def setUp(self):
self.N = 4
self.D = 2
self.Xmu = rnd.rand(self.N, self.D)
self.Z = rnd.rand(3, self.D)
unconstrained = rnd.randn(self.N, 2 * self.D, self.D)
t = TriDiagonalBlockRep()
self.Xcov = t.forward(unconstrained)
variance = 0.3 + rnd.rand()
k1 = ekernels.RBF(1, variance, active_dims=[0])
k2 = ekernels.RBF(1, variance, active_dims=[1])
klin = ekernels.Linear(1, variance, active_dims=[1])
self.ekernels = [k1, k2, klin]
k1 = ekernels.RBF(2, variance)
k2 = ekernels.RBF(2, variance)
klin = ekernels.Linear(2, variance)
self.pekernels = [k1, k2, klin]
k1 = kernels.RBF(1, variance, active_dims=[0])
klin = kernels.Linear(1, variance, active_dims=[1])
self.kernels = [k1, klin]
k1 = kernels.RBF(2, variance)
klin = kernels.Linear(2, variance)
self.pkernels = [k1, klin]
def setUp(self):
self.rng = np.random.RandomState(0)
self.N = 4
self.D = 2
self.Xmu = self.rng.rand(self.N, self.D)
self.Z = self.rng.rand(2, self.D)
self.Xcov_diag = 0.05 + self.rng.rand(self.N, self.D)
self.Xcov = np.zeros((self.Xcov_diag.shape[0], self.Xcov_diag.shape[1],
self.Xcov_diag.shape[1]))
self.Xcov[(np.s_[:], ) +
np.diag_indices(self.Xcov_diag.shape[1])] = self.Xcov_diag
# Set up "normal" kernels
ekernel_classes = [ekernels.RBF, ekernels.Linear]
kernel_classes = [kernels.RBF, kernels.Linear]
params = [(self.D, 0.3 + self.rng.rand(),
self.rng.rand(2) + [0.5, 1.5], None, True),
(self.D, 0.3 + self.rng.rand(), None)]
self.ekernels = [c(*p) for c, p in zip(ekernel_classes, params)]
self.kernels = [c(*p) for c, p in zip(kernel_classes, params)]
# Test summed kernels, non-overlapping
rbfvariance = 0.3 + self.rng.rand()
rbfard = [self.rng.rand() + 0.5]
linvariance = 0.3 + self.rng.rand()
self.kernels.append(
kernels.Add([
kernels.RBF(1, rbfvariance, rbfard, [1], False),
kernels.Linear(1, linvariance, [0])
]))
self.kernels[-1].input_size = self.kernels[-1].input_dim
for k in self.kernels[-1].kern_list:
k.input_size = self.kernels[-1].input_size
self.ekernels.append(
ekernels.Add([
ekernels.RBF(1, rbfvariance, rbfard, [1], False),
ekernels.Linear(1, linvariance, [0])
]))
self.ekernels[-1].input_size = self.ekernels[-1].input_dim
for k in self.ekernels[-1].kern_list:
k.input_size = self.ekernels[-1].input_size
# Test summed kernels, overlapping
rbfvariance = 0.3 + self.rng.rand()
rbfard = [self.rng.rand() + 0.5]
linvariance = 0.3 + self.rng.rand()
self.kernels.append(
kernels.Add([
kernels.RBF(self.D, rbfvariance, rbfard),
kernels.Linear(self.D, linvariance)
]))
self.ekernels.append(
ekernels.Add([
ekernels.RBF(self.D, rbfvariance, rbfard),
ekernels.Linear(self.D, linvariance)
]))
self.assertTrue(self.ekernels[-2].on_separate_dimensions)
self.assertTrue(not self.ekernels[-1].on_separate_dimensions)
def setUp(self):
self.N = 4
self.D = 2
self.Xmu = rnd.rand(self.N, self.D)
self.Z = rnd.rand(3, self.D)
unconstrained = rnd.randn(self.N, 2 * self.D, self.D)
t = TriDiagonalBlockRep()
self.Xcov = t.forward(unconstrained)
variance = 0.3 + rnd.rand()
k1 = ekernels.RBF(1, variance, active_dims=[0])
k2 = ekernels.RBF(1, variance, active_dims=[1])
klin = ekernels.Linear(1, variance, active_dims=[1])
self.ekernels = [
k1, k2, klin
] # Kernels doing the expectation in closed form, doing the slicing
k1 = ekernels.RBF(1, variance)
k2 = ekernels.RBF(1, variance)
klin = ekernels.Linear(1, variance)
self.pekernels = [
k1, k2, klin
] # kernels doing the expectations in closed form, without slicing
