def sample(model, t, noise_f):
"""Sample from a model.
Args:
model (:class:`gpcm.model.AbstractGPCM`): Model to sample from.
t (vector): Time points to sample at.
noise_f (vector): Noise for the sample of the function. Should have the
same size as `t`.
Returns:
tuple[vector, ...]: Tuple containing kernel samples, filter samples, and
function samples.
"""
ks, us, fs = [], [], []
# In the below, we look at the third inducing point, because that is the one
# determining the value of the filter at zero: the CGPCM adds two extra inducing
# points to the left.
# Get a smooth sample.
u1 = B.ones(model.n_u)
while B.abs(u1[2]) > 1e-2:
u1 = B.sample(model.compute_K_u())[:, 0]
u = GP(model.k_h())
u = u | (u(model.t_u), u1)
u1_full = u(t).mean.flatten()
# Get a rough sample.
u2 = B.zeros(model.n_u)
while u2[2] < 0.5:
u2 = B.sample(model.compute_K_u())[:, 0]
u = GP(model.k_h())
u = u | (u(model.t_u), u2)
u2_full = u(t).mean.flatten()
with wbml.out.Progress(name="Sampling", total=5) as progress:
for c in [0, 0.1, 0.23, 0.33, 0.5]:
# Sample kernel.
K = model.kernel_approx(t, t, c * u2 + (1 - c) * u1)
wbml.out.kv("Sampled variance", K[0, 0])
K = K / K[0, 0]
ks.append(K[0, :])
# Store filter.
us.append(c * u2_full + (1 - c) * u1_full)
# Sample function.
f = B.matmul(B.chol(closest_psd(K)), noise_f)
fs.append(f)
progress()
return ks, us, fs
def sample(model, t, noise_f):
"""Sample from a model.
Args:
model (:class:`gpcm.model.AbstractGPCM`): Model to sample from.
t (vector): Time points to sample at.
noise_f (vector): Noise for the sample of the function. Should have the
same size as `t`.
Returns:
tuple[vector]: Tuple containing kernel samples and function samples.
"""
ks, fs = [], []
with wbml.out.Progress(name="Sampling", total=5) as progress:
for i in range(5):
# Sample kernel.
u = B.sample(model.compute_K_u())[:, 0]
K = model.kernel_approx(t, t, u)
wbml.out.kv("Sampled variance", K[0, 0])
K = K / K[0, 0]
ks.append(K[0, :])
# Sample function.
f = B.matmul(B.chol(closest_psd(K)), noise_f)
fs.append(f)
progress()
return ks, fs
def test_prior_power(Model):
t_u = B.zeros(1)
model = Model(window=2, scale=1, n_u=10, t=(0, 10))
K_u = model.compute_K_u()
# Estimate power with Monte Carlo.
powers = []
for _ in range(2_000):
u = B.sample(K_u)[:, 0]
powers.append(model.kernel_approx(t_u, t_u, u)[0, 0])
def test_sample_conversion():
const = Constant(1, 5, 5)
sample = B.sample(const)
assert B.issubdtype(B.dtype(sample), np.floating)
def _est_cov(a):
num = 500_000
samples = B.dense(B.sample(a, num=num))
cov_est = B.matmul(samples, samples, tr_b=True) / num
err = B.max(B.abs(B.dense(a) - cov_est)) / B.max(B.abs(B.dense(a)))
assert err < 1e-1
def sample(a: Woodbury, num=1):
return B.sample(a.diag, num=num) + B.sample(a.lr, num=num)