
#Bi, _ = dpotri(LB_all, lower=1)
#symmetrify(Bi)
#Bi = -dpotri(LB_all, lower=1)[0]
#from ...util import diag
#diag.add(Bi, 1)
#woodbury_inv = backsub_both_sides(Lm, Bi)
post = Posterior(woodbury_inv=woodbury_inv_all, woodbury_vector=woodbury_vector, K=Kmm, mean=None, cov=None, K_chol=Lm)
return post, log_marginal, grad_dict

View file

@ -22,21 +22,21 @@ class VarDTC_minibatch(LatentFunctionInference):
"""
const_jitter = 1e-6
def __init__(self, batchsize, limit=1):
self.batchsize = batchsize
# Cache functions
from ...util.caching import Cacher
self.get_trYYT = Cacher(self._get_trYYT, limit)
self.get_YYTfactor = Cacher(self._get_YYTfactor, limit)
self.midRes = {}
self.batch_pos = 0 # the starting position of the current mini-batch
def set_limit(self, limit):
self.get_trYYT.limit = limit
self.get_YYTfactor.limit = limit
def _get_trYYT(self, Y):
return param_to_array(np.sum(np.square(Y)))
@ -51,23 +51,23 @@ class VarDTC_minibatch(LatentFunctionInference):
return param_to_array(Y)
else:
return jitchol(tdot(Y))
def inference_likelihood(self, kern, X, Z, likelihood, Y):
"""
The first phase of inference:
Compute: log-likelihood, dL_dKmm
Cached intermediate results: Kmm, KmmInv,
"""
num_inducing = Z.shape[0]
num_inducing = Z.shape[0]
num_data, output_dim = Y.shape
if isinstance(X, VariationalPosterior):
uncertain_inputs = True
else:
uncertain_inputs = False
#see whether we've got a different noise variance for each datum
beta = 1./np.fmax(likelihood.variance, 1e-6)
het_noise = beta.size > 1
@ -77,19 +77,19 @@ class VarDTC_minibatch(LatentFunctionInference):
#self.YYTfactor = beta*self.get_YYTfactor(Y)
YYT_factor = Y
trYYT = self.get_trYYT(Y)
psi2_full = np.zeros((num_inducing,num_inducing))
psi1Y_full = np.zeros((output_dim,num_inducing)) # DxM
psi0_full = 0
YRY_full = 0
for n_start in xrange(0,num_data,self.batchsize):
n_end = min(self.batchsize+n_start, num_data)
Y_slice = YYT_factor[n_start:n_end]
X_slice = X[n_start:n_end]
if uncertain_inputs:
psi0 = kern.psi0(Z, X_slice)
psi1 = kern.psi1(Z, X_slice)
@ -98,7 +98,7 @@ class VarDTC_minibatch(LatentFunctionInference):
psi0 = kern.Kdiag(X_slice)
psi1 = kern.K(X_slice, Z)
psi2 = None
if het_noise:
beta_slice = beta[n_start:n_end]
psi0_full += (beta_slice*psi0).sum()
@ -106,33 +106,33 @@ class VarDTC_minibatch(LatentFunctionInference):
YRY_full += (beta_slice*np.square(Y_slice).sum(axis=-1)).sum()
else:
psi0_full += psi0.sum()
psi1Y_full += np.dot(Y_slice.T,psi1) # DxM
psi1Y_full += np.dot(Y_slice.T,psi1) # DxM
if uncertain_inputs:
if het_noise:
psi2_full += beta_slice*psi2
else:
psi2_full += psi2
psi2_full += psi2.sum(0)
else:
if het_noise:
psi2_full += beta_slice*np.outer(psi1,psi1)
else:
psi2_full += np.outer(psi1,psi1)
psi2_full += np.einsum('nm,jk->mk',psi1,psi1)
if not het_noise:
psi0_full *= beta
psi1Y_full *= beta
psi2_full *= beta
YRY_full = trYYT*beta
#======================================================================
# Compute Common Components
#======================================================================
self.psi1Y = psi1Y_full
Kmm = kern.K(Z).copy()
diag.add(Kmm, self.const_jitter)
Lm = jitchol(Kmm)
Lambda = Kmm+psi2_full
LL = jitchol(Lambda)
b,_ = dtrtrs(LL, psi1Y_full.T)
@ -140,18 +140,18 @@ class VarDTC_minibatch(LatentFunctionInference):
v,_ = dtrtrs(LL.T,b,lower=False)
vvt = np.einsum('md,od->mo',v,v)
LmInvPsi2LmInvT = backsub_both_sides(Lm,psi2_full,transpose='right')
Psi2LLInvT = dtrtrs(LL,psi2_full)[0].T
LmInvPsi2LLInvT= dtrtrs(Lm,Psi2LLInvT)[0]
KmmInvPsi2LLInvT = dtrtrs(Lm,LmInvPsi2LLInvT,trans=True)[0]
KmmInvPsi2P = dtrtrs(LL,KmmInvPsi2LLInvT.T, trans=True)[0].T
dL_dpsi2R = (output_dim*KmmInvPsi2P - vvt)/2. # dL_dpsi2 with R inside psi2
# Cache intermediate results
self.midRes['dL_dpsi2R'] = dL_dpsi2R
self.midRes['v'] = v
#======================================================================
# Compute log-likelihood
#======================================================================
@ -159,30 +159,33 @@ class VarDTC_minibatch(LatentFunctionInference):
logL_R = -np.log(beta).sum()
else:
logL_R = -num_data*np.log(beta)
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())
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())
)
#======================================================================
# Compute dL_dKmm
#======================================================================
dL_dKmm = -(output_dim*np.einsum('md,od->mo',KmmInvPsi2LLInvT,KmmInvPsi2LLInvT) + vvt)/2.
