def test_combine():
x1 = B.linspace(0, 2, 10)
x2 = B.linspace(2, 4, 10)
m = Measure()
p1 = GP(EQ(), measure=m)
p2 = GP(Matern12(), measure=m)
y1 = p1(x1).sample()
y2 = p2(x2).sample()
# Check the one-argument case.
assert_equal_normals(combine(p1(x1, 1)), p1(x1, 1))
fdd_combined, y_combined = combine((p1(x1, 1), B.squeeze(y1)))
assert_equal_normals(fdd_combined, p1(x1, 1))
approx(y_combined, y1)
# Check the two-argument case.
fdd_combined = combine(p1(x1, 1), p2(x2, 2))
assert_equal_normals(
fdd_combined,
Normal(B.block_diag(p1(x1, 1).var,
p2(x2, 2).var)),
)
fdd_combined, y_combined = combine((p1(x1, 1), B.squeeze(y1)),
(p2(x2, 2), y2))
assert_equal_normals(
fdd_combined,
Normal(B.block_diag(p1(x1, 1).var,
p2(x2, 2).var)),
)
approx(y_combined, B.concat(y1, y2, axis=0))
def construct_model(vs):
kernels = [
vs.pos(1, name=f"{i}/var") *
Matern12().stretch(vs.pos(0.1, name=f"{i}/scale"))
for i in range(p)
]
noises = vs.pos(1e-2 * B.ones(p), name="noises")
return IGP(kernels, noises)
def construct_model(vs):
kernels = [
vs.pos(1, name=f"{i}/var") *
Matern12().stretch(vs.pos(0.1, name=f"{i}/scale"))
for i in range(m)
]
noise = vs.pos(1e-2, name="noise")
latent_noises = vs.pos(1e-2 * B.ones(m), name="latent_noises")
h = Dense(vs.get(shape=(p, m), name="h"))
return ILMMPP(kernels, h, noise, latent_noises)
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)
def construct_model(vs):
kernels = [
vs.pos(1, name=f"{i}/var") *
Matern12().stretch(vs.pos(0.1, name=f"{i}/scale"))
for i in range(m)
]
noise = vs.pos(1e-2, name="noise")
latent_noises = vs.pos(1e-2 * B.ones(m), name="latent_noises")
u = Dense(vs.orth(shape=(p, m), name="u"))
s_sqrt = Diagonal(vs.pos(shape=(m, ), name="s_sqrt"))
return OILMM(kernels, u, s_sqrt, noise, latent_noises)
def construct_model_ilmm_equivalent(vs):
kernels = [
vs.pos(1, name=f"{i}/var") *
Matern12().stretch(vs.pos(0.1, name=f"{i}/scale"))
for i in range(m)
]
noise = vs.pos(1e-2, name="noise")
latent_noises = vs.pos(1e-2 * B.ones(m), name="latent_noises")
u = vs.orth(shape=(p, m), name="u")
s_sqrt = vs.pos(shape=(m, ), name="s_sqrt")
h = Dense(u * s_sqrt[None, :])
return ILMMPP(kernels, h, noise, latent_noises)