def simple_categorical():
p = floatX_array([0.1, 0.2, 0.3, 0.4])
v = floatX_array([0.0, 1.0, 2.0, 3.0])
with Model() as model:
Categorical("x", p, size=3, initval=[1, 2, 3])
mu = np.dot(p, v)
var = np.dot(p, (v - mu)**2)
return model.compute_initial_point(), model, (mu, var)
def mv_simple():
mu = floatX_array([-0.1, 0.5, 1.1])
p = floatX_array([[2.0, 0, 0], [0.05, 0.1, 0], [1.0, -0.05, 5.5]])
tau = np.dot(p, p.T)
with pm.Model() as model:
pm.MvNormal(
"x",
at.constant(mu),
tau=at.constant(tau),
initval=floatX_array([0.1, 1.0, 0.8]),
)
H = tau
C = np.linalg.inv(H)
return model.compute_initial_point(), model, (mu, C)
def simple_model():
mu = -2.1
tau = 1.3
with Model() as model:
Normal("x", mu, tau=tau, size=2, initval=floatX_array([0.1, 0.1]))
return model.compute_initial_point(), model, (mu, tau**-0.5)
def mv_prior_simple():
n = 3
noise = 0.1
X = np.linspace(0, 1, n)[:, None]
K = pm.gp.cov.ExpQuad(1, 1)(X).eval()
L = np.linalg.cholesky(K)
K_noise = K + noise * np.eye(n)
obs = floatX_array([-0.1, 0.5, 1.1])
# Posterior mean
L_noise = np.linalg.cholesky(K_noise)
alpha = np.linalg.solve(L_noise.T, np.linalg.solve(L_noise, obs))
mu_post = np.dot(K.T, alpha)
# Posterior standard deviation
v = np.linalg.solve(L_noise, K)
std_post = (K - np.dot(v.T, v)).diagonal()**0.5
with pm.Model() as model:
x = pm.Flat("x", size=n)
x_obs = pm.MvNormal("x_obs", observed=obs, mu=x, cov=noise * np.eye(n))
return model.compute_initial_point(), model, (K, L, mu_post, std_post,
noise)
def simple_arbitrary_det():
scalar_type = at.dscalar if aesara.config.floatX == "float64" else at.fscalar
@as_op(itypes=[scalar_type], otypes=[scalar_type])
def arbitrary_det(value):
return value
with Model() as model:
a = Normal("a")
b = arbitrary_det(a)
Normal("obs", mu=b.astype("float64"), observed=floatX_array([1, 3, 5]))
return model.compute_initial_point(), model
def mv_simple_discrete():
d = 2
n = 5
p = floatX_array([0.15, 0.85])
with pm.Model() as model:
pm.Multinomial("x", n, at.constant(p), initval=np.array([1, 4]))
mu = n * p
# covariance matrix
C = np.zeros((d, d))
for (i, j) in product(range(d), range(d)):
if i == j:
C[i, i] = n * p[i] * (1 - p[i])
else:
C[i, j] = -n * p[i] * p[j]
return model.compute_initial_point(), model, (mu, C)
