def test_logpdf(x, w):
prior = Measure()
f1, noise1 = GP(EQ(), measure=prior), 2e-1
f2, noise2 = GP(Linear(), measure=prior), 1e-1
gpar = GPAR().add_layer(lambda: (f1, noise1)).add_layer(lambda: (f2, noise2))
# Generate some data.
y = gpar.sample(x, w, latent=True)
# Compute logpdf.
x1 = x
x2 = B.concat(x, y[:, 0:1], axis=1)
logpdf1 = f1(x1, noise1 / w[:, 0]).logpdf(y[:, 0])
logpdf2 = f2(x2, noise2 / w[:, 1]).logpdf(y[:, 1])
# Test computation of GPAR.
assert gpar.logpdf(x, y, w) == logpdf1 + logpdf2
assert gpar.logpdf(x, y, w, only_last_layer=True) == logpdf2
# Test resuming computation.
x_partial, x_ind_partial = gpar.logpdf(x, y, w, return_inputs=True, outputs=[0])
assert gpar.logpdf(x_partial, y, w, x_ind=x_ind_partial, outputs=[1]) == logpdf2
# Test that sampling missing gives a stochastic estimate.
y[1, 0] = np.nan
all_different(
gpar.logpdf(x, y, w, sample_missing=True),
gpar.logpdf(x, y, w, sample_missing=True),
)
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_logpdf(x, w):
prior = Measure()
f1, e1 = GP(EQ(), measure=prior), GP(2e-1 * Delta(), measure=prior)
f2, e2 = GP(Linear(), measure=prior), GP(1e-1 * Delta(), measure=prior)
gpar = GPAR().add_layer(lambda: (f1, e1)).add_layer(lambda: (f2, e2))
# Generate some data.
y = gpar.sample(x, w, latent=True)
# Compute logpdf.
x1 = WeightedUnique(x, w[:, 0])
x2 = WeightedUnique(B.concat(x, y[:, 0:1], axis=1), w[:, 1])
logpdf1 = (f1 + e1)(x1).logpdf(y[:, 0])
logpdf2 = (f2 + e2)(x2).logpdf(y[:, 1])
# Test computation of GPAR.
assert gpar.logpdf(x, y, w) == logpdf1 + logpdf2
assert gpar.logpdf(x, y, w, only_last_layer=True) == logpdf2
# Test resuming computation.
x_partial, x_ind_partial = gpar.logpdf(x,
y,
w,
return_inputs=True,
outputs=[0])
assert gpar.logpdf(x_partial, y, w, x_ind=x_ind_partial,
outputs=[1]) == logpdf2
# Test that sampling missing gives a stochastic estimate.
y[1, 0] = np.nan
all_different(
gpar.logpdf(x, y, w, sample_missing=True),
gpar.logpdf(x, y, w, sample_missing=True),
)
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_sample(x, w):
prior = Measure()
# Test that it produces random samples.
f1, noise1 = GP(EQ(), measure=prior), 1e-1
f2, noise2 = GP(EQ(), measure=prior), 2e-1
gpar = GPAR().add_layer(lambda: (f1, noise1)).add_layer(lambda: (f2, noise2))
all_different(gpar.sample(x, w), gpar.sample(x, w))
all_different(gpar.sample(x, w, latent=True), gpar.sample(x, w, latent=True))
# Test that posterior latent samples are around the data that is conditioned on.
prior = Measure()
f1, noise1 = GP(EQ(), measure=prior), 1e-10
f2, noise2 = GP(EQ(), measure=prior), 2e-10
gpar = GPAR().add_layer(lambda: (f1, noise1)).add_layer(lambda: (f2, noise2))
y = gpar.sample(x, w, latent=True)
gpar = gpar | (x, y, w)
approx(gpar.sample(x, w), y, atol=1e-3)
approx(gpar.sample(x, w, latent=True), y, atol=1e-3)