def test_mixture_of_mvn(self):
mu1 = np.asarray([0.0, 1.0])
cov1 = np.diag([1.5, 2.5])
mu2 = np.asarray([1.0, 0.0])
cov2 = np.diag([2.5, 3.5])
obs = np.asarray([[0.5, 0.5], mu1, mu2])
with Model() as model:
w = Dirichlet("w", floatX(np.ones(2)), transform=None, shape=(2,))
mvncomp1 = MvNormal.dist(mu=mu1, cov=cov1)
mvncomp2 = MvNormal.dist(mu=mu2, cov=cov2)
y = Mixture("x_obs", w, [mvncomp1, mvncomp2], observed=obs)
# check logp of each component
complogp_st = np.vstack(
(
st.multivariate_normal.logpdf(obs, mu1, cov1),
st.multivariate_normal.logpdf(obs, mu2, cov2),
)
).T
complogp = y.distribution._comp_logp(aesara.shared(obs)).eval()
assert_allclose(complogp, complogp_st)
# check logp of mixture
testpoint = model.recompute_initial_point()
mixlogp_st = logsumexp(np.log(testpoint["w"]) + complogp_st, axis=-1, keepdims=False)
assert_allclose(y.logp_elemwise(testpoint), mixlogp_st)
# check logp of model
priorlogp = st.dirichlet.logpdf(
x=testpoint["w"],
alpha=np.ones(2),
)
assert_allclose(model.logp(testpoint), mixlogp_st.sum() + priorlogp)
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)