Open cdagher opened 11 months ago
Thanks, I'm glad you like Equinox! I've not tried that particular combination myself, so I don't have a ready-made example to hand. If anyone else has then maybe they can chime in.
For what it's worth, Equinox basically operates "at the same level" as JAX -- it's all just pytrees and eqx.Module
is really just a neat syntax for a parameterised function -- so I suspect this is probably doable. If you figure it out then I'd be happy to host an example in the docs.
I've only used numpyro a little, but as Patrick noted, equinox is pretty compatible with most jax libraries because it operates (or you can get it to operate) at a level very similar to jax itself. As an example, I did a simple adaptation of https://num.pyro.ai/en/0.7.1/examples/bnn.html (the equinox usage is simple, but it highlights some possibility, since there wasn't really a specific question).
import argparse
import os
import time
import matplotlib
import matplotlib.pyplot as plt
import numpy as np
from jax import vmap
import jax.numpy as jnp
import jax.random as random
import numpyro
from numpyro import handlers
import numpyro.distributions as dist
from numpyro.infer import MCMC, NUTS
import equinox as eqx
matplotlib.use("Agg") # noqa: E402
# the non-linearity we use in our neural network
def nonlin(x):
return jnp.tanh(x)
# a two-layer bayesian neural network with computational flow
# given by D_X => D_H => D_H => D_Y where D_H is the number of
# hidden units. (note we indicate tensor dimensions in the comments)
class Model(eqx.Module):
w1: dist.Normal
w2: dist.Normal
def __init__(self, D_X, D_H):
self.w1 = dist.Normal(jnp.zeros((D_X, D_H)), jnp.ones((D_X, D_H)))
self.w2 = dist.Normal(jnp.zeros((D_H, D_H)), jnp.ones((D_H, D_H)))
def __call__(self, X, Y, D_H, D_Y=1):
N, D_X = X.shape
# sample first layer (we put unit normal priors on all weights)
w1 = numpyro.sample("w1", self.w1)
assert w1.shape == (D_X, D_H)
z1 = nonlin(jnp.matmul(X, w1)) # <= first layer of activations
assert z1.shape == (N, D_H)
# sample second layer
w2 = numpyro.sample("w2", self.w2)
assert w2.shape == (D_H, D_H)
z2 = nonlin(jnp.matmul(z1, w2)) # <= second layer of activations
assert z2.shape == (N, D_H)
# sample final layer of weights and neural network output
w3 = numpyro.sample("w3", dist.Normal(jnp.zeros((D_H, D_Y)), jnp.ones((D_H, D_Y))))
assert w3.shape == (D_H, D_Y)
z3 = jnp.matmul(z2, w3) # <= output of the neural network
assert z3.shape == (N, D_Y)
# we put a prior on the observation noise
prec_obs = numpyro.sample("prec_obs", dist.Gamma(3.0, 1.0))
sigma_obs = 1.0 / jnp.sqrt(prec_obs)
# observe data
with numpyro.plate("data", N):
# note we use to_event(1) because each observation has shape (1,)
numpyro.sample("Y", dist.Normal(z3, sigma_obs).to_event(1), obs=Y)
# helper function for HMC inference
def run_inference(model, args, rng_key, X, Y, D_H):
start = time.time()
kernel = NUTS(model)
mcmc = MCMC(
kernel,
num_warmup=args.num_warmup,
num_samples=args.num_samples,
num_chains=args.num_chains,
progress_bar=False if "NUMPYRO_SPHINXBUILD" in os.environ else True,
)
mcmc.run(rng_key, X, Y, D_H)
mcmc.print_summary()
print("\nMCMC elapsed time:", time.time() - start)
return mcmc.get_samples()
# helper function for prediction
def predict(model, rng_key, samples, X, D_H):
model = handlers.substitute(handlers.seed(model, rng_key), samples)
