def test_sample():
graph = Graph()
x = array([1, 2, 3])[:, None]
# Test that it produces random samples. Not sure how to test for
# correctness.
f1, e1 = GP(EQ(), graph=graph), GP(1e-1 * Delta(), graph=graph)
f2, e2 = GP(EQ(), graph=graph), GP(1e-1 * Delta(), graph=graph)
gpar = GPAR().add_layer(lambda: (f1, e1)).add_layer(lambda: (f2, e2))
yield ge, B.sum(B.abs(gpar.sample(x) - gpar.sample(x))), 1e-3
yield ge, \
B.sum(B.abs(gpar.sample(x, latent=True) -
gpar.sample(x, latent=True))), \
1e-3
# Test that posterior latent samples are around the data that is
# conditioned on.
graph = Graph()
f1, e1 = GP(EQ(), graph=graph), GP(1e-8 * Delta(), graph=graph)
f2, e2 = GP(EQ(), graph=graph), GP(1e-8 * Delta(), graph=graph)
gpar = GPAR().add_layer(lambda: (f1, e1)).add_layer(lambda: (f2, e2))
y = gpar.sample(x, latent=True)
gpar = gpar | (x, y)
yield approx, gpar.sample(x), y, 3
yield approx, gpar.sample(x, latent=True), y, 3
def test_logpdf():
graph = Graph()
f1, e1 = GP(EQ(), graph=graph), GP(2e-1 * Delta(), graph=graph)
f2, e2 = GP(Linear(), graph=graph), GP(1e-1 * Delta(), graph=graph)
gpar = GPAR().add_layer(lambda: (f1, e1)).add_layer(lambda: (f2, e2))
# Sample some data from GPAR.
x = B.linspace(0, 2, 10, dtype=torch.float64)[:, None]
y = gpar.sample(x, latent=True)
# Compute logpdf.
logpdf1 = (f1 + e1)(x).logpdf(y[:, 0])
logpdf2 = (f2 + e2)(B.concat([x, y[:, 0:1]], axis=1)).logpdf(y[:, 1])
# Test computation of GPAR.
yield eq, gpar.logpdf(x, y), logpdf1 + logpdf2
yield eq, gpar.logpdf(x, y, only_last_layer=True), logpdf2
# Test resuming computation.
x_int, x_ind_int = gpar.logpdf(x, y, return_inputs=True, outputs=[0])
yield eq, gpar.logpdf(x_int, y, x_ind=x_ind_int, outputs=[1]), logpdf2
# Test that sampling missing gives a stochastic estimate.
y[1, 0] = np.nan
yield ge, \
B.abs(gpar.logpdf(x, y, sample_missing=True) -
gpar.logpdf(x, y, sample_missing=True)).numpy(), \
1e-3
def test_conditioning():
graph = Graph()
f1, e1 = GP(EQ(), graph=graph), GP(1e-8 * Delta(), graph=graph)
f2, e2 = GP(EQ(), graph=graph), GP(2e-8 * Delta(), graph=graph)
gpar = GPAR().add_layer(lambda: (f1, e1)).add_layer(lambda: (f2, e2))
x = array([[1], [2], [3]])
y = array([[4, 5], [6, 7], [8, 9]])
gpar = gpar | (x, y)
# Extract posterior processes.
f1_post, e1_post = gpar.layers[0]()
f2_post, e2_post = gpar.layers[1]()
# Test independence of noises.
yield eq, graph.kernels[f1_post, e1_post], ZeroKernel()
yield eq, graph.kernels[f2_post, e2_post], ZeroKernel()
# Test form of noises.
yield eq, e1.mean, e1_post.mean
yield eq, e1.kernel, e1_post.kernel
yield eq, e2.mean, e2_post.mean
yield eq, e2.kernel, e2_post.kernel
# Test posteriors.
yield approx, f1_post.mean(x), y[:, 0:1]
yield approx, f2_post.mean(B.concat([x, y[:, 0:1]], axis=1)), y[:, 1:2]
def test_conditioning():
graph = Graph()
f1, e1 = GP(EQ(), graph=graph), GP(1e-8 * Delta(), graph=graph)
f2, e2 = GP(EQ(), graph=graph), GP(2e-8 * Delta(), graph=graph)
gpar = GPAR().add_layer(lambda: (f1, e1)).add_layer(lambda: (f2, e2))
x = tensor([[1], [2], [3]])
y = tensor([[4, 5],
[6, 7],
[8, 9]])
gpar = gpar | (x, y)
# Extract posterior processes.
f1_post, e1_post = gpar.layers[0]()
f2_post, e2_post = gpar.layers[1]()
# Test independence of noises.
assert graph.kernels[f1_post, e1_post] == ZeroKernel()
assert graph.kernels[f2_post, e2_post] == ZeroKernel()
# Test form of noises.
assert e1.mean == e1_post.mean
assert e1.kernel == e1_post.kernel
assert e2.mean == e2_post.mean
assert e2.kernel == e2_post.kernel
# Test posteriors.
approx(f1_post.mean(x), y[:, 0:1])
approx(f2_post.mean(B.concat(x, y[:, 0:1], axis=1)), y[:, 1:2])
def model(vs, m):
"""Construct model.
