K, d, N, T = 3, 4, 1000, 5000
# toy data generation
x_train = np.vstack([
inf.models.Normal(loc=0, scale=1, dim=d).sample(300),
inf.models.Normal(loc=10, scale=1, dim=d).sample(700)
])
######## Inferpy ##########
# model definition
with inf.ProbModel() as m:
# prior distributions
with inf.replicate(size=K):
mu = inf.models.Normal(loc=0, scale=1, dim=d)
sigma = inf.models.InverseGamma(
concentration=1,
rate=1,
dim=d,
)
p = inf.models.Dirichlet(np.ones(K) / K)
# define the generative model
with inf.replicate(size=N):
z = inf.models.Categorical(probs=p)
x = inf.models.Normal(mu[z], sigma[z], observed=True, dim=d)
# compile and fit the model with training data
data = {x: x_train}
# different ways of declaring 1 batch of 5 Normal distributions
x = inf.models.Normal(loc = 0, scale=1, dim=5) # x.shape = [5]
x = inf.models.Normal(loc = [0, 0, 0, 0, 0], scale=1) # x.shape = [5]
x = inf.models.Normal(loc = np.zeros(5), scale=1) # x.shape = [5]
x = inf.models.Normal(loc = 0, scale=tf.ones(5)) # x.shape = [5]
with inf.replicate(size=10):
x = inf.models.Normal(loc=0, scale=1, dim=5) # x.shape = [10,5]
x = inf.models.Normal(loc=0, scale=1, dim=5, batches=10) # x.shape = [10,5]
x = inf.models.Normal(loc=0, scale=1, dim=5, batches=[2,5]) # x.shape = [10,5]
y = x[7,4] # y.shape = [1]
y2 = x[7] # y2.shape = [5]
y3 = x[7,:] # y2.shape = [5]
y4 = x[:,4] # y4.shape = [10]
z = inf.models.Categorical(logits = np.zeros(5))
def test(self):
#### learning a 1-dim parameter from 1-dim data
N = 500
sampling_mean = [30.]
sampling_std = 0.000000001
sess = ed.util.get_session()
with inf.ProbModel() as m:
theta = inf.models.Normal(loc=0., scale=1.)
with inf.replicate(size=N):
x = inf.models.Normal(loc=theta, scale=1., observed=True)
m.compile()
x_train = inf.models.Normal(loc=sampling_mean, scale=sampling_std).sample(N)
data = {x.name: x_train}
m.fit(data)
p1 = m.posterior(theta).loc[0]
#### learning two 1-dim parameter from 2-dim data
sampling_mean = [30., 10.]
sess = ed.util.get_session()
with inf.ProbModel() as m:
theta1 = inf.models.Normal(loc=0., scale=1., dim=1)
theta2 = inf.models.Normal(loc=0., scale=1., dim=1)
with inf.replicate(size=N):
x = inf.models.Normal(loc=[theta1, theta2], scale=1., observed=True)
m.compile()
x_train = inf.models.Normal(loc=sampling_mean, scale=sampling_std).sample(N)
data = {x.name: x_train}
m.fit(data)
p3_1 = m.posterior(theta1).loc[0]
p3_2 = m.posterior(theta2).loc[0]
#### learning two 1-dim parameter from 2-dim data (with qmodel)
sampling_mean = [30., 10.]
sess = ed.util.get_session()
with inf.ProbModel() as m:
theta1 = inf.models.Normal(loc=0., scale=1., dim=1)
theta2 = inf.models.Normal(loc=0., scale=1., dim=1)
with inf.replicate(size=N):
x = inf.models.Normal(loc=[theta1, theta2], scale=1., observed=True)
# define the Qmodel
q_theta1 = inf.Qmodel.new_qvar(theta1)
q_theta2 = inf.Qmodel.new_qvar(theta2, initializer="ones")
qmodel = inf.Qmodel([q_theta1, q_theta2])
m.compile(Q=qmodel)
x_train = inf.models.Normal(loc=sampling_mean, scale=sampling_std).sample(N)
data = {x.name: x_train}
m.fit(data)
p4_1 = m.posterior(theta1).loc[0]
p4_2 = m.posterior(theta2).loc[0]
print(p4_1)
print(p4_2)
## asserts
self.assertTrue(abs(p1 - 29.66) < 0.1)
self.assertTrue(abs(p3_1-29.66)<0.1)
self.assertTrue(abs(p3_2-9.98)<0.1)
self.assertTrue(abs(p4_1 - 29.66) < 0.1)
self.assertTrue(abs(p4_2 - 9.98) < 0.1)
import inferpy as inf
with inf.replicate(size=50,name="A"):
# Define some random variables here
print("Variable replicated " + str(inf.replicate.get_total_size()) + " times")
with inf.replicate(size=10):
# Define some random variables here
print("Variable replicated " + str(inf.replicate.get_total_size()) + " times")
with inf.replicate(size=2, name="C"):
# Define some random variables here
print("Variable replicated " + str(inf.replicate.get_total_size()) + " times")
print(inf.replicate.in_replicate())
# Define some random variables here
print("Variable replicated " + str(inf.replicate.get_total_size()) + " times")
