def main(args):
print("Start vanilla HMC...")
nuts_kernel = NUTS(dual_moon_model)
mcmc = MCMC(
nuts_kernel,
args.num_warmup,
args.num_samples,
num_chains=args.num_chains,
progress_bar=False if "NUMPYRO_SPHINXBUILD" in os.environ else True,
)
mcmc.run(random.PRNGKey(0))
mcmc.print_summary()
vanilla_samples = mcmc.get_samples()["x"].copy()
guide = AutoBNAFNormal(
dual_moon_model,
hidden_factors=[args.hidden_factor, args.hidden_factor])
svi = SVI(dual_moon_model, guide, optim.Adam(0.003), Trace_ELBO())
print("Start training guide...")
svi_result = svi.run(random.PRNGKey(1), args.num_iters)
print("Finish training guide. Extract samples...")
guide_samples = guide.sample_posterior(
random.PRNGKey(2),
svi_result.params,
sample_shape=(args.num_samples, ))["x"].copy()
print("\nStart NeuTra HMC...")
neutra = NeuTraReparam(guide, svi_result.params)
neutra_model = neutra.reparam(dual_moon_model)
nuts_kernel = NUTS(neutra_model)
mcmc = MCMC(
nuts_kernel,
args.num_warmup,
args.num_samples,
num_chains=args.num_chains,
progress_bar=False if "NUMPYRO_SPHINXBUILD" in os.environ else True,
)
mcmc.run(random.PRNGKey(3))
mcmc.print_summary()
zs = mcmc.get_samples(group_by_chain=True)["auto_shared_latent"]
print("Transform samples into unwarped space...")
samples = neutra.transform_sample(zs)
print_summary(samples)
zs = zs.reshape(-1, 2)
samples = samples["x"].reshape(-1, 2).copy()
# make plots
# guide samples (for plotting)
guide_base_samples = dist.Normal(jnp.zeros(2),
1.0).sample(random.PRNGKey(4), (1000, ))
guide_trans_samples = neutra.transform_sample(guide_base_samples)["x"]
x1 = jnp.linspace(-3, 3, 100)
x2 = jnp.linspace(-3, 3, 100)
X1, X2 = jnp.meshgrid(x1, x2)
P = jnp.exp(DualMoonDistribution().log_prob(jnp.stack([X1, X2], axis=-1)))
fig = plt.figure(figsize=(12, 8), constrained_layout=True)
gs = GridSpec(2, 3, figure=fig)
ax1 = fig.add_subplot(gs[0, 0])
ax2 = fig.add_subplot(gs[1, 0])
ax3 = fig.add_subplot(gs[0, 1])
ax4 = fig.add_subplot(gs[1, 1])
ax5 = fig.add_subplot(gs[0, 2])
ax6 = fig.add_subplot(gs[1, 2])
ax1.plot(svi_result.losses[1000:])
ax1.set_title("Autoguide training loss\n(after 1000 steps)")
ax2.contourf(X1, X2, P, cmap="OrRd")
sns.kdeplot(x=guide_samples[:, 0],
y=guide_samples[:, 1],
n_levels=30,
ax=ax2)
ax2.set(
xlim=[-3, 3],
ylim=[-3, 3],
xlabel="x0",
ylabel="x1",
title="Posterior using\nAutoBNAFNormal guide",
)
sns.scatterplot(
x=guide_base_samples[:, 0],
y=guide_base_samples[:, 1],
ax=ax3,
hue=guide_trans_samples[:, 0] < 0.0,
)
ax3.set(
xlim=[-3, 3],
ylim=[-3, 3],
xlabel="x0",
ylabel="x1",
title="AutoBNAFNormal base samples\n(True=left moon; False=right moon)",
)
ax4.contourf(X1, X2, P, cmap="OrRd")
sns.kdeplot(x=vanilla_samples[:, 0],
y=vanilla_samples[:, 1],
n_levels=30,
ax=ax4)
ax4.plot(vanilla_samples[-50:, 0],
vanilla_samples[-50:, 1],
"bo-",
alpha=0.5)
ax4.set(
xlim=[-3, 3],
ylim=[-3, 3],
xlabel="x0",
ylabel="x1",
title="Posterior using\nvanilla HMC sampler",
)
sns.scatterplot(
x=zs[:, 0],
y=zs[:, 1],
ax=ax5,
hue=samples[:, 0] < 0.0,
s=30,
alpha=0.5,
edgecolor="none",
)
ax5.set(
xlim=[-5, 5],
ylim=[-5, 5],
xlabel="x0",
ylabel="x1",
title="Samples from the\nwarped posterior - p(z)",
)
ax6.contourf(X1, X2, P, cmap="OrRd")
sns.kdeplot(x=samples[:, 0], y=samples[:, 1], n_levels=30, ax=ax6)
ax6.plot(samples[-50:, 0], samples[-50:, 1], "bo-", alpha=0.2)
ax6.set(
xlim=[-3, 3],
ylim=[-3, 3],
