def __init__(self,
latent_dim,
Z,
mean_function=None,
kern=None,
likelihood=None,
name=None):
super().__init__(name=name)
self.latent_dim = latent_dim
self.obs_dim = 1
self.n_ind_pts = Z.shape[0]
self.mean_function = mean_function or mean_fns.Zero(
output_dim=self.obs_dim)
self.kern = kern or gp.kernels.RBF(self.latent_dim, ARD=True)
self.likelihood = likelihood or gp.likelihoods.Gaussian()
self.Z = gp.features.InducingPoints(Z)
self.Umu = gp.Param(np.zeros(
(self.n_ind_pts, self.latent_dim))) # (Lm^-1)(Umu - m(Z))
self.Ucov_chol = gp.Param(np.tile(
np.eye(self.n_ind_pts)[None, ...], [self.obs_dim, 1, 1]),
transform=gp.transforms.LowerTriangular(
self.n_ind_pts,
num_matrices=self.obs_dim,
squeeze=False)) # (Lm^-1)Lu
def zero_mean():
return mean_functions.Zero(output_dim=Data.D_out)
def markov_gauss():
cov_params = rng.randn(num_data + 1, D_in, 2 * D_in) / 2.0 # (N+1)xDx2D
Xcov = cov_params @ np.transpose(cov_params, (0, 2, 1)) # (N+1)xDxD
Xcross = cov_params[:-1] @ np.transpose(cov_params[1:], (0, 2, 1)) # NxDxD
Xcross = np.concatenate((Xcross, np.zeros((1, D_in, D_in))),
0) # (N+1)xDxD
Xcov = np.stack([Xcov, Xcross]) # 2x(N+1)xDxD
return MarkovGaussian(Xmu_markov, ctt(Xcov))
_means = {
"lin": mf.Linear(A=rng.randn(D_in, D_out), b=rng.randn(D_out)),
"identity": mf.Identity(input_dim=D_in),
"const": mf.Constant(c=rng.randn(D_out)),
"zero": mf.Zero(output_dim=D_out),
}
_distrs = {
"gauss":
Gaussian(Xmu, Xcov),
"dirac_gauss":
Gaussian(Xmu, np.zeros((num_data, D_in, D_in))),
"gauss_diag":
DiagonalGaussian(Xmu, rng.rand(num_data, D_in)),
"dirac_diag":
DiagonalGaussian(Xmu, np.zeros((num_data, D_in))),
"dirac_markov_gauss":
MarkovGaussian(Xmu_markov, np.zeros((2, num_data + 1, D_in, D_in))),
"markov_gauss":
markov_gauss(),
def markov_gauss():
cov_params = rng.randn(num_data + 1, D_in, 2 * D_in) / 2. # (N+1)xDx2D
Xcov = cov_params @ np.transpose(cov_params, (0, 2, 1)) # (N+1)xDxD
Xcross = cov_params[:-1] @ np.transpose(cov_params[1:], (0, 2, 1)) # NxDxD
Xcross = np.concatenate((Xcross, np.zeros((1, D_in, D_in))),
0) # (N+1)xDxD
Xcov = np.stack([Xcov, Xcross]) # 2x(N+1)xDxD
return MarkovGaussian(Xmu_markov, ctt(Xcov))
_means = {
'lin': mf.Linear(A=rng.randn(D_in, D_out), b=rng.randn(D_out)),
'identity': mf.Identity(input_dim=D_in),
'const': mf.Constant(c=rng.randn(D_out)),
'zero': mf.Zero(output_dim=D_out)
}
_distrs = {
'gauss':
Gaussian(Xmu, Xcov),
'dirac_gauss':
Gaussian(Xmu, np.zeros((num_data, D_in, D_in))),
'gauss_diag':
DiagonalGaussian(Xmu, rng.rand(num_data, D_in)),
'dirac_diag':
DiagonalGaussian(Xmu, np.zeros((num_data, D_in))),
'dirac_markov_gauss':
MarkovGaussian(Xmu_markov, np.zeros((2, num_data + 1, D_in, D_in))),
'markov_gauss':
markov_gauss()
class Data:
rng = np.random.RandomState(1)
num_data = 5
num_ind = 4
D_in = 2
D_out = 2
Xmu = rng.randn(num_data, D_in)
L = gen_L(rng, num_data, D_in, D_in)
Xvar = np.array([l @ l.T for l in L])
Z = rng.randn(num_ind, D_in)
# distributions don't need to be compiled (No Parameter objects)
# but the members should be Tensors created in the same graph
graph = tf.Graph()
with test_util.session_context(graph) as sess:
gauss = Gaussian(tf.constant(Xmu), tf.constant(Xvar))
dirac = Gaussian(tf.constant(Xmu),
tf.constant(np.zeros((num_data, D_in, D_in))))
gauss_diag = DiagonalGaussian(tf.constant(Xmu),
tf.constant(rng.rand(num_data, D_in)))
dirac_diag = DiagonalGaussian(tf.constant(Xmu),
tf.constant(np.zeros((num_data, D_in))))
dirac_markov_gauss = MarkovGaussian(
tf.constant(Xmu), tf.constant(np.zeros((2, num_data, D_in, D_in))))
# create the covariance for the pairwise markov-gaussian
dummy_gen = lambda rng, n, *shape: np.array(
[rng.randn(*shape) for _ in range(n)])
L_mg = dummy_gen(rng, num_data, D_in, 2 * D_in) # N+1 x D x 2D
LL = np.concatenate((L_mg[:-1], L_mg[1:]), 1) # N x 2D x 2D
Xcov = LL @ np.transpose(LL, (0, 2, 1))
Xc = np.concatenate((Xcov[:, :D_in, :D_in], Xcov[-1:, D_in:, D_in:]),
0) # N+1 x D x D
Xcross = np.concatenate(
(Xcov[:, :D_in, D_in:], np.zeros(
(1, D_in, D_in))), 0) # N+1 x D x D
Xcc = np.stack([Xc, Xcross]) # 2 x N+1 x D x D
markov_gauss = MarkovGaussian(Xmu, Xcc)
with gpflow.decors.defer_build():
# features
ip = features.InducingPoints(Z)
# kernels
rbf_prod_seperate_dims = kernels.Product([
kernels.RBF(1,
variance=rng.rand(),
lengthscales=rng.rand(),
active_dims=[0]),
kernels.RBF(1,
variance=rng.rand(),
lengthscales=rng.rand(),
active_dims=[1])
])
rbf_lin_sum = kernels.Sum([
kernels.RBF(D_in, variance=rng.rand(), lengthscales=rng.rand()),
kernels.RBF(D_in, variance=rng.rand(), lengthscales=rng.rand()),
kernels.Linear(D_in, variance=rng.rand())
])
rbf = kernels.RBF(D_in, variance=rng.rand(), lengthscales=rng.rand())
lin_kern = kernels.Linear(D_in, variance=rng.rand())
# mean functions
lin = mean_functions.Linear(rng.rand(D_in, D_out), rng.rand(D_out))
iden = mean_functions.Identity(
D_in) # Note: Identity can only be used if Din == Dout
zero = mean_functions.Zero(output_dim=D_out)
const = mean_functions.Constant(rng.rand(D_out))