k1 = kernels.RBF(1, variance, active_dims=[0])
klin = kernels.Linear(1, variance, active_dims=[1])
self.kernels = [k1, klin]
k1 = kernels.RBF(1, variance)
klin = kernels.Linear(1, variance)
self.pkernels = [k1, klin]
def setUp(self):
self.rng = np.random.RandomState(
1) # this seed works with 60 GH points
self.N = 4
self.D = 2
self.Xmu = self.rng.rand(self.N, self.D)
self.Z = self.rng.rand(2, self.D)
unconstrained = self.rng.randn(self.N, 2 * self.D, self.D)
t = TriDiagonalBlockRep()
self.Xcov = t.forward(unconstrained)
# Set up "normal" kernels
ekernel_classes = [ekernels.RBF, ekernels.Linear]
kernel_classes = [kernels.RBF, kernels.Linear]
params = [(self.D, 0.3 + self.rng.rand(),
self.rng.rand(2) + [0.5, 1.5], None, True),
(self.D, 0.3 + self.rng.rand(), None)]
self.ekernels = [c(*p) for c, p in zip(ekernel_classes, params)]
self.kernels = [c(*p) for c, p in zip(kernel_classes, params)]
# Test summed kernels, non-overlapping
rbfvariance = 0.3 + self.rng.rand()
rbfard = [self.rng.rand() + 0.5]
linvariance = 0.3 + self.rng.rand()
self.kernels.append(
kernels.Add([
kernels.RBF(1, rbfvariance, rbfard, [1], False),
kernels.Linear(1, linvariance, [0])
]))
self.kernels[-1].input_size = self.kernels[-1].input_dim
for k in self.kernels[-1].kern_list:
k.input_size = self.kernels[-1].input_size
self.ekernels.append(
ekernels.Add([
ekernels.RBF(1, rbfvariance, rbfard, [1], False),
ekernels.Linear(1, linvariance, [0])
]))
self.ekernels[-1].input_size = self.ekernels[-1].input_dim
for k in self.ekernels[-1].kern_list:
k.input_size = self.ekernels[-1].input_size
# Test summed kernels, overlapping
rbfvariance = 0.3 + self.rng.rand()
rbfard = [self.rng.rand() + 0.5]
linvariance = 0.3 + self.rng.rand()
self.kernels.append(
kernels.Add([
kernels.RBF(self.D, rbfvariance, rbfard, active_dims=[0, 1]),
kernels.Linear(self.D, linvariance, active_dims=[0, 1])
]))
self.ekernels.append(
ekernels.Add([
ekernels.RBF(self.D, rbfvariance, rbfard, active_dims=[0, 1]),
ekernels.Linear(self.D, linvariance, active_dims=[0, 1])
]))
self.assertTrue(self.ekernels[-2].on_separate_dimensions)
self.assertTrue(not self.ekernels[-1].on_separate_dimensions)
def __init__(self,
Y,
latent_dim,
X_mean=None,
kern=None,
mean_function=Zero()):
"""
Y is a data matrix, size N x R
Z is a matrix of pseudo inputs, size M x D
X_mean is a matrix, size N x Q, for the initialisation of the latent space.
kern, mean_function are appropriate GPflow objects
This method only works with a Gaussian likelihood.
"""
if kern is None:
kern = kernels.RBF(latent_dim, ARD=True)
if X_mean is None:
X_mean = PCA_reduce(Y, latent_dim)
assert X_mean.shape[
1] == latent_dim, 'Passed in number of latent ' + str(
latent_dim) + ' does not match initial X ' + str(
X_mean.shape[1])
self.num_latent = X_mean.shape[1]
assert Y.shape[
1] >= self.num_latent, 'More latent dimensions than observed.'
GPR.__init__(self, X_mean, Y, kern, mean_function=mean_function)
del self.X # in GPLVM this is a Param
self.X = Param(X_mean)
def __init__(self,
Y,
latent_dim,
X_mean=None,
kern=None,
back_kern=None,
mean_function=Zero()):
"""
Initialise GPLVM object. This method only works with a Gaussian likelihood.
:param Y: data matrix (N x D)
:param X_mean: latent positions (N x Q), by default initialized using PCA.
:param kern: kernel specification, by default RBF
:param mean_function: mean function, by default None.
