def test_logpdf():
m = Measure()
p1 = GP(EQ(), measure=m)
p2 = GP(Exp(), measure=m)
e = GP(Delta(), 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 `SparseObs`.
obs = Obs(p3(x3), y3)
approx(m.logpdf(obs), p3(x3).logpdf(y3))
obs = SparseObs(p3(x3), e, p3(x3), y3)
approx(m.logpdf(obs), (p3 + e)(x3).logpdf(y3))
def test_case_blr():
m = Measure()
x = B.linspace(0, 10, 100)
slope = GP(1, measure=m)
intercept = GP(1, measure=m)
f = slope * (lambda x: x) + intercept
y = f + 1e-2 * GP(Delta(), measure=m)
# Sample observations, true slope, and intercept.
y_obs, true_slope, true_intercept = m.sample(y(x), slope(0), intercept(0))
# Predict.
post = m | (y(x), y_obs)
approx(post(slope)(0).mean, true_slope, atol=5e-2)
approx(post(intercept)(0).mean, true_intercept, atol=5e-2)
def test_multi_sample():
m = Measure()
p1 = GP(1, 0, measure=m)
p2 = GP(2, 0, measure=m)
p3 = GP(3, 0, measure=m)
x1 = B.linspace(0, 1, 5)
x2 = B.linspace(0, 1, 10)
x3 = B.linspace(0, 1, 15)
s1, s2, s3 = m.sample(p1(x1), p2(x2), p3(x3))
assert B.shape(p1(x1).sample()) == s1.shape == (5, 1)
assert B.shape(p2(x2).sample()) == s2.shape == (10, 1)
assert B.shape(p3(x3).sample()) == s3.shape == (15, 1)
approx(s1, 1 * B.ones(5, 1))
approx(s2, 2 * B.ones(10, 1))
approx(s3, 3 * B.ones(15, 1))
def test_approximate_multiplication():
m = Measure()
p1 = GP(20, EQ(), measure=m)
p2 = GP(20, EQ(), measure=m)
p_prod = p1 * p2
# Sample functions.
x = B.linspace(0, 10, 50)
s1, s2 = m.sample(p1(x), p2(x))
# Perform product.
post = m | ((p1(x), s1), (p2(x), s2))
approx(post(p_prod)(x).mean, s1 * s2, rtol=1e-2)
# Perform division.
cur_epsilon = B.epsilon
B.epsilon = 1e-8
post = m | ((p1(x), s1), (p_prod(x), s1 * s2))
approx(post(p2)(x).mean, s2, rtol=1e-2)
B.epsilon = cur_epsilon