# note that Y will be sampled in the model because we pass Y=None here
model_trace = handlers.trace(model).get_trace(X=X, Y=None, D_H=D_H)
return model_trace["Y"]["value"]
# create artificial regression dataset
def get_data(N=50, D_X=3, sigma_obs=0.05, N_test=500):
D_Y = 1 # create 1d outputs
np.random.seed(0)
X = jnp.linspace(-1, 1, N)
X = jnp.power(X[:, np.newaxis], jnp.arange(D_X))
W = 0.5 * np.random.randn(D_X)
Y = jnp.dot(X, W) + 0.5 * jnp.power(0.5 + X[:, 1], 2.0) * jnp.sin(4.0 * X[:, 1])
Y += sigma_obs * np.random.randn(N)
Y = Y[:, np.newaxis]
Y -= jnp.mean(Y)
Y /= jnp.std(Y)
assert X.shape == (N, D_X)
assert Y.shape == (N, D_Y)
X_test = jnp.linspace(-1.3, 1.3, N_test)
X_test = jnp.power(X_test[:, np.newaxis], jnp.arange(D_X))
return X, Y, X_test
def main(args):
N, D_X, D_H = args.num_data, 3, args.num_hidden
model = Model(D_X, D_H)
X, Y, X_test = get_data(N=N, D_X=D_X)
# do inference
rng_key, rng_key_predict = random.split(random.PRNGKey(0))
samples = run_inference(model, args, rng_key, X, Y, D_H)
# predict Y_test at inputs X_test
vmap_args = (
samples,
random.split(rng_key_predict, args.num_samples * args.num_chains),
)
predictions = vmap(
lambda samples, rng_key: predict(model, rng_key, samples, X_test, D_H)
)(*vmap_args)
predictions = predictions[..., 0]
# compute mean prediction and confidence interval around median
mean_prediction = jnp.mean(predictions, axis=0)
percentiles = np.percentile(predictions, [5.0, 95.0], axis=0)
# make plots
fig, ax = plt.subplots(figsize=(8, 6), constrained_layout=True)
# plot training data
ax.plot(X[:, 1], Y[:, 0], "kx")
# plot 90% confidence level of predictions
ax.fill_between(
X_test[:, 1], percentiles[0, :], percentiles[1, :], color="lightblue"
)
# plot mean prediction
ax.plot(X_test[:, 1], mean_prediction, "blue", ls="solid", lw=2.0)
ax.set(xlabel="X", ylabel="Y", title="Mean predictions with 90% CI")
plt.savefig("bnn_plot_eqx.pdf")
plt.show()
if __name__ == "__main__":
#assert numpyro.__version__.startswith("0.13.2")
#parser = argparse.ArgumentParser(description="Bayesian neural network example")
#parser.add_argument("-n", "--num-samples", nargs="?", default=2000, type=int)
#parser.add_argument("--num-warmup", nargs="?", default=1000, type=int)
#parser.add_argument("--num-chains", nargs="?", default=1, type=int)
#parser.add_argument("--num-data", nargs="?", default=100, type=int)
#parser.add_argument("--num-hidden", nargs="?", default=5, type=int)
#parser.add_argument("--device", default="cpu", type=str, help='use "cpu" or "gpu".')
#args = parser.parse_args()
from dataclasses import dataclass
@dataclass
class A:
num_samples: int = 2000
num_warmup: int = 1000
num_chains: int = 1
num_data: int = 100
num_hidden: int = 5
device: str = "gpu"
args = A()
numpyro.set_platform(args.device)
numpyro.set_host_device_count(args.num_chains)
main(args)
Yields
This is really an exploratory question about implementing a Bayesian layer in Equinox. My research requires Bayesian neural networks, and I've been playing with Equinox to see how it stacks up to Flax - definitely impressed with the ease of using Equinox.
I'm thinking that it shouldn't be too hard to add this functionality with another
Module
innn
, but I figured I'd throw the question out there and see if there are any other thoughts or suggestions. Maybe a library like NumPyro could be used alongside Equinox?