"""
# define kernel function
if kern is None:
kern = kernels.RBF(latent_dim)
back_kern = kernels.RBF(latent_dim)
# initialize latent_positions
if X_mean is None:
X_mean = PCA_reduce(Y, latent_dim)
# initialize variables
self.num_latent = X_mean.shape[1]
# initialize variables
likelihood = likelihoods.Gaussian()
Y = DataHolder(Y, on_shape_change='pass')
X = DataHolder(X_mean, on_shape_change='pass')
# initialize parent GPModel
GPModel.__init__(self, X, Y, kern, likelihood, mean_function)
# initialize back constraint model
self.back_kern = back_kern
self.back_mean_function = Zero()
self.back_likelihood = likelihoods.Gaussian()
# set latent positions as model param
del self.X
self.X = Param(X_mean)
def test_kernelsActiveDims(self):
''' Test sum and product compositional kernels '''
Q = 2 # latent dimensions
X_mean = GPflow.gplvm.PCA_reduce(self.Y, Q)
kernsQuadratu = [kernels.RBF(1, active_dims=[0])+kernels.Linear(1, active_dims=[1]),
kernels.RBF(1, active_dims=[0])+kernels.PeriodicKernel(1, active_dims=[1]),
kernels.RBF(1, active_dims=[0])*kernels.Linear(1, active_dims=[1]),
kernels.RBF(Q)+kernels.Linear(Q)] # non-overlapping
kernsAnalytic = [ekernels.Add([ekernels.RBF(1, active_dims=[0]), ekernels.Linear(1, active_dims=[1])]),
ekernels.Add([ekernels.RBF(1, active_dims=[0]), kernels.PeriodicKernel(1, active_dims=[1])]),
ekernels.Prod([ekernels.RBF(1, active_dims=[0]), ekernels.Linear(1, active_dims=[1])]),
ekernels.Add([ekernels.RBF(Q), ekernels.Linear(Q)])]
fOnSeparateDims = [True, True, True, False]
Z = np.random.permutation(X_mean.copy())[:self.M]
# Also test default N(0,1) is used
X_prior_mean = np.zeros((self.N, Q))
X_prior_var = np.ones((self.N, Q))
Xtest = self.rng.randn(10, Q)
for kq, ka, sepDims in zip(kernsQuadratu, kernsAnalytic, fOnSeparateDims):
kq.num_gauss_hermite_points = 20 # speed up quadratic for tests
ka.kern_list[0].num_gauss_hermite_points = 0 # RBF should throw error if quadrature is used
if(sepDims):
self.assertTrue(ka.on_separate_dimensions, 'analytic kernel must not use quadrature')
mq = GPflow.gplvm.BayesianGPLVM(X_mean=X_mean, X_var=np.ones((self.N, Q)), Y=self.Y,
kern=kq, M=self.M, Z=Z, X_prior_mean=X_prior_mean, X_prior_var=X_prior_var)
ma = GPflow.gplvm.BayesianGPLVM(X_mean=X_mean, X_var=np.ones((self.N, Q)), Y=self.Y,
kern=ka, M=self.M, Z=Z)
mq._compile()
ma._compile()
ql = mq.compute_log_likelihood()
al = ma.compute_log_likelihood()
self.assertTrue(np.allclose(ql, al, atol=1e-2), 'Likelihood not equal %f<>%f' % (ql, al))
mu_f_a, var_f_a = ma.predict_f(Xtest)
mu_f_q, var_f_q = mq.predict_f(Xtest)
self.assertTrue(np.allclose(mu_f_a, mu_f_q, atol=1e-4), ('Posterior means different', mu_f_a-mu_f_q))
self.assertTrue(np.allclose(mu_f_a, mu_f_q, atol=1e-4), ('Posterior vars different', var_f_a-var_f_q))
def setUp(self):
self._threshold = 0.5
self.rng = np.random.RandomState(0)
self.N = 4
self.D = 2
# Test summed kernels, non-overlapping
rbfvariance = 0.3 + self.rng.rand()
rbfard = [self.rng.rand() + 0.5]
linvariance = 0.3 + self.rng.rand()
self.kernel = kernels.Prod([
kernels.RBF(1, rbfvariance, rbfard, [1], False),
kernels.Linear(1, linvariance, [0])
])
self.ekernel = ekernels.Prod([
ekernels.RBF(1, rbfvariance, rbfard, [1], False),
ekernels.Linear(1, linvariance, [0])
])
self.Xmu = self.rng.rand(self.N, self.D)
self.Xcov = self.rng.rand(self.N, self.D)
self.Z = self.rng.rand(2, self.D)
