Note
Go to the end to download the full example code.
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 config, nn, numpy as jnp, random
import numpyro
from numpyro import deterministic, plate, sample, set_platform, subsample
from numpyro.contrib.einstein import MixtureGuidePredictive, RBFKernel, SteinVI
from numpyro.distributions import Gamma, Normal
from numpyro.examples.datasets import BOSTON_HOUSING, load_dataset
from numpyro.infer.autoguide import AutoNormal
from numpyro.optim import Adagrad
DataState = namedtuple("data", ["xtr", "xte", "ytr", "yte"])
def load_data() -> DataState:
_, fetch = load_dataset(BOSTON_HOUSING, shuffle=False)
x, y = fetch()
xtr, xte, ytr, yte = train_test_split(x, y, train_size=0.90, random_state=1)
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, sub_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 = sample(
"prec_nn", Gamma(1.0, 0.1)
) # hyper prior for precision of nn weights and biases
n, m = x.shape
with plate("l1_hidden", hidden_dim, dim=-1):
# prior l1 bias term
b1 = sample(
"nn_b1",
Normal(
0.0,
1.0 / jnp.sqrt(prec_nn),
),
)
assert b1.shape == (hidden_dim,)
with plate("l1_feat", m, dim=-2):
w1 = sample(
"nn_w1", Normal(0.0, 1.0 / jnp.sqrt(prec_nn))
) # prior on l1 weights
assert w1.shape == (m, hidden_dim)
with plate("l2_hidden", hidden_dim, dim=-1):
w2 = sample(
"nn_w2", Normal(0.0, 1.0 / jnp.sqrt(prec_nn))
) # prior on output weights
b2 = sample(
"nn_b2", Normal(0.0, 1.0 / jnp.sqrt(prec_nn))
) # prior on output bias term
# precision prior on observations
prec_obs = sample("prec_obs", Gamma(1.0, 0.1))
with plate("data", x.shape[0], subsample_size=sub_size, dim=-1):
batch_x = subsample(x, event_dim=1)
if y is not None:
batch_y = subsample(y, event_dim=0)
else:
batch_y = y
loc_y = deterministic("y_bnn", nn.relu(batch_x @ w1 + b1) @ w2 + b2)
sample(
"y",
Normal(
loc_y, 1.0 / jnp.sqrt(prec_obs)
), # 1 hidden layer with ReLU activation
obs=batch_y,
)
def main(args):
data = load_data()
inf_key, pred_key, data_key = random.split(random.PRNGKey(args.rng_key), 3)
# Normalize features to zero mean unit variance.
x, xtr_mean, xtr_std = normalize(data.xtr)
rng_key, inf_key = random.split(inf_key)
guide = AutoNormal(model)
stein = SteinVI(
model,
guide,
Adagrad(1.0),
RBFKernel(),
repulsion_temperature=args.repulsion,
num_stein_particles=args.num_stein_particles,
num_elbo_particles=args.num_elbo_particles,
)
start = time()
# Use keyword params for static (shape etc.)
result = stein.run(
rng_key,
args.max_iter,
x,
data.ytr,
hidden_dim=args.hidden_dim,
sub_size=args.subsample_size,
progress_bar=args.progress_bar,
)
time_taken = time() - start
pred = MixtureGuidePredictive(
model,
guide=stein.guide,
params=stein.get_params(result.state),
num_samples=100,
guide_sites=stein.guide_sites,
)
xte, _, _ = normalize(
data.xte, xtr_mean, xtr_std
) # Use train data statistics when accessing generalization.
n = xte.shape[0]
pred_y = pred(pred_key, xte, sub_size=n, hidden_dim=args.hidden_dim)["y"]
rmse = jnp.sqrt(jnp.mean((pred_y.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
percentiles = jnp.percentile(pred_y, jnp.array([5.0, 95.0]), axis=0)
# Make plots
fig, ax = plt.subplots(figsize=(8, 6), constrained_layout=True)
ran = np.arange(pred_y.shape[1])
ax.add_collection(
LineCollection(
zip(zip(ran, percentiles[0]), zip(ran, percentiles[1])), colors="lightblue"
)
)
ax.plot(data.yte, "kx", label="y true")
ax.plot(pred_y.mean(0), "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__":
assert numpyro.__version__.startswith("0.18.0")
config.update("jax_debug_nans", True)
parser = argparse.ArgumentParser()
parser.add_argument("--subsample-size", type=int, default=100)
parser.add_argument("--max-iter", type=int, default=1000)
parser.add_argument("--repulsion", type=float, default=1.0)
parser.add_argument("--verbose", type=bool, default=True)
parser.add_argument("--num-elbo-particles", type=int, default=50)
parser.add_argument("--num-stein-particles", type=int, default=5)
parser.add_argument("--progress-bar", type=bool, default=True)
parser.add_argument("--rng-key", type=int, default=142)
parser.add_argument("--device", default="cpu", choices=["gpu", "cpu"])
parser.add_argument("--hidden-dim", default=50, type=int)
args = parser.parse_args()
set_platform(args.device)
main(args)