Args:
vs (:class:`varz.Vars`): Variable container.
m (int): Number of latent processes.
Returns:
tuple: Tuple containing a list of the latent processes, the
observation noise, and the noises on the latent processes.
"""
g = Graph()
# Observation noise:
noise_obs = vs.bnd(0.1, name='noise_obs')
def make_latent_process(i):
# Long-term trend:
variance = vs.bnd(0.9, name=f'{i}/long_term/var')
scale = vs.bnd(2 * 30, name=f'{i}/long_term/scale')
kernel = variance * EQ().stretch(scale)
# Short-term trend:
variance = vs.bnd(0.1, name=f'{i}/short_term/var')
scale = vs.bnd(20, name=f'{i}/short_term/scale')
kernel += variance * Matern12().stretch(scale)
return GP(kernel, graph=g)
# Latent processes:
xs = [make_latent_process(i) for i in range(m)]
# Latent noises:
noises_latent = vs.bnd(0.1 * B.ones(m), name='noises_latent')
return xs, noise_obs, noises_latent
def test_obs():
graph = Graph()
f = GP(EQ(), graph=graph)
e = GP(1e-8 * Delta(), graph=graph)
# Check that it produces the correct observations.
x = B.linspace(0, 0.1, 10, dtype=torch.float64)
y = f(x).sample()
# Set some observations to be missing.
y_missing = y.clone()
y_missing[::2] = np.nan
# Check dense case.
gpar = GPAR()
obs = gpar._obs(x, None, y_missing, f, e)
yield eq, type(obs), Obs
yield approx, y, (f | obs).mean(x)
# Check sparse case.
gpar = GPAR(x_ind=x)
obs = gpar._obs(x, x, y_missing, f, e)
yield eq, type(obs), SparseObs
yield approx, y, (f | obs).mean(x)
def test_update_inputs():
graph = Graph()
f = GP(EQ(), graph=graph)
x = array([[1], [2], [3]])
y = array([[4], [5], [6]])
res = B.concat([x, y], axis=1)
x_ind = array([[6], [7]])
res_ind = array([[6, 0], [7, 0]])
# Check vanilla case.
gpar = GPAR(x_ind=x_ind)
yield allclose, gpar._update_inputs(x, x_ind, y, f, None), (res, res_ind)
# Check imputation with prior.
gpar = GPAR(impute=True, x_ind=x_ind)
this_y = y.clone()
this_y[1] = np.nan
this_res = res.clone()
this_res[1, 1] = 0
yield allclose, \
gpar._update_inputs(x, x_ind, this_y, f, None), \
(this_res, res_ind)
# Check replacing with prior.
gpar = GPAR(replace=True, x_ind=x_ind)
this_y = y.clone()
this_y[1] = np.nan
this_res = res.clone()
this_res[0, 1] = 0
this_res[1, 1] = np.nan
this_res[2, 1] = 0
yield allclose, \
gpar._update_inputs(x, x_ind, this_y, f, None), \
(this_res, res_ind)
# Check imputation and replacing with prior.
gpar = GPAR(impute=True, replace=True, x_ind=x_ind)
this_res = res.clone()
this_res[:, 1] = 0
yield allclose, \
gpar._update_inputs(x, x_ind, y, f, None), \
(this_res, res_ind)
# Construct observations and update result for inducing points.
obs = Obs(f(array([1, 2, 3, 6, 7])), array([9, 10, 11, 12, 13]))
res_ind = array([[6, 12], [7, 13]])
# Check imputation with posterior.
gpar = GPAR(impute=True, x_ind=x_ind)
this_y = y.clone()
this_y[1] = np.nan
this_res = res.clone()
this_res[1, 1] = 10
yield allclose, \
gpar._update_inputs(x, x_ind, this_y, f, obs), \
(this_res, res_ind)
# Check replacing with posterior.
gpar = GPAR(replace=True, x_ind=x_ind)
this_y = y.clone()
this_y[1] = np.nan
this_res = res.clone()
this_res[0, 1] = 9
this_res[1, 1] = np.nan
this_res[2, 1] = 11
yield allclose, \
gpar._update_inputs(x, x_ind, this_y, f, obs), \
(this_res, res_ind)
# Check imputation and replacing with posterior.
gpar = GPAR(impute=True, replace=True, x_ind=x_ind)
this_res = res.clone()
this_res[0, 1] = 9
this_res[1, 1] = 10
this_res[2, 1] = 11
yield allclose, \
gpar._update_inputs(x, x_ind, y, f, obs), \
(this_res, res_ind)