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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 Benchmark NumPyro in large dataset
This notebook uses numpyro and replicates experiments in references [1] which evaluates the performance of NUTS on various frameworks. The benchmark is run with CUDA 10.1 on a NVIDIA RTX 2070.
Step1:  We do preprocessing steps as in source code of reference [1]
Step2:  Now, we construct the model
Step3:  Benchmark HMC
Step4:  In CPU, we get avg. time for each step 
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Python Code:
!pip install -q numpyro@git+https://github.com/pyro-ppl/numpyro
import time
import numpy as np
import jax.numpy as jnp
from jax import random
import numpyro
import numpyro.distributions as dist
from numpyro.examples.datasets import COVTYPE, load_dataset
from numpyro.infer import HMC, MCMC, NUTS
assert numpyro.__version__.startswith("0.9.2")
# NB: replace gpu by cpu to run this notebook in cpu
numpyro.set_platform("gpu")
Explanation: Benchmark NumPyro in large dataset
This notebook uses numpyro and replicates experiments in references [1] which evaluates the performance of NUTS on various frameworks. The benchmark is run with CUDA 10.1 on a NVIDIA RTX 2070.
End of explanation
_, fetch = load_dataset(COVTYPE, shuffle=False)
features, labels = fetch()
# normalize features and add intercept
features = (features - features.mean(0)) / features.std(0)
features = jnp.hstack([features, jnp.ones((features.shape[0], 1))])
# make binary feature
_, counts = np.unique(labels, return_counts=True)
specific_category = jnp.argmax(counts)
labels = labels == specific_category
N, dim = features.shape
print("Data shape:", features.shape)
print(
    "Label distribution: {} has label 1, {} has label 0".format(
        labels.sum(), N - labels.sum()
    )
)
Explanation: We do preprocessing steps as in source code of reference [1]:
End of explanation
def model(data, labels):
    coefs = numpyro.sample("coefs", dist.Normal(jnp.zeros(dim), jnp.ones(dim)))
    logits = jnp.dot(data, coefs)
    return numpyro.sample("obs", dist.Bernoulli(logits=logits), obs=labels)
Explanation: Now, we construct the model:
End of explanation
step_size = jnp.sqrt(0.5 / N)
kernel = HMC(
    model,
    step_size=step_size,
    trajectory_length=(10 * step_size),
    adapt_step_size=False,
)
mcmc = MCMC(kernel, num_warmup=500, num_samples=500, progress_bar=False)
mcmc.warmup(random.PRNGKey(2019), features, labels, extra_fields=("num_steps",))
mcmc.get_extra_fields()["num_steps"].sum().copy()
tic = time.time()
mcmc.run(random.PRNGKey(2020), features, labels, extra_fields=["num_steps"])
num_leapfrogs = mcmc.get_extra_fields()["num_steps"].sum().copy()
toc = time.time()
print("number of leapfrog steps:", num_leapfrogs)
print("avg. time for each step :", (toc - tic) / num_leapfrogs)
mcmc.print_summary()
Explanation: Benchmark HMC
End of explanation
mcmc = MCMC(NUTS(model), num_warmup=50, num_samples=50, progress_bar=False)
mcmc.warmup(random.PRNGKey(2019), features, labels, extra_fields=("num_steps",))
mcmc.get_extra_fields()["num_steps"].sum().copy()
tic = time.time()
mcmc.run(random.PRNGKey(2020), features, labels, extra_fields=["num_steps"])
num_leapfrogs = mcmc.get_extra_fields()["num_steps"].sum().copy()
toc = time.time()
print("number of leapfrog steps:", num_leapfrogs)
print("avg. time for each step :", (toc - tic) / num_leapfrogs)
mcmc.print_summary()
Explanation: In CPU, we get avg. time for each step : 0.02782863507270813.
Benchmark NUTS
End of explanation
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