### existing replicate construct can be reused.
### This is done by ommiting the size argument and only setting the name with the name of
### an existing one.
with inf.replicate(name="A"):
with inf.replicate(name="C"):
# Define some random variables here
print("Variable replicated " + str(inf.replicate.get_total_size()) + " times")
def test(self):
# import the package for using it
sess = ed.get_session()
flag_y = True
f = 2
# graph
N = 1000 # number of observations
# model definition
with inf.ProbModel() as m:
# prior (latent variable)
beta = inf.models.Normal(loc=0, scale=1, name="beta")
w = inf.models.Normal(loc=0, scale=1, name="w")
b = inf.models.Normal(loc=0, scale=1, name="b")
betaz = inf.models.Normal(loc=0, scale=1, name="beta")
# observed variable
with inf.replicate(size=N):
z = inf.models.Normal(loc=betaz,
scale=1,
observed=False,
name="z")
x = inf.models.Normal(loc=beta + z,
scale=1,
observed=True,
name="x")
y = inf.models.Normal(loc=w * x + b + z,
scale=1,
observed=True,
name="y")
# toy data generation
x_train = inf.models.Normal(loc=10, scale=3, dim=1).sample(N)
y_train = x_train * f + inf.models.Normal(loc=1, scale=0.1,
dim=1).sample(N)
data = {x.name: x_train, y.name: y_train}
m.compile()
m.fit(data)
qbeta = m.posterior(beta)
qw = m.posterior(w)
qb = m.posterior(b)
qz = m.posterior(z)
x_test = inf.models.Normal(loc=10, scale=3, dim=1).sample(N)
y_test = x_test * f + inf.models.Normal(loc=1, scale=0.1,
dim=1).sample(N)
y_pred = m.predict(y, data={x: x_test})
self.assertTrue(np.max((y_pred - y_test) < 0.5))
inf.evaluate("log_lik",
data={
x: x_test,
y_pred: y_test
},
output_key=y_pred)
inf.evaluate("mean_squared_error",
data={
x: x_test,
y_pred: y_test
},
output_key=y_pred)
import inferpy as inf
with inf.replicate(size=50):
# Define some random variables here
print("Variable replicated " + str(inf.replicate.get_total_size()) +
" times")
with inf.replicate(size=10):
# Define some random variables here
print("Variable replicated " + str(inf.replicate.get_total_size()) +
" times")
with inf.replicate(size=2):
# Define some random variables here
print("Variable replicated " + str(inf.replicate.get_total_size()) +
" times")
print(inf.replicate.in_replicate())
# Define some random variables here
print("Variable replicated " + str(inf.replicate.get_total_size()) + " times")
print(inf.replicate.in_replicate())
def test(self):
inf.replicate.delete_all()
self.assertTrue(inf.replicate.in_replicate() == False)
self.assertTrue(inf.replicate.get_active_replicate() == [])
self.assertTrue(inf.replicate.get_all_replicate() == [])
self.assertTrue(inf.replicate.get_total_size() == 1)
with inf.replicate(size=5):
print(inf.replicate.get_active_replicate()[-1].name)
self.assertTrue(inf.replicate.in_replicate() == True)
self.assertTrue(len(inf.replicate.get_active_replicate()) == 1)
self.assertTrue(len(inf.replicate.get_all_replicate()) == 1)
self.assertTrue(inf.replicate.get_total_size() == 5)
with inf.replicate(size=5, name="A"):