#======================================================================
# Compute the Posterior distribution of inducing points p(u|Y)
#======================================================================
# phi_u_mean = np.dot(Kmm,v)
# LLInvKmm,_ = dtrtrs(LL,Kmm)
# # phi_u_var = np.einsum('ma,mb->ab',LLInvKmm,LLInvKmm)
# phi_u_var = Kmm - np.dot(LLInvKmm.T,LLInvKmm)
post = Posterior(woodbury_inv=KmmInvPsi2P, woodbury_vector=v, K=Kmm, mean=None, cov=None, K_chol=Lm)
return logL, dL_dKmm, post
def inference_minibatch(self, kern, X, Z, likelihood, Y):
"""
The second phase of inference: Computing the derivatives over a minibatch of Y
The second phase of inference: Computing the derivatives over a minibatch of Y
Compute: dL_dpsi0, dL_dpsi1, dL_dpsi2, dL_dthetaL
return a flag showing whether it reached the end of Y (isEnd)
"""
@ -193,14 +196,14 @@ class VarDTC_minibatch(LatentFunctionInference):
uncertain_inputs = True
else:
uncertain_inputs = False
#see whether we've got a different noise variance for each datum
beta = 1./np.fmax(likelihood.variance, 1e-6)
het_noise = beta.size > 1
# VVT_factor is a matrix such that tdot(VVT_factor) = VVT...this is for efficiency!
#self.YYTfactor = beta*self.get_YYTfactor(Y)
YYT_factor = Y
n_start = self.batch_pos
n_end = min(self.batchsize+n_start, num_data)
if n_end==num_data:
@ -209,11 +212,11 @@ class VarDTC_minibatch(LatentFunctionInference):
else:
isEnd = False
self.batch_pos = n_end
num_slice = n_end-n_start
Y_slice = YYT_factor[n_start:n_end]
X_slice = X[n_start:n_end]
if uncertain_inputs:
psi0 = kern.psi0(Z, X_slice)
psi1 = kern.psi1(Z, X_slice)
@ -222,51 +225,51 @@ class VarDTC_minibatch(LatentFunctionInference):
psi0 = kern.Kdiag(X_slice)
psi1 = kern.K(X_slice, Z)
psi2 = None
if het_noise:
beta = beta[n_start] # assuming batchsize==1
betaY = beta*Y_slice
betapsi1 = np.einsum('n,nm->nm',beta,psi1)
#======================================================================
# Load Intermediate Results
#======================================================================
dL_dpsi2R = self.midRes['dL_dpsi2R']
v = self.midRes['v']
#======================================================================
# Compute dL_dpsi
#======================================================================
dL_dpsi0 = -0.5 * output_dim * (beta * np.ones((n_end-n_start,)))
dL_dpsi1 = np.dot(betaY,v.T)
if uncertain_inputs:
dL_dpsi2 = beta* dL_dpsi2R
else:
dL_dpsi1 += np.dot(betapsi1,dL_dpsi2R)*2.
