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.examples.datasets import BOSTON_HOUSING, load_dataset
from numpyro.infer import Predictive, Trace_ELBO, init_to_uniform
from numpyro.infer.autoguide import AutoDelta
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)

    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):
    data = load_data()

    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,
        AutoDelta(model, init_loc_fn=partial(init_to_uniform, radius=0.1)),
        Adagrad(0.05),
        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)
    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(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()
    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-particles", type=int, default=100)
    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()

    numpyro.set_platform(args.device)

    main(args)