def test_logpdf():
m = Measure()
p1 = GP(EQ(), measure=m)
p2 = GP(Exp(), measure=m)
p3 = p1 + p2
x1 = B.linspace(0, 2, 5)
x2 = B.linspace(1, 3, 6)
x3 = B.linspace(2, 4, 7)
y1, y2, y3 = m.sample(p1(x1), p2(x2), p3(x3))
# Test case that only one process is fed.
approx(p1(x1).logpdf(y1), m.logpdf(p1(x1), y1))
approx(p1(x1).logpdf(y1), m.logpdf((p1(x1), y1)))
# Compute the logpdf with the product rule.
d1 = m
d2 = d1 | (p1(x1), y1)
d3 = d2 | (p2(x2), y2)
approx(
d1(p1)(x1).logpdf(y1) + d2(p2)(x2).logpdf(y2) + d3(p3)(x3).logpdf(y3),
m.logpdf((p1(x1), y1), (p2(x2), y2), (p3(x3), y3)),
)
# Check that `Measure.logpdf` allows `Obs` and `PseudoObs`.
obs = Obs(p3(x3), y3)
approx(m.logpdf(obs), p3(x3).logpdf(y3))
obs = PseudoObs(p3(x3), p3(x3, 1), y3)
approx(m.logpdf(obs), p3(x3, 1).logpdf(y3))
def test_pseudo_conditioning_and_elbo(generate_noise_tuple):
m = Measure()
p1 = GP(EQ(), measure=m)
p2 = GP(Exp(), measure=m)
p_sum = p1 + p2
# Sample some data to condition on.
x1 = B.linspace(0, 2, 3)
n1 = generate_noise_tuple(x1)
y1 = p1(x1, *n1).sample()
tup1 = (p1(x1, *n1), y1)
x_sum = B.linspace(3, 5, 3)
n_sum = generate_noise_tuple(x_sum)
y_sum = p_sum(x_sum, *n_sum).sample()
tup_sum = (p_sum(x_sum, *n_sum), y_sum)
# Determine FDDs to check.
x_check = B.linspace(0, 5, 5)
fdds_check = [
cross(p1, p2, p_sum)(x_check),
p1(x_check),
p2(x_check),
p_sum(x_check),
]
# Check conditioning and ELBO on one data set.
assert_equal_measures(
fdds_check,
m | tup_sum,
m | PseudoObs(p_sum(x_sum), *tup_sum),
m | PseudoObs((p_sum(x_sum), ), *tup_sum),
m | PseudoObs((p_sum(x_sum), p1(x1)), *tup_sum),
m | PseudoObs(p_sum(x_sum), tup_sum),
m | PseudoObs((p_sum(x_sum), ), tup_sum),
m.condition(PseudoObs((p_sum(x_sum), p1(x1)), tup_sum)),
)
approx(
m.logpdf(Obs(*tup_sum)),
PseudoObs(p_sum(x_sum), tup_sum).elbo(m),
)
# Check conditioning and ELBO on two data sets.
assert_equal_measures(
fdds_check,
m | (tup_sum, tup1),
m.condition(PseudoObs((p_sum(x_sum), p1(x1)), tup_sum, tup1)),
)
approx(
m.logpdf(Obs(tup_sum, tup1)),
PseudoObs((p_sum(x_sum), p1(x1)), tup_sum, tup1).elbo(m),
)
# The following lose information, so check them separately.
assert_equal_measures(
fdds_check,
m | PseudoObs(p_sum(x_sum), tup_sum, tup1),
m | PseudoObs((p_sum(x_sum), ), tup_sum, tup1),
)
# Test caching.
for name in ["K_z", "elbo", "mu", "A"]:
obs = PseudoObs(p_sum(x_sum), *tup_sum)
assert getattr(obs, name)(m) is getattr(obs, name)(m)
# Test requirement that noise must be diagonal.
with pytest.raises(RuntimeError):
PseudoObs(p_sum(x_sum), (p_sum(x_sum,
p_sum(x_sum).var), y_sum)).elbo(m)
# Test that noise on inducing points loses information.
with pytest.raises(AssertionError):
assert_equal_measures(
fdds_check,
m | tup_sum,
m | PseudoObs(p_sum(x_sum, 0.1), *tup_sum),
)