# Example: Bayesian Neural Network with SteinVI¶

We demonstrate how to use SteinVI to predict housing prices using a BNN for the Boston Housing prices dataset from the UCI regression benchmarks.

import argparse
from collections import namedtuple
import datetime
from functools import partial
from time import time

from matplotlib.collections import LineCollection
import matplotlib.pyplot as plt
import numpy as np
from sklearn.model_selection import train_test_split

from jax import random
import jax.numpy as jnp

import numpyro
from numpyro.contrib.einstein import RBFKernel, SteinVI
from numpyro.distributions import Gamma, Normal
from numpyro.infer import Predictive, Trace_ELBO, init_to_uniform
from numpyro.infer.autoguide import AutoDelta

DataState = namedtuple("data", ["xtr", "xte", "ytr", "yte"])

x, y = fetch()
xtr, xte, ytr, yte = train_test_split(x, y, train_size=0.90)

return DataState(*map(partial(jnp.array, dtype=float), (xtr, xte, ytr, yte)))

def normalize(val, mean=None, std=None):
"""Normalize data to zero mean, unit variance"""
if mean is None and std is None:
# Only use training data to estimate mean and std.
std = jnp.std(val, 0, keepdims=True)
std = jnp.where(std == 0, 1.0, std)
mean = jnp.mean(val, 0, keepdims=True)
return (val - mean) / std, mean, std

def model(x, y=None, hidden_dim=50, subsample_size=100):
"""BNN described in section 5 of [1].

**References:**
1. *Stein variational gradient descent: A general purpose bayesian inference algorithm*
Qiang Liu and Dilin Wang (2016).
"""

prec_nn = numpyro.sample(
"prec_nn", Gamma(1.0, 0.1)
)  # hyper prior for precision of nn weights and biases

n, m = x.shape

with numpyro.plate("l1_hidden", hidden_dim, dim=-1):
# prior l1 bias term
b1 = numpyro.sample(
"nn_b1",
Normal(
0.0,
1.0 / jnp.sqrt(prec_nn),
),
)
assert b1.shape == (hidden_dim,)

with numpyro.plate("l1_feat", m, dim=-2):
w1 = numpyro.sample(
"nn_w1", Normal(0.0, 1.0 / jnp.sqrt(prec_nn))
)  # prior on l1 weights
assert w1.shape == (m, hidden_dim)

with numpyro.plate("l2_hidden", hidden_dim, dim=-1):
w2 = numpyro.sample(
"nn_w2", Normal(0.0, 1.0 / jnp.sqrt(prec_nn))
)  # prior on output weights

b2 = numpyro.sample(
"nn_b2", Normal(0.0, 1.0 / jnp.sqrt(prec_nn))
)  # prior on output bias term

# precision prior on observations
prec_obs = numpyro.sample("prec_obs", Gamma(1.0, 0.1))
with numpyro.plate(
"data",
x.shape[0],
subsample_size=subsample_size,
dim=-1,
):
batch_x = numpyro.subsample(x, event_dim=1)
if y is not None:
batch_y = numpyro.subsample(y, event_dim=0)
else:
batch_y = y

numpyro.sample(
"y",
Normal(
jnp.maximum(batch_x @ w1 + b1, 0) @ w2 + b2, 1.0 / jnp.sqrt(prec_obs)
),  # 1 hidden layer with ReLU activation
obs=batch_y,
)

def main(args):

inf_key, pred_key, data_key = random.split(random.PRNGKey(args.rng_key), 3)
# normalize data and labels to zero mean unit variance!
x, xtr_mean, xtr_std = normalize(data.xtr)
y, ytr_mean, ytr_std = normalize(data.ytr)

rng_key, inf_key = random.split(inf_key)

stein = SteinVI(
model,
Trace_ELBO(20),  # estimate elbo with 20 particles (not stein particles!)
RBFKernel(),
repulsion_temperature=args.repulsion,
num_particles=args.num_particles,
)
start = time()

# use keyword params for static (shape etc.)!
result = stein.run(
rng_key,
args.max_iter,
x,
y,
hidden_dim=args.hidden_dim,
subsample_size=args.subsample_size,
progress_bar=args.progress_bar,
)
time_taken = time() - start

pred = Predictive(
model,
guide=stein.guide,
params=stein.get_params(result.state),
num_samples=200,
batch_ndims=1,  # stein particle dimension
)
xte, _, _ = normalize(
data.xte, xtr_mean, xtr_std
)  # use train data statistics when accessing generalization
preds = pred(
pred_key, xte, subsample_size=xte.shape[0], hidden_dim=args.hidden_dim
)["y"]

y_pred = jnp.mean(preds, 1) * ytr_std + ytr_mean
rmse = jnp.sqrt(jnp.mean((y_pred.mean(0) - data.yte) ** 2))

print(rf"Time taken: {datetime.timedelta(seconds=int(time_taken))}")
print(rf"RMSE: {rmse:.2f}")

# compute mean prediction and confidence interval around median
mean_prediction = jnp.mean(y_pred, 0)

ran = np.arange(mean_prediction.shape[0])
percentiles = np.percentile(
preds.reshape(-1, xte.shape[0]) * ytr_std + ytr_mean, [5.0, 95.0], axis=0
)

# make plots
fig, ax = plt.subplots(figsize=(8, 6), constrained_layout=True)
LineCollection(
zip(zip(ran, percentiles[0]), zip(ran, percentiles[1])), colors="lightblue"
)
)
ax.plot(data.yte, "kx", label="y true")
ax.plot(mean_prediction, "ko", label="y pred")
ax.set(xlabel="example", ylabel="y", title="Mean predictions with 90% CI")
ax.legend()
fig.savefig("stein_bnn.pdf")

if __name__ == "__main__":
from jax.config import config

config.update("jax_debug_nans", True)

parser = argparse.ArgumentParser()