Hello all,
I have been trying to implement a very simple linear regression based on the pyro tutorials.
When using MCMC to get my parameters posterior distributions, I am getting a strange behaviour with values being sampled remaining the same during the MCMC run. this lead to very low variance.
I was more expecting an output like the one described in this topic : Simple MCMC Linear Regression - #3 by ymp.
The code used is given below.
Can any of you provide me with some guidance?
Thank you in advance.
JPN
import matplotlib.pyplot as plt
import seaborn as sns
import numpy as np
import torch
import torch.nn as nn
import pyro
from pyro.infer import EmpiricalMarginal
from pyro.infer.mcmc import MCMC, NUTS
from pyro.distributions import Normal, Uniform
def generate_data(size = 30, true_intercept = 1, true_slope = 2):
#
# generating data
#
x = np.linspace(0, 1, size)
# y = a + b*x
true_regression_line = true_intercept + true_slope * x
# add noise
np.random.seed(453)
y = true_regression_line + np.random.normal(scale=.5, size=size)
return x, y, true_regression_line
# Linear regression class build from NN with only one linear level
class RegressionModel(nn.Module):
def __init__(self, p, q):
# p = number of features
# q = number of targets
super(RegressionModel, self).__init__()
self.linear = nn.Linear(p, q)
def forward(self, x):
return self.linear(x)
def Bayesian_model(x_data, y_data, n_features=1, n_outputs=1):
w_prior = Uniform(-7.*torch.ones(n_outputs, n_features),
7.*torch.ones(n_outputs, n_features))
b_prior = Uniform(-10.*torch.ones(n_outputs), 10.*torch.ones(n_outputs))
priors = {'linear.weight': w_prior, 'linear.bias': b_prior}
scale = pyro.sample("sigma", Uniform(0., 5.))
# lift module parameters to random variables sampled from the priors
lifted_module = pyro.random_module("module", regression_model, priors)
# sample a nn (which also samples w and b)
lifted_reg_model = lifted_module()
# run the nn forward on data
prediction_mean = lifted_reg_model(x_data)
#with pyro.plate("map"):
#with pyro.plate("data", len(x_data)):
# condition on the observed data
pyro.sample("obs",
Normal(prediction_mean, scale),
obs=y_data)
return prediction_mean
if __name__ == '__main__':
print("Pytorch version=", torch.__version__)
# data generation
x_data, y_data, true_regression_line = generate_data()
# display data & true regression line
fig = plt.figure(figsize=(7, 7))
ax = fig.add_subplot(111, xlabel='x', ylabel='y', title='Generated data and underlying model')
ax.plot(x_data, y_data, 'x', label='sampled data')
ax.plot(x_data, true_regression_line, label='true regression line', lw=2.)
plt.legend(loc=0);
plt.show()
x_data = torch.tensor(x_data, dtype=torch.float)
y_data = torch.tensor(y_data, dtype=torch.float)
# adding dummy dimension to 1D vector to allow matrix multiplication in nn.Linear
x_data.unsqueeze_(1)
y_data.unsqueeze_(1)
print("\nData size")
print("x:", x_data.shape)
print("y:", y_data.shape)
# Model definition
regression_model = RegressionModel(1, 1)
nuts_kernel = NUTS(Bayesian_model, adapt_step_size=False)
hmc_posterior = MCMC(nuts_kernel, num_samples=1000, warmup_steps=200) \
.run(x_data, y_data)
marginal_bias = EmpiricalMarginal(hmc_posterior, sites=['module$$$linear.bias'])
marginal_weight = EmpiricalMarginal(hmc_posterior, sites=['module$$$linear.weight'])
marginal_sigma = EmpiricalMarginal(hmc_posterior, sites=['sigma'])
print("\nWeight:")
print(" Mean=", marginal_weight.mean.item())
print("Variance=", marginal_weight.variance.item())
print("\nBias:")
print(" Mean=", marginal_bias.mean.item())
print("Variance=", marginal_bias.variance.item())
print("\nsigma:")
print(" Mean=", marginal_sigma.mean.item())
print("Variance=", marginal_sigma.variance.item())
sns.distplot(marginal_bias._get_samples_and_weights()[0].numpy())
plt.show()
MCMC is working as expected now.