dL_dpsi2 = None
#======================================================================
# Compute dL_dthetaL
#======================================================================
if het_noise:
if uncertain_inputs:
psiR = np.einsum('mo,nmo->n',dL_dpsi2R,psi2)
psiR = np.einsum('mo,nmo->',dL_dpsi2R,psi2)
else:
psiR = np.einsum('nm,no,mo->n',psi1,psi1,dL_dpsi2R)
psiR = np.einsum('nm,no,mo->',psi1,psi1,dL_dpsi2R)
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)
else:
if uncertain_inputs:
psiR = np.einsum('mo,mo->',dL_dpsi2R,psi2)
psiR = np.einsum('mo,nmo->',dL_dpsi2R,psi2)
else:
psiR = np.einsum('nm,no,mo->',psi1,psi1,dL_dpsi2R)
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()
if uncertain_inputs:
@ -278,15 +281,15 @@ class VarDTC_minibatch(LatentFunctionInference):
grad_dict = {'dL_dKdiag':dL_dpsi0,
'dL_dKnm':dL_dpsi1,
'dL_dthetaL':dL_dthetaL}
return isEnd, (n_start,n_end), grad_dict
def update_gradients(model):
model._log_marginal_likelihood, dL_dKmm, model.posterior = model.inference_method.inference_likelihood(model.kern, model.X, model.Z, model.likelihood, model.Y)
het_noise = model.likelihood.variance.size > 1
if het_noise:
dL_dthetaL = np.empty((model.Y.shape[0],))
else:
@ -295,40 +298,54 @@ def update_gradients(model):
#gradients w.r.t. kernel
model.kern.update_gradients_full(dL_dKmm, model.Z, None)
kern_grad = model.kern.gradient.copy()
#gradients w.r.t. Z
model.Z.gradient = model.kern.gradients_X(dL_dKmm, model.Z)
isEnd = False
while not isEnd:
isEnd, n_range, grad_dict = model.inference_method.inference_minibatch(model.kern, model.X, model.Z, model.likelihood, model.Y)
if isinstance(model.X, VariationalPosterior):
X_slice = model.X[n_range[0]:n_range[1]]
dL_dpsi1 = grad_dict['dL_dpsi1']#[None, :]
dL_dpsi2 = grad_dict['dL_dpsi2'][None, :, :]
#gradients w.r.t. kernel
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'])
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)
kern_grad += model.kern.gradient
#gradients w.r.t. Z
model.Z.gradient += model.kern.gradients_Z_expectations(
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)
dL_dpsi0=grad_dict['dL_dpsi0'],
dL_dpsi1=dL_dpsi1,
dL_dpsi2=dL_dpsi2,
Z=model.Z, variational_posterior=X_slice)
#gradients w.r.t. posterior parameters of X
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'])
model.set_X_gradients(X_slice, X_grad)
X_grad = model.kern.gradients_qX_expectations(
variational_posterior=X_slice,
Z=model.Z,
dL_dpsi0=grad_dict['dL_dpsi0'],
dL_dpsi1=dL_dpsi1,
dL_dpsi2=dL_dpsi2)
model.X.mean[n_range[0]:n_range[1]].gradient = X_grad[0]
model.X.variance[n_range[0]:n_range[1]].gradient = X_grad[1]
if het_noise:
dL_dthetaL[n_range[0]:n_range[1]] = grad_dict['dL_dthetaL']
else:
dL_dthetaL += grad_dict['dL_dthetaL']
#import ipdb;ipdb.set_trace()
model.grad_dict = grad_dict
if isinstance(model.X, VariationalPosterior):
# Update Log-likelihood
model._log_marginal_likelihood -= model.variational_prior.KL_divergence(model.X)
# update for the KL divergence
model.variational_prior.update_gradients_KL(model.X)
# Set the gradients w.r.t. kernel
model.kern.gradient = kern_grad
# Update Log-likelihood
model._log_marginal_likelihood -= model.variational_prior.KL_divergence(model.X)
# update for the KL divergence
model.variational_prior.update_gradients_KL(model.X)
# dL_dthetaL
model.likelihood.update_gradients(dL_dthetaL)

View file

@ -56,13 +56,13 @@ def SCG(f, gradf, x, optargs=(), maxiters=500, max_f_eval=np.inf, display=True,
if gtol is None:
gtol = 1e-5
sigma0 = 1.0e-8
sigma0 = 1.0e-7
fold = f(x, *optargs) # Initial function value.
function_eval = 1
fnow = fold
gradnew = gradf(x, *optargs) # Initial gradient.
if any(np.isnan(gradnew)):
raise UnexpectedInfOrNan, "Gradient contribution resulted in a NaN value"
#if any(np.isnan(gradnew)):
# raise UnexpectedInfOrNan, "Gradient contribution resulted in a NaN value"
current_grad = np.dot(gradnew, gradnew)
gradold = gradnew.copy()
d = -gradnew # Initial search direction.
@ -168,13 +168,13 @@ def SCG(f, gradf, x, optargs=(), maxiters=500, max_f_eval=np.inf, display=True,
if Delta < 0.25:
beta = min(4.0 * beta, betamax)
if Delta > 0.75:
beta = max(0.5 * beta, betamin)
beta = max(0.25 * beta, betamin)
# Update search direction using Polak-Ribiere formula, or re-start
# in direction of negative gradient after nparams steps.
if nsuccess == x.size:
d = -gradnew
# beta = 1. # TODO: betareset!!
beta = 1. # This is not in the original paper
nsuccess = 0
elif success:
Gamma = np.dot(gradold - gradnew, gradnew) / (mu)