xlabel="x0",
ylabel="x1",
title="Posterior using\nNeuTra HMC sampler",
)
plt.savefig("neutra.pdf")
def benchmark_hmc(args, features, labels):
rng_key = random.PRNGKey(1)
start = time.time()
# a MAP estimate at the following source
# https://github.com/google/edward2/blob/master/examples/no_u_turn_sampler/logistic_regression.py#L117
ref_params = {
"coefs":
jnp.array([
+2.03420663e00,
-3.53567265e-02,
-1.49223924e-01,
-3.07049364e-01,
-1.00028366e-01,
-1.46827862e-01,
-1.64167881e-01,
-4.20344204e-01,
+9.47479829e-02,
-1.12681836e-02,
+2.64442056e-01,
-1.22087866e-01,
-6.00568838e-02,
-3.79419506e-01,
-1.06668741e-01,
-2.97053963e-01,
-2.05253899e-01,
-4.69537191e-02,
-2.78072730e-02,
-1.43250525e-01,
-6.77954629e-02,
-4.34899796e-03,
+5.90927452e-02,
+7.23133609e-02,
+1.38526391e-02,
-1.24497898e-01,
-1.50733739e-02,
-2.68872194e-02,
-1.80925727e-02,
+3.47936489e-02,
+4.03552800e-02,
-9.98773426e-03,
+6.20188080e-02,
+1.15002751e-01,
+1.32145107e-01,
+2.69109547e-01,
+2.45785132e-01,
+1.19035013e-01,
-2.59744357e-02,
+9.94279515e-04,
+3.39266285e-02,
-1.44057125e-02,
-6.95222765e-02,
-7.52013028e-02,
+1.21171586e-01,
+2.29205526e-02,
+1.47308692e-01,
-8.34354162e-02,
-9.34122875e-02,
-2.97472421e-02,
-3.03937674e-01,
-1.70958012e-01,
-1.59496680e-01,
-1.88516974e-01,
-1.20889175e00,
])
}
if args.algo == "HMC":
step_size = jnp.sqrt(0.5 / features.shape[0])
trajectory_length = step_size * args.num_steps
kernel = HMC(
model,
step_size=step_size,
trajectory_length=trajectory_length,
adapt_step_size=False,
dense_mass=args.dense_mass,
)
subsample_size = None
elif args.algo == "NUTS":
kernel = NUTS(model, dense_mass=args.dense_mass)
subsample_size = None
elif args.algo == "HMCECS":
subsample_size = 1000
inner_kernel = NUTS(
model,
init_strategy=init_to_value(values=ref_params),
dense_mass=args.dense_mass,
)
# note: if num_blocks=100, we'll update 10 index at each MCMC step
# so it took 50000 MCMC steps to iterative the whole dataset
kernel = HMCECS(inner_kernel,
num_blocks=100,
proxy=HMCECS.taylor_proxy(ref_params))
elif args.algo == "SA":
# NB: this kernel requires large num_warmup and num_samples
# and running on GPU is much faster than on CPU
kernel = SA(model,
adapt_state_size=1000,
init_strategy=init_to_value(values=ref_params))
subsample_size = None
elif args.algo == "FlowHMCECS":
subsample_size = 1000
guide = AutoBNAFNormal(model, num_flows=1, hidden_factors=[8])
svi = SVI(model, guide, numpyro.optim.Adam(0.01), Trace_ELBO())
params, losses = svi.run(random.PRNGKey(2), 2000, features, labels)
plt.plot(losses)
plt.show()
neutra = NeuTraReparam(guide, params)
neutra_model = neutra.reparam(model)
neutra_ref_params = {"auto_shared_latent": jnp.zeros(55)}
# no need to adapt mass matrix if the flow does a good job
inner_kernel = NUTS(
neutra_model,
init_strategy=init_to_value(values=neutra_ref_params),
adapt_mass_matrix=False,
)
kernel = HMCECS(inner_kernel,
num_blocks=100,
proxy=HMCECS.taylor_proxy(neutra_ref_params))
else:
raise ValueError(
"Invalid algorithm, either 'HMC', 'NUTS', or 'HMCECS'.")
mcmc = MCMC(kernel, args.num_warmup, args.num_samples)
mcmc.run(rng_key,
features,
labels,
subsample_size,
extra_fields=("accept_prob", ))
print("Mean accept prob:",
jnp.mean(mcmc.get_extra_fields()["accept_prob"]))
mcmc.print_summary(exclude_deterministic=False)
print("\nMCMC elapsed time:", time.time() - start)