def get_joint_instance(self, query_points):
x = var2link(query_points)
return MultivariateNormalVariable(
loc=self.mean_function(x),
covariance_matrix=self.covariance_function(x),
name=self.name + "(" + query_points.name + ")")
h_mean2.append(h_mean)
z_mean2.append(z_mean)
lower_bound2.append(mean - sd)
upper_bound2.append(mean + sd)
MSE = np.mean((np.array(ground_truth) - np.array(x_mean2))**2)
var = 0.5 * (np.array(upper_bound2) - np.array(lower_bound2))**2
Lk = np.mean(0.5 *
(np.array(ground_truth) - np.array(x_mean2))**2 / var +
0.5 * np.log(var) + 0.5 * np.log(2 * np.pi))
print("MF MSE {}".format(MSE))
print("MF lk {}".format(Lk))
MSE2.append(MSE)
Lk2.append(Lk)
QV = MultivariateNormalVariable(loc=np.zeros((3 * T, )),
scale_tril=0.1 * np.identity(3 * T),
name="V",
learnable=True)
Qx = [DeterministicVariable(QV[0], 'x0')]
Qh = [DeterministicVariable(QV[0], 'h0')]
Qz = [DeterministicVariable(QV[0], 'z0')]
for t in range(1, T):
Qx.append(DeterministicVariable(x_mean2[t] + QV[t], x_names[t]))
Qh.append(DeterministicVariable(h_mean2[t] + QV[T + t],
h_names[t]))
Qz.append(
DeterministicVariable(z_mean2[t] + QV[2 * T + t], z_names[t]))
variational_posterior = ProbabilisticModel(Qx + Qh + Qz)
AR_model.set_posterior_model(variational_posterior)
# Inference #
inference.perform_inference(AR_model,
number_iterations=N_itr,
number_samples=N_smpl,
optimizer=optimizer,
lr=lr)
loss_list2 = AR_model.diagnostics["loss curve"]
# ELBO
ELBO2.append(float(AR_model.estimate_log_model_evidence(N_ELBO_smpl).detach().numpy()))
print("MF {}".format(ELBO2[-1]))
# Multivariate normal variational distribution #
QV = MultivariateNormalVariable(loc=np.zeros((T,)),
scale_tril=np.identity(T),
learnable=True)
Qx = [NormalVariable(QV[0], 0.1, 'x0', learnable=True)]
for t in range(1, T):
Qx.append(NormalVariable(QV[t], 0.1, x_names[t], learnable=True))
variational_posterior = ProbabilisticModel(Qx)
AR_model.set_posterior_model(variational_posterior)
# Inference #
inference.perform_inference(AR_model,
number_iterations=N_itr,
number_samples=N_smpl,
optimizer=optimizer,
lr=lr)
weights = NormalVariable(np.zeros((1, number_regressors)), 0.5*np.ones((1, number_regressors)), "weights")
x = DeterministicVariable(input_variable, "x", is_observed=True)
logit_p = BF.matmul(weights, x)
k = BinomialVariable(1, logit_p=logit_p, name="k")
model = ProbabilisticModel([k])
samples = model._get_sample(300)
# Observations
k.observe(labels)
# Variational Model
#Qweights = NormalVariable(np.zeros((1, number_regressors)),
# np.ones((1, number_regressors)), "weights", learnable=True)
Qweights = MultivariateNormalVariable(loc=np.zeros((1, number_regressors)),
covariance_matrix=np.identity(number_regressors),
name="weights", learnable=True)
variational_model = ProbabilisticModel([Qweights])
model.set_posterior_model(variational_model)
# Inference
inference.perform_inference(model,
number_iterations=3000,
number_samples=50,
optimizer='Adam',
lr=0.001)
loss_list = model.diagnostics["loss curve"]
# Statistics
posterior_samples = model._get_posterior_sample(1000)
import numpy as np
import matplotlib.pyplot as plt
from brancher.variables import ProbabilisticModel
from brancher.standard_variables import MultivariateNormalVariable
mean = np.zeros((2, 1))
chol_cov = np.array([[1., -1.], [0., 4.]])
x = MultivariateNormalVariable(mean, chol_cov=chol_cov)
number_samples = 500
samples = x._get_sample(number_samples)
for sample in samples[x].data:
plt.scatter(sample[0, 0, 0], sample[0, 1, 0], c="b")
plt.show()
mean = np.zeros((1, 2, 1))
diag_cov = np.ones((1, 2, 1))
y = MultivariateNormalVariable(mean, diag_cov=diag_cov)
number_samples = 500
samples = y._get_sample(number_samples)
for sample in samples[y].data:
plt.scatter(sample[0, 0, 0], sample[0, 1, 0], c="b")
plt.show()
for xt in x:
x_posterior_samples2 = posterior_samples2[xt].detach().numpy().flatten()
mean2 = np.mean(x_posterior_samples2)
sd2 = np.sqrt(np.var(x_posterior_samples2))
x_mean2.append(mean2)
lower_bound2.append(mean2 - sd2)
upper_bound2.append(mean2 + sd2)
# Multivariate normal variational distribution #
rank = 5
cov_factor = RootVariable(np.random.normal(0, 0.5, (T, rank)), "cov_factor")
cov_shift = RootVariable(0.01 * np.identity(T), "cov_shift", learnable=False)
mean_shift = RootVariable(np.zeros((T, )), "mean_shift", learnable=True)
QV = MultivariateNormalVariable(
loc=mean_shift,
covariance_matrix=cov_shift +
BF.matmul(cov_factor, BF.transpose(cov_factor, 2, 1)),
name="V",
learnable=True)
Qomega = NormalVariable(2 * np.pi * 8, 5., 'omega', learnable=True)
Qdrift = NormalVariable(0., 1., 'drift', learnable=True)
Qx = [NormalVariable(QV[0], 0.1, 'x0', learnable=True)]
for t in range(1, T):
Qx.append(NormalVariable(QV[t], 0.1, x_names[t], learnable=True))
variational_posterior = ProbabilisticModel([Qomega, Qdrift] + Qx)
AR_model.set_posterior_model(variational_posterior)
# Inference #
inference.perform_inference(AR_model,
number_iterations=N_itr,
number_samples=N_smpl,
import numpy as np
import matplotlib.pyplot as plt
from brancher.variables import ProbabilisticModel
from brancher.standard_variables import MultivariateNormalVariable
mean = np.zeros((2, 1))
covariance_matrix = np.array([[1., -0.3],
[-0.3, 1.]])
x = MultivariateNormalVariable(mean, covariance_matrix=covariance_matrix)
number_samples = 500
samples = x._get_sample(number_samples)
for sample in samples[x].data:
plt.scatter(sample[0, 0, 0], sample[0, 1, 0], c="b")
plt.show()