def test_dimensions(self):
a1 = Normal.dist(mu=0, sigma=1)
a2 = Normal.dist(mu=10, sigma=1)
mix = Mixture.dist(w=np.r_[0.5, 0.5], comp_dists=[a1, a2])
assert mix.mode.ndim == 0
assert mix.logp(0.0).ndim == 0
value = np.r_[0.0, 1.0, 2.0]
assert mix.logp(value).ndim == 1
def test_mixture_of_mixture(self):
if aesara.config.floatX == "float32":
rtol = 1e-4
else:
rtol = 1e-7
nbr = 4
with Model() as model:
# mixtures components
g_comp = Normal.dist(
mu=Exponential("mu_g", lam=1.0, shape=nbr, transform=None), sigma=1, shape=nbr
)
l_comp = LogNormal.dist(
mu=Exponential("mu_l", lam=1.0, shape=nbr, transform=None), sigma=1, shape=nbr
)
# weight vector for the mixtures
g_w = Dirichlet("g_w", a=floatX(np.ones(nbr) * 0.0000001), transform=None, shape=(nbr,))
l_w = Dirichlet("l_w", a=floatX(np.ones(nbr) * 0.0000001), transform=None, shape=(nbr,))
# mixture components
g_mix = Mixture.dist(w=g_w, comp_dists=g_comp)
l_mix = Mixture.dist(w=l_w, comp_dists=l_comp)
# mixture of mixtures
mix_w = Dirichlet("mix_w", a=floatX(np.ones(2)), transform=None, shape=(2,))
mix = Mixture("mix", w=mix_w, comp_dists=[g_mix, l_mix], observed=np.exp(self.norm_x))
test_point = model.recompute_initial_point()
def mixmixlogp(value, point):
floatX = aesara.config.floatX
priorlogp = (
st.dirichlet.logpdf(
x=point["g_w"],
alpha=np.ones(nbr) * 0.0000001,
).astype(floatX)
+ st.expon.logpdf(x=point["mu_g"]).sum(dtype=floatX)
+ st.dirichlet.logpdf(
x=point["l_w"],
alpha=np.ones(nbr) * 0.0000001,
).astype(floatX)
+ st.expon.logpdf(x=point["mu_l"]).sum(dtype=floatX)
+ st.dirichlet.logpdf(
x=point["mix_w"],
alpha=np.ones(2),
).astype(floatX)
)
complogp1 = st.norm.logpdf(x=value, loc=point["mu_g"]).astype(floatX)
mixlogp1 = logsumexp(
np.log(point["g_w"]).astype(floatX) + complogp1, axis=-1, keepdims=True
)
complogp2 = st.lognorm.logpdf(value, 1.0, 0.0, np.exp(point["mu_l"])).astype(floatX)
mixlogp2 = logsumexp(
np.log(point["l_w"]).astype(floatX) + complogp2, axis=-1, keepdims=True
)
complogp_mix = np.concatenate((mixlogp1, mixlogp2), axis=1)
mixmixlogpg = logsumexp(
np.log(point["mix_w"]).astype(floatX) + complogp_mix, axis=-1, keepdims=False
)
return priorlogp, mixmixlogpg
value = np.exp(self.norm_x)[:, None]
priorlogp, mixmixlogpg = mixmixlogp(value, test_point)
# check logp of mixture
assert_allclose(mixmixlogpg, mix.logp_elemwise(test_point), rtol=rtol)
# check model logp
assert_allclose(priorlogp + mixmixlogpg.sum(), model.logp(test_point), rtol=rtol)
# check input and check logp again
test_point["g_w"] = np.asarray([0.1, 0.1, 0.2, 0.6])
test_point["mu_g"] = np.exp(np.random.randn(nbr))
priorlogp, mixmixlogpg = mixmixlogp(value, test_point)
assert_allclose(mixmixlogpg, mix.logp_elemwise(test_point), rtol=rtol)
assert_allclose(priorlogp + mixmixlogpg.sum(), model.logp(test_point), rtol=rtol)