print(inf.replicate.get_active_replicate()[-1].name)
self.assertTrue(inf.replicate.in_replicate() == True)
self.assertTrue(len(inf.replicate.get_active_replicate()) == 2)
self.assertTrue(len(inf.replicate.get_all_replicate()) == 2)
self.assertTrue(inf.replicate.get_total_size() == 25)
with inf.replicate(size=10, name="B"):
print(inf.replicate.get_active_replicate()[-1].name)
self.assertTrue(inf.replicate.in_replicate() == True)
self.assertTrue(len(inf.replicate.get_active_replicate()) == 2)
self.assertTrue(len(inf.replicate.get_all_replicate()) == 3)
self.assertTrue(inf.replicate.get_total_size() == 50)
with inf.replicate(name="A"):
print(inf.replicate.get_active_replicate()[-1].name)
with inf.replicate(name="B"):
print(inf.replicate.get_active_replicate()[-1].name)
self.assertTrue(inf.replicate.in_replicate() == True)
self.assertTrue(
len(inf.replicate.get_active_replicate()) == 3)
self.assertTrue(
len(inf.replicate.get_all_replicate()) == 3)
self.assertTrue(inf.replicate.get_total_size() == 250)
with inf.replicate(name="A"):
print(inf.replicate.get_active_replicate()[-1].name)
with inf.replicate(name="B"):
print(inf.replicate.get_active_replicate()[-1].name)
self.assertTrue(inf.replicate.in_replicate() == True)
self.assertTrue(len(inf.replicate.get_active_replicate()) == 2)
self.assertTrue(len(inf.replicate.get_all_replicate()) == 3)
self.assertTrue(inf.replicate.get_total_size() == 50)
with inf.replicate(size=2):
print(inf.replicate.get_active_replicate()[-1].name)
self.assertTrue(inf.replicate.in_replicate() == True)
self.assertTrue(
len(inf.replicate.get_active_replicate()) == 3)
self.assertTrue(
len(inf.replicate.get_all_replicate()) == 4)
self.assertTrue(inf.replicate.get_total_size() == 100)
self.assertTrue(inf.replicate.in_replicate() == False)
self.assertTrue(len(inf.replicate.get_active_replicate()) == 0)
self.assertTrue(len(inf.replicate.get_all_replicate()) == 4)
self.assertTrue(inf.replicate.get_total_size() == 1)
def test(self):
#### learning a 1-dim parameter from 1-dim data
N = 500
sampling_mean = [30.]
sampling_std = 0.000000001
sess = ed.util.get_session()
with inf.ProbModel() as m:
theta = inf.models.Normal(loc=0., scale=1.)
with inf.replicate(size=N):
x = inf.models.Normal(loc=theta, scale=1., observed=True)
m.compile()
x_train = inf.models.Normal(loc=sampling_mean,
scale=sampling_std).sample(N)
data = {x.name: x_train}
m.fit(data)
p1 = m.posterior(theta).loc[0]
#### learning a 2-dim parameter from 2-dim data
sampling_mean = [30., 10.]
sess = ed.util.get_session()
with inf.ProbModel() as m:
theta = inf.models.Normal(loc=0., scale=1., dim=2)
with inf.replicate(size=N):
x = inf.models.Normal(loc=theta, scale=1., observed=True)
m.compile()
x_train = inf.models.Normal(loc=sampling_mean,
scale=sampling_std).sample(N)
data = {x.name: x_train}
m.fit(data)
p2_1 = m.posterior(theta).loc[0]
p2_2 = m.posterior(theta).loc[1]
#### learning two 1-dim parameter from 2-dim data
sampling_mean = [30., 10.]
