if j % 100 == 0:
print("[iteration %04d] loss: %.4f" % (j + 1, loss / len(data)))
guide.requires_grad_(False)
for name, value in pyro.get_param_store().items():
print(name, pyro.param(name))
guide.quantiles([0.25, 0.5, 0.75])
from pyro.infer import Predictive
def summary(samples):
site_stats = {}
for k, v in samples.items():
site_stats[k] = {
"mean": torch.mean(v, 0),
"std": torch.std(v, 0),
"5%": v.kthvalue(int(len(v) * 0.05), dim=0)[0],
def bayesian_regression(x_data, y_data, num_iterations):
# BAYESIAN REGRESSION WITH SVI
class BayesianRegression(PyroModule):
def __init__(self, in_features, out_features):
super().__init__()
self.linear = PyroModule[nn.Linear](in_features, out_features)
self.linear.weight = PyroSample(dist.Normal(0., 1.).expand([out_features, in_features]).to_event(2))
self.linear.bias = PyroSample(dist.Normal(0., 10.).expand([out_features]).to_event(1))
def forward(self, x, y=None):
# forward() specifies the data generating process
sigma = pyro.sample("sigma", dist.Uniform(0., 10.)) # this is the error term (typically called epsilon in regression equations)
mean = self.linear(x).squeeze(-1)
with pyro.plate("data", x.shape[0]):
obs = pyro.sample("obs", dist.Normal(mean, sigma), obs=y)
return mean
"""
Guides -- posterior distribution classes
The guide determines a family of distributions, and SVI aims to find an
approximate posterior distribution from this family that has the lowest
KL divergence from the true posterior.
"""
model = BayesianRegression(3, 1)
"""
Under the hood, this defines a guide that uses a Normal distribution with
learnable parameters corresponding to each sample statement in the model.
e.g. in our case, this distribution should have a size of (5,) correspoding
to the 3 regression coefficients for each of the terms, and 1 component
contributed each by the intercept term and sigma in the model.
"""
guide = AutoDiagonalNormal(model)
adam = pyro.optim.Adam({"lr": 0.03}) # note this is from Pyro's optim module, not PyTorch's
svi = SVI(model, guide, adam, loss=Trace_ELBO())
"""
We do not need to pass in learnable parameters to the optimizer
(unlike the PyTorch example above) since that is determined by the guide
code and happens behind the scenes within the SVI class automatically.
To take an ELBO gradient step we simply call the step method of SVI.
The data argument we pass to SVI.step will be passed to both
model() and guide().
"""
pyro.clear_param_store()
for j in range(num_iterations):
# calculate the loss and take a gradient step
loss = svi.step(x_data, y_data)
if (j+1) % 100 == 0:
print("[iteration %04d] loss: %.4f" % (j + 1, loss / len(data)))
# We can examine the optimized parameter values by fetching from Pyro’s param store.
guide.requires_grad_(False) # not sure what this does
for name, value in pyro.get_param_store().items():
print(name, pyro.param(name))
# This gets us quantiles from the posterior distribution
guide.quantiles([0.25, 0.5, 0.75])
"""
Since Bayesian models give you a posterior distribution,
model evalution needs to be a compbination of sampling the posterior and
running the samples through the model.
We generate 800 samples from our trained model. Internally, this is done
by first generating samples for the unobserved sites in the guide, and
then running the model forward by conditioning the sites to values sampled
from the guide. Refer to the Model Serving section for insight on how the
Predictive class works.
"""
def summary(samples):
site_stats = {}
for k, v in samples.items():
site_stats[k] = {
"mean": torch.mean(v, 0),
"std": torch.std(v, 0),
"5%": v.kthvalue(int(len(v) * 0.05), dim=0)[0],
"95%": v.kthvalue(int(len(v) * 0.95), dim=0)[0],
}
return site_stats
"""
Note that in return_sites, we specify both the outcome ("obs" site) as
well as the return value of the model ("_RETURN") which captures the
regression line. Additionally, we would also like to capture the regression
coefficients (given by "linear.weight") for further analysis.
"""
predictive = Predictive(model, guide=guide, num_samples=800,
return_sites=("linear.weight", "obs", "_RETURN"))
samples = predictive(x_data)
pred_summary = summary(samples)
