def make_model(cls):
with pm.Model() as model:
sd_mu = np.array([1, 2, 3, 4, 5])
sd_dist = pm.LogNormal.dist(mu=sd_mu, sigma=sd_mu / 10.0, size=5)
chol_packed = pm.LKJCholeskyCov("chol_packed", eta=3, n=5, sd_dist=sd_dist)
chol = pm.expand_packed_triangular(5, chol_packed, lower=True)
cov = at.dot(chol, chol.T)
stds = at.sqrt(at.diag(cov))
pm.Deterministic("log_stds", at.log(stds))
corr = cov / stds[None, :] / stds[:, None]
corr_entries_unit = (corr[np.tril_indices(5, -1)] + 1) / 2
pm.Deterministic("corr_entries_unit", corr_entries_unit)
return model
def test_sample_prior_and_posterior(self):
def build_toy_dataset(N, K):
pi = np.array([0.2, 0.5, 0.3])
mus = [[1, 1, 1], [-1, -1, -1], [2, -2, 0]]
stds = [[0.1, 0.1, 0.1], [0.1, 0.2, 0.2], [0.2, 0.3, 0.3]]
x = np.zeros((N, 3), dtype=np.float32)
y = np.zeros((N, ), dtype=np.int)
for n in range(N):
k = np.argmax(np.random.multinomial(1, pi))
x[n, :] = np.random.multivariate_normal(
mus[k], np.diag(stds[k]))
y[n] = k
return x, y
N = 100 # number of data points
K = 3 # number of mixture components
D = 3 # dimensionality of the data
X, y = build_toy_dataset(N, K)
with pm.Model() as model:
pi = pm.Dirichlet("pi", np.ones(K), shape=(K, ))
comp_dist = []
mu = []
packed_chol = []
chol = []
for i in range(K):
mu.append(pm.Normal("mu%i" % i, 0, 10, shape=D))
packed_chol.append(
pm.LKJCholeskyCov("chol_cov_%i" % i,
eta=2,
n=D,
sd_dist=pm.HalfNormal.dist(2.5)))
chol.append(
pm.expand_packed_triangular(D, packed_chol[i], lower=True))
comp_dist.append(
pm.MvNormal.dist(mu=mu[i], chol=chol[i], shape=D))
pm.Mixture("x_obs", pi, comp_dist, observed=X)
with model:
idata = pm.sample(30, tune=10, chains=1)
n_samples = 20
with model:
ppc = pm.sample_posterior_predictive(idata, n_samples)
prior = pm.sample_prior_predictive(samples=n_samples)
assert ppc["x_obs"].shape == (n_samples, ) + X.shape
assert prior["x_obs"].shape == (n_samples, ) + X.shape
assert prior["mu0"].shape == (n_samples, D)
assert prior["chol_cov_0"].shape == (n_samples, D * (D + 1) // 2)