sess = ed.util.get_session()
with inf.ProbModel() as m:
theta1 = inf.models.Normal(loc=0., scale=1., dim=1)
theta2 = inf.models.Normal(loc=0., scale=1., dim=1)
with inf.replicate(size=N):
x = inf.models.Normal(loc=[theta1, theta2],
scale=1.,
observed=True)
m.compile()
x_train = inf.models.Normal(loc=sampling_mean,
scale=sampling_std).sample(N)
data = {x.name: x_train}
m.fit(data)
p3_1 = m.posterior(theta1).loc[0]
p3_2 = m.posterior(theta2).loc[0]
## asserts
print(p1)
print(p2_1)
print(p2_2)
print(p3_1)
print(p3_2)
self.assertTrue(abs(p1 - 29.66) < 0.1)
self.assertTrue(abs(p2_1 - 29.66) < 0.1)
self.assertTrue(abs(p2_2 - 9.98) < 0.1)
self.assertTrue(abs(p3_1 - 29.66) < 0.1)
self.assertTrue(abs(p3_2 - 9.98) < 0.1)
import inferpy as inf # define a 2-dimension Normal distribution of 2·3=6 batches with inf.replicate(size=2): with inf.replicate(size=3): x = inf.models.Normal(loc=0., scale=1., dim=2) # print its parameters print(x.loc) print(x.scale) # the shape of the distribution is (6,2) print(x.shape) # get a sample sample_x = x.sample([4,10]) # the shape of the sample is (4, 10, 6, 2) print(sample_x.shape) x.sample(1, tf_run=False) x.sample(1) # probability and log probability of the sample x.prob(sample_x) x.log_prob(sample_x)
def test(self):
N = 1
d = 1
with inf.replicate(size=N):
c = inf.models.Categorical(probs=[0.4, 0.6], dim=d)
m = inf.models.Multinomial(probs=[0.4, 0.2, 0.4],
total_count=5,
dim=d)
n = inf.models.Normal(0, 1, dim=d)
mn = inf.models.MultivariateNormalDiag(loc=[0, 0],
scale_diag=[1, 1],
dim=d)
D = [c, m, n, mn]
self.assertTrue([x.shape for x in D] == [[1], [1, 3], [1], [1, 2]])
self.assertTrue([x.dim for x in D] == [1, 1, 1, 1])
self.assertTrue([x.batches for x in D] == [1, 1, 1, 1])
self.assertTrue([x.event_shape for x in D] == [[], [3], [], [2]])
############
N = 10
d = 1
with inf.replicate(size=N):
c = inf.models.Categorical(probs=[0.4, 0.6], dim=d)
m = inf.models.Multinomial(probs=[0.4, 0.2, 0.4],
total_count=5,
dim=d)
n = inf.models.Normal(0, 1, dim=d)
mn = inf.models.MultivariateNormalDiag(loc=[0, 0],
scale_diag=[1, 1],
dim=d)
D = [c, m, n, mn]
self.assertTrue(
[x.shape for x in D] == [[10, 1], [10, 1, 3], [10, 1], [10, 1, 2]])
self.assertTrue([x.dim for x in D] == [d * i for i in [1, 1, 1, 1]])
self.assertTrue([x.batches
for x in D] == [N * i for i in [1, 1, 1, 1]])
self.assertTrue([x.event_shape for x in D] == [[], [3], [], [2]])
############
N = 1
d = 10
with inf.replicate(size=N):
c = inf.models.Categorical(probs=[0.4, 0.6], dim=d)
m = inf.models.Multinomial(probs=[0.4, 0.2, 0.4],
total_count=5,
dim=d)
n = inf.models.Normal(0, 1, dim=d)
mn = inf.models.MultivariateNormalDiag(loc=[0, 0],
scale_diag=[1, 1],
dim=d)
D = [c, m, n, mn]
self.assertTrue([x.shape for x in D] == [[10], [10, 3], [10], [10, 2]])
self.assertTrue([x.dim for x in D] == [d * i for i in [1, 1, 1, 1]])
self.assertTrue([x.batches
for x in D] == [N * i for i in [1, 1, 1, 1]])
self.assertTrue([x.event_shape for x in D] == [[], [3], [], [2]])
############
N = 10
d = 5
with inf.replicate(size=N):
c = inf.models.Categorical(probs=[0.4, 0.6], dim=d)
m = inf.models.Multinomial(probs=[0.4, 0.2, 0.4],
total_count=5,
dim=d)
n = inf.models.Normal(0, 1, dim=d)
mn = inf.models.MultivariateNormalDiag(loc=[0, 0],
scale_diag=[1, 1],
dim=d)
D = [c, m, n, mn]
self.assertTrue(
[x.shape for x in D] == [[10, 5], [10, 5, 3], [10, 5], [10, 5, 2]])
self.assertTrue([x.dim for x in D] == [d * i for i in [1, 1, 1, 1]])
self.assertTrue([x.batches
for x in D] == [N * i for i in [1, 1, 1, 1]])
self.assertTrue([x.event_shape for x in D] == [[], [3], [], [2]])
