def test_logpdf_missing_data():
# Setup model.
m = 3
noise = 1e-2
latent_noises = 2e-2 * B.ones(m)
kernels = [0.5 * EQ().stretch(0.75) for _ in range(m)]
x = B.linspace(0, 10, 20)
# Concatenate two orthogonal matrices, to make the missing data
# approximation exact.
u1 = B.svd(B.randn(m, m))[0]
u2 = B.svd(B.randn(m, m))[0]
u = Dense(B.concat(u1, u2, axis=0) / B.sqrt(2))
s_sqrt = Diagonal(B.rand(m))
# Construct a reference model.
oilmm_pp = ILMMPP(kernels, u @ s_sqrt, noise, latent_noises)
# Sample to generate test data.
y = oilmm_pp.sample(x, latent=False)
# Throw away data, but retain orthogonality.
y[5:10, 3:] = np.nan
y[10:, :3] = np.nan
# Construct OILMM to test.
oilmm = OILMM(kernels, u, s_sqrt, noise, latent_noises)
# Check that evidence is still exact.
approx(oilmm_pp.logpdf(x, y), oilmm.logpdf(x, y), atol=1e-7)
def test_compare_ilmm():
# Setup models.
kernels = [EQ(), 2 * EQ().stretch(1.5)]
noise_obs = 0.1
noises_latent = np.array([0.1, 0.2])
u, s_sqrt = B.svd(B.randn(3, 2))[:2]
u = Dense(u)
s_sqrt = Diagonal(s_sqrt)
# Construct models.
ilmm = ILMMPP(kernels, u @ s_sqrt, noise_obs, noises_latent)
oilmm = OILMM(kernels, u, s_sqrt, noise_obs, noises_latent)
# Construct data.
x = B.linspace(0, 3, 5)
y = ilmm.sample(x, latent=False)
x2 = B.linspace(4, 7, 5)
y2 = ilmm.sample(x2, latent=False)
# Check LML before conditioning.
approx(ilmm.logpdf(x, y), oilmm.logpdf(x, y))
approx(ilmm.logpdf(x2, y2), oilmm.logpdf(x2, y2))
ilmm = ilmm.condition(x, y)
oilmm = oilmm.condition(x, y)
# Check LML after conditioning.
approx(ilmm.logpdf(x, y), oilmm.logpdf(x, y))
approx(ilmm.logpdf(x2, y2), oilmm.logpdf(x2, y2))
# Predict.
means_pp, lowers_pp, uppers_pp = ilmm.predict(x2)
means, lowers, uppers = oilmm.predict(x2)
# Check predictions.
approx(means_pp, means)
approx(lowers_pp, lowers)
approx(uppers_pp, uppers)