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 theano.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)
l_w = Dirichlet('l_w', a=floatX(np.ones(nbr)*0.0000001), transform=None)
# 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)
mix = Mixture('mix', w=mix_w,
comp_dists=[g_mix, l_mix],
observed=np.exp(self.norm_x))
test_point = model.test_point
def mixmixlogp(value, point):
floatX = theano.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.,
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=True)
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([.1, .1, .2, .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)
def test_mixture_of_mixture(self):
if theano.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.test_point
def mixmixlogp(value, point):
floatX = theano.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)
def test_mixture_of_mixture(self):
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)
l_w = Dirichlet('l_w',
a=floatX(np.ones(nbr) * 0.0000001),
transform=None)
# 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)
mix = Mixture('mix',
w=mix_w,
comp_dists=[g_mix, l_mix],
observed=np.exp(self.norm_x))
test_point = model.test_point
def mixmixlogp(value, point):
priorlogp = st.dirichlet.logpdf(x=point['g_w'],
alpha=np.ones(nbr)*0.0000001,
) + \
st.expon.logpdf(x=point['mu_g']).sum() + \
st.dirichlet.logpdf(x=point['l_w'],
alpha=np.ones(nbr)*0.0000001,
) + \
st.expon.logpdf(x=point['mu_l']).sum() + \
st.dirichlet.logpdf(x=point['mix_w'],
alpha=np.ones(2),
)
complogp1 = st.norm.logpdf(x=value, loc=point['mu_g'])
mixlogp1 = logsumexp(np.log(point['g_w']) + complogp1,
axis=-1,
keepdims=True)
complogp2 = st.lognorm.logpdf(value, 1., 0., np.exp(point['mu_l']))
mixlogp2 = logsumexp(np.log(point['l_w']) + complogp2,
axis=-1,
keepdims=True)
complogp_mix = np.concatenate((mixlogp1, mixlogp2), axis=1)
mixmixlogpg = logsumexp(np.log(point['mix_w']) + complogp_mix,
axis=-1,
keepdims=True)
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))
# check model logp
assert_allclose(priorlogp + mixmixlogpg.sum(), model.logp(test_point))
# check input and check logp again
test_point['g_w'] = np.asarray([.1, .1, .2, .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))
assert_allclose(priorlogp + mixmixlogpg.sum(), model.logp(test_point))
