Comparison of beta bernoulli process in edward and pyro

Hello, pyro and pytorch beginner here. When I did code from pyro SVI tutorial:

# clear the param store in case we're in a REPL

# create some data with 6 observed heads and 4 observed tails
data = []
for _ in range(6):
for _ in range(4):

def model(data):
    # define the hyperparameters that control the beta prior
    alpha0 = Variable(torch.Tensor([10.0]))
    beta0 = Variable(torch.Tensor([10.0]))
    # sample f from the beta prior
    f = pyro.sample("latent_fairness", dist.beta, alpha0, beta0)
    # loop over the observed data
    for i in range(len(data)):
        # observe datapoint i using the bernoulli likelihood
        pyro.observe("obs_{}".format(i), dist.bernoulli, data[i], f)

def guide(data):
    # define the initial values of the two variational parameters
    # we initialize the guide near the model prior (except a bit sharper)
    log_alpha_q_0 = Variable(torch.Tensor([np.log(15.0)]), requires_grad=True)
    log_beta_q_0 = Variable(torch.Tensor([np.log(15.0)]), requires_grad=True)
    # register the two variational parameters with Pyro
    log_alpha_q = pyro.param("log_alpha_q", log_alpha_q_0)
    log_beta_q = pyro.param("log_beta_q", log_beta_q_0)
    alpha_q, beta_q = torch.exp(log_alpha_q), torch.exp(log_beta_q)
    # sample latent_fairness from Beta(alpha_q, beta_q)
    pyro.sample("latent_fairness", dist.beta, alpha_q, beta_q)

# setup the optimizer
adam_params = {"lr": 0.0005, "betas": (0.90, 0.999)}
optimizer = Adam(adam_params)

# setup the inference algorithm
svi = SVI(model, guide, optimizer, loss="ELBO", num_particles=7)

n_steps = 4000
# do gradient steps
start = time.time()

for step in range(n_steps):
    if step % 100 == 0:
        print('.', end='')
end = time.time()
print(start - end)
# grab the learned variational parameters
alpha_q = torch.exp(pyro.param("log_alpha_q")).data.numpy()[0]
beta_q = torch.exp(pyro.param("log_beta_q")).data.numpy()[0]

# here we use some facts about the beta distribution
# compute the inferred mean of the coin's fairness
inferred_mean = alpha_q / (alpha_q + beta_q)
# compute inferred standard deviation
factor = beta_q / (alpha_q * (1.0 + alpha_q + beta_q))
inferred_std = inferred_mean * np.sqrt(factor)

print("\nbased on the data and our prior belief, the fairness " +
      "of the coin is %.3f +- %.3f" % (inferred_mean, inferred_std))

I compared it with edward:

import edward as ed
from edward import models as mod
import tensorflow as tf
import matplotlib.pyplot as plt
import numpy as np
data = np.random.binomial(1, P, N_TRIAL)

graph = tf.Graph()
with graph.as_default():
    with tf.name_scope("input"):
        X = tf.constant(data, dtype=tf.int32)
    with tf.name_scope("model"):
        theta = mod.Beta(1.0,1.0)
        model = mod.Bernoulli(probs=tf.ones(N_TRIAL)*theta)
    with tf.name_scope("posterior"):
        alpha = tf.Variable(tf.ones(theta.shape) )
        beta = tf.Variable(tf.ones(theta.shape) )
        qtheta = mod.Beta(alpha, beta)

with tf.Session(graph=graph) as sess:
    n_iter = 3000
    loss = np.zeros(n_iter)
    inference = ed.KLqp(
            theta: qtheta,
        }, data={
            model: X,
    optimizer = tf.train.AdamOptimizer(0.0005,0.90, 0.999)
        n_iter=n_iter, optimizer=optimizer, n_samples=1, n_print=n_iter // 20)
    for i in range(inference.n_iter):
        info_dict = inference.update()
        loss[i] = info_dict["loss"]
        if i % inference.n_print == 0:

    alpha_result = alpha.eval()
    beta_result = beta.eval()
    theta_sample = qtheta.eval()
#, optimizer=optimizer)
plt.plot(range(n_iter), loss)


The execution time for pyro is about 10 minutes but edward code is about 13 seconds. Why pyro code is much slower than comparable edward code? I performed these code in non-gpu laptop with 8core cpu.

Hi @yusri_dh. Since these are all tiny tensors, I would expect Pyro to be around 10x slower than Edward, but 100x slower surprises me. One thing that would speed up your model is to make a vectorized observation:

data = torch.tensor([1.0] * 6 + [0.0] * 4)  # using Pyro 0.2 syntax
#data = Variable(torch.Tensor([1] * 6 + [0] * 4))  # in Pyro 0.1 syntax

def model(data):
    # observe all data at once
    with pyro.iarange("data", len(data)):

Thanks fritzo. I am sorry for late reply because I went on vacation last weekend. When I change my code as your suggestion. It becomes error:

ValueError: The event size for the data and distribution parameters must match.
Expected x.size()[-1] ==[-1], but got 10 vs 1

Also when I check my CPU load(using my first code), I think it is not distributed? Do I need to put something so the computation become parallel or it will be automatically distributed into my CPUs?

@yusri_dh I’ve updated the example by adding .expand_by(data.shape).independent(1). This should hopefully work in Pyro 0.2. If you’re using Pyro 0.1.2 you might try dist.Bernoulli(f.expand(data.shape)).

Thank you @fritzo . Now the code is faster even though still slower than Edward. As you expect it is 10x slower than Edward (120 seconds).
Why is pytorch slower than Edward in this case? Is it because of the backend, pytorch vs tensorflow?
In what case, pyro will be faster than Edward because in Dustin Tran’s blog it’s said pyro will be faster in CPU than Edward?
I want to use pyro because, in my old university server, it is difficult to install tensorflow and Edward (it needs a newer version of GCC).

PyTorch will be slower than Tensorflow for small tensor computations because Tensorflow can compile the computation graph and thereby avoid Python overhead. For larger tensor computations the two frameworks may be closer, though Tensorflow is still better at executing multiple tensor ops in parallel.

We’re currently looking into two ways to speed up Pyro:

  1. First we’re parallelizing gradient calculations to reduce variance. This can help in models with small tensors. Currently we only support parallelizing by hand (e.g. see, but we’re working to automate this.
  2. PyTorch has a JIT compiler that can help eliminate Python overhead. This may speed up Pyro models in the future.