def test_density_scaling_with_generator(self):
# We have different size generators
def true_dens():
g = gen1()
for i, point in enumerate(g):
yield stats.norm.logpdf(point).sum() * 10
t = true_dens()
# We have same size models
with pm.Model() as model1:
Normal("n", observed=gen1(), total_size=100)
p1 = aesara.function([], model1.logp())
with pm.Model() as model2:
gen_var = generator(gen2())
Normal("n", observed=gen_var, total_size=100)
p2 = aesara.function([], model2.logp())
for i in range(10):
_1, _2, _t = p1(), p2(), next(t)
decimals = select_by_precision(float64=7, float32=1)
np.testing.assert_almost_equal(
_1, _t, decimal=decimals) # Value O(-50,000)
np.testing.assert_almost_equal(_1, _2)
def test_joint_logp_subtensor():
"""Make sure we can compute a log-likelihood for ``Y[I]`` where ``Y`` and ``I`` are random variables."""
size = 5
mu_base = floatX(np.power(10, np.arange(np.prod(size)))).reshape(size)
mu = np.stack([mu_base, -mu_base])
sigma = 0.001
rng = aesara.shared(np.random.RandomState(232), borrow=True)
A_rv = Normal.dist(mu, sigma, rng=rng)
A_rv.name = "A"
p = 0.5
I_rv = Bernoulli.dist(p, size=size, rng=rng)
I_rv.name = "I"
A_idx = A_rv[I_rv, at.ogrid[A_rv.shape[-1]:]]
assert isinstance(A_idx.owner.op,
(Subtensor, AdvancedSubtensor, AdvancedSubtensor1))
A_idx_value_var = A_idx.type()
A_idx_value_var.name = "A_idx_value"
I_value_var = I_rv.type()
I_value_var.name = "I_value"
A_idx_logps = joint_logp(A_idx, {
A_idx: A_idx_value_var,
I_rv: I_value_var
},
sum=False)
A_idx_logp = at.add(*A_idx_logps)
logp_vals_fn = aesara.function([A_idx_value_var, I_value_var], A_idx_logp)
# The compiled graph should not contain any `RandomVariables`
assert_no_rvs(logp_vals_fn.maker.fgraph.outputs[0])
decimals = select_by_precision(float64=6, float32=4)
for i in range(10):
bern_sp = sp.bernoulli(p)
I_value = bern_sp.rvs(size=size).astype(I_rv.dtype)
norm_sp = sp.norm(mu[I_value, np.ogrid[mu.shape[1]:]], sigma)
A_idx_value = norm_sp.rvs().astype(A_idx.dtype)
exp_obs_logps = norm_sp.logpdf(A_idx_value)
exp_obs_logps += bern_sp.logpmf(I_value)
logp_vals = logp_vals_fn(A_idx_value, I_value)
np.testing.assert_almost_equal(logp_vals,
exp_obs_logps,
decimal=decimals)
def test_GARCH11():
# test data ~ N(0, 1)
data = np.array([
-1.35078362,
-0.81254164,
0.28918551,
-2.87043544,
-0.94353337,
0.83660719,
-0.23336562,
-0.58586298,
-1.36856736,
-1.60832975,
-1.31403141,
0.05446936,
-0.97213128,
-0.18928725,
1.62011258,
-0.95978616,
-2.06536047,
0.6556103,
-0.27816645,
-1.26413397,
])
omega = 0.6
alpha_1 = 0.4
beta_1 = 0.5
initial_vol = np.float64(0.9)
vol = np.empty_like(data)
vol[0] = initial_vol
for i in range(len(data) - 1):
vol[i + 1] = np.sqrt(omega + beta_1 * vol[i]**2 + alpha_1 * data[i]**2)
with Model() as t:
y = GARCH11(
"y",
omega=omega,
alpha_1=alpha_1,
beta_1=beta_1,
initial_vol=initial_vol,
shape=data.shape,
)
z = Normal("z", mu=0, sigma=vol, shape=data.shape)
garch_like = t["y"].logp({"z": data, "y": data})
reg_like = t["z"].logp({"z": data, "y": data})
decimal = select_by_precision(float64=7, float32=4)
np.testing.assert_allclose(garch_like, reg_like, 10**(-decimal))
def test_accuracy_non_normal():
_, model, (mu, _) = non_normal(4)
with model:
newstart = find_MAP(Point(x=[0.5, 0.01, 0.95, 0.99]))
close_to(newstart["x"], mu,
select_by_precision(float64=1e-5, float32=1e-4))
def test_accuracy_normal():
_, model, (mu, _) = simple_model()
with model:
newstart = find_MAP(Point(x=[-10.5, 100.5]))
close_to(newstart["x"], [mu, mu],
select_by_precision(float64=1e-5